125.31/76.84 YES 125.31/76.86 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 125.31/76.86 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 125.31/76.86 125.31/76.86 125.31/76.86 H-Termination with start terms of the given HASKELL could be proven: 125.31/76.86 125.31/76.86 (0) HASKELL 125.31/76.86 (1) LR [EQUIVALENT, 0 ms] 125.31/76.86 (2) HASKELL 125.31/76.86 (3) CR [EQUIVALENT, 0 ms] 125.31/76.86 (4) HASKELL 125.31/76.86 (5) IFR [EQUIVALENT, 0 ms] 125.31/76.86 (6) HASKELL 125.31/76.86 (7) BR [EQUIVALENT, 0 ms] 125.31/76.86 (8) HASKELL 125.31/76.86 (9) COR [EQUIVALENT, 0 ms] 125.31/76.86 (10) HASKELL 125.31/76.86 (11) LetRed [EQUIVALENT, 43 ms] 125.31/76.86 (12) HASKELL 125.31/76.86 (13) NumRed [SOUND, 0 ms] 125.31/76.86 (14) HASKELL 125.31/76.86 (15) Narrow [SOUND, 0 ms] 125.31/76.86 (16) AND 125.31/76.86 (17) QDP 125.31/76.86 (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (19) YES 125.31/76.86 (20) QDP 125.31/76.86 (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (22) YES 125.31/76.86 (23) QDP 125.31/76.86 (24) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (25) YES 125.31/76.86 (26) QDP 125.31/76.86 (27) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (28) YES 125.31/76.86 (29) QDP 125.31/76.86 (30) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (31) YES 125.31/76.86 (32) QDP 125.31/76.86 (33) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (34) AND 125.31/76.86 (35) QDP 125.31/76.86 (36) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (37) YES 125.31/76.86 (38) QDP 125.31/76.86 (39) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (40) YES 125.31/76.86 (41) QDP 125.31/76.86 (42) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (43) YES 125.31/76.86 (44) QDP 125.31/76.86 (45) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (46) YES 125.31/76.86 (47) QDP 125.31/76.86 (48) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (49) YES 125.31/76.86 (50) QDP 125.31/76.86 (51) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (52) QDP 125.31/76.86 (53) QDPSizeChangeProof [EQUIVALENT, 594 ms] 125.31/76.86 (54) YES 125.31/76.86 (55) QDP 125.31/76.86 (56) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (57) YES 125.31/76.86 (58) QDP 125.31/76.86 (59) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (60) QDP 125.31/76.86 (61) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (62) YES 125.31/76.86 (63) QDP 125.31/76.86 (64) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (65) YES 125.31/76.86 (66) QDP 125.31/76.86 (67) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (68) AND 125.31/76.86 (69) QDP 125.31/76.86 (70) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (71) YES 125.31/76.86 (72) QDP 125.31/76.86 (73) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (74) YES 125.31/76.86 (75) QDP 125.31/76.86 (76) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (77) QDP 125.31/76.86 (78) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (79) YES 125.31/76.86 (80) QDP 125.31/76.86 (81) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (82) AND 125.31/76.86 (83) QDP 125.31/76.86 (84) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (85) YES 125.31/76.86 (86) QDP 125.31/76.86 (87) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (88) YES 125.31/76.86 (89) QDP 125.31/76.86 (90) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (91) QDP 125.31/76.86 (92) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (93) YES 125.31/76.86 (94) QDP 125.31/76.86 (95) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (96) YES 125.31/76.86 (97) QDP 125.31/76.86 (98) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (99) AND 125.31/76.86 (100) QDP 125.31/76.86 (101) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (102) QDP 125.31/76.86 (103) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (104) QDP 125.31/76.86 (105) QReductionProof [EQUIVALENT, 23 ms] 125.31/76.86 (106) QDP 125.31/76.86 (107) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (108) QDP 125.31/76.86 (109) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (110) QDP 125.31/76.86 (111) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (112) QDP 125.31/76.86 (113) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (114) QDP 125.31/76.86 (115) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (116) QDP 125.31/76.86 (117) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (118) QDP 125.31/76.86 (119) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (120) QDP 125.31/76.86 (121) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (122) QDP 125.31/76.86 (123) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (124) QDP 125.31/76.86 (125) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (126) QDP 125.31/76.86 (127) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (128) QDP 125.31/76.86 (129) QReductionProof [EQUIVALENT, 0 ms] 125.31/76.86 (130) QDP 125.31/76.86 (131) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (132) QDP 125.31/76.86 (133) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (134) QDP 125.31/76.86 (135) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (136) QDP 125.31/76.86 (137) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (138) QDP 125.31/76.86 (139) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (140) QDP 125.31/76.86 (141) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (142) QDP 125.31/76.86 (143) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (144) QDP 125.31/76.86 (145) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (146) QDP 125.31/76.86 (147) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (148) QDP 125.31/76.86 (149) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (150) QDP 125.31/76.86 (151) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (152) QDP 125.31/76.86 (153) QReductionProof [EQUIVALENT, 15 ms] 125.31/76.86 (154) QDP 125.31/76.86 (155) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (156) QDP 125.31/76.86 (157) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (158) QDP 125.31/76.86 (159) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (160) QDP 125.31/76.86 (161) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (162) QDP 125.31/76.86 (163) QReductionProof [EQUIVALENT, 0 ms] 125.31/76.86 (164) QDP 125.31/76.86 (165) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (166) QDP 125.31/76.86 (167) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (168) QDP 125.31/76.86 (169) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (170) QDP 125.31/76.86 (171) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (172) QDP 125.31/76.86 (173) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (174) QDP 125.31/76.86 (175) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (176) QDP 125.31/76.86 (177) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (178) QDP 125.31/76.86 (179) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (180) QDP 125.31/76.86 (181) QReductionProof [EQUIVALENT, 0 ms] 125.31/76.86 (182) QDP 125.31/76.86 (183) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (184) QDP 125.31/76.86 (185) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (186) QDP 125.31/76.86 (187) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (188) QDP 125.31/76.86 (189) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (190) QDP 125.31/76.86 (191) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (192) QDP 125.31/76.86 (193) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (194) QDP 125.31/76.86 (195) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (196) QDP 125.31/76.86 (197) TransformationProof [EQUIVALENT, 1 ms] 125.31/76.86 (198) QDP 125.31/76.86 (199) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (200) QDP 125.31/76.86 (201) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (202) QDP 125.31/76.86 (203) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (204) QDP 125.31/76.86 (205) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (206) QDP 125.31/76.86 (207) QReductionProof [EQUIVALENT, 0 ms] 125.31/76.86 (208) QDP 125.31/76.86 (209) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (210) QDP 125.31/76.86 (211) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (212) QDP 125.31/76.86 (213) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (214) QDP 125.31/76.86 (215) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (216) QDP 125.31/76.86 (217) QReductionProof [EQUIVALENT, 0 ms] 125.31/76.86 (218) QDP 125.31/76.86 (219) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (220) QDP 125.31/76.86 (221) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (222) QDP 125.31/76.86 (223) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (224) QDP 125.31/76.86 (225) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (226) QDP 125.31/76.86 (227) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (228) QDP 125.31/76.86 (229) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (230) QDP 125.31/76.86 (231) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (232) QDP 125.31/76.86 (233) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (234) QDP 125.31/76.86 (235) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (236) QDP 125.31/76.86 (237) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (238) QDP 125.31/76.86 (239) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (240) QDP 125.31/76.86 (241) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (242) QDP 125.31/76.86 (243) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (244) QDP 125.31/76.86 (245) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (246) QDP 125.31/76.86 (247) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (248) QDP 125.31/76.86 (249) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (250) QDP 125.31/76.86 (251) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (252) QDP 125.31/76.86 (253) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (254) QDP 125.31/76.86 (255) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (256) QDP 125.31/76.86 (257) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (258) QDP 125.31/76.86 (259) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (260) QDP 125.31/76.86 (261) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (262) QDP 125.31/76.86 (263) TransformationProof [EQUIVALENT, 1 ms] 125.31/76.86 (264) QDP 125.31/76.86 (265) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (266) QDP 125.31/76.86 (267) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (268) QDP 125.31/76.86 (269) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (270) QDP 125.31/76.86 (271) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (272) QDP 125.31/76.86 (273) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (274) QDP 125.31/76.86 (275) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (276) QDP 125.31/76.86 (277) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (278) QDP 125.31/76.86 (279) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (280) QDP 125.31/76.86 (281) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (282) QDP 125.31/76.86 (283) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (284) QDP 125.31/76.86 (285) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (286) QDP 125.31/76.86 (287) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (288) QDP 125.31/76.86 (289) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (290) QDP 125.31/76.86 (291) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (292) QDP 125.31/76.86 (293) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (294) QDP 125.31/76.86 (295) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (296) QDP 125.31/76.86 (297) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (298) QDP 125.31/76.86 (299) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (300) QDP 125.31/76.86 (301) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (302) QDP 125.31/76.86 (303) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (304) QDP 125.31/76.86 (305) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (306) QDP 125.31/76.86 (307) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (308) QDP 125.31/76.86 (309) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (310) QDP 125.31/76.86 (311) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (312) QDP 125.31/76.86 (313) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (314) QDP 125.31/76.86 (315) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (316) QDP 125.31/76.86 (317) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (318) QDP 125.31/76.86 (319) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (320) QDP 125.31/76.86 (321) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (322) QDP 125.31/76.86 (323) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (324) QDP 125.31/76.86 (325) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (326) QDP 125.31/76.86 (327) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (328) QDP 125.31/76.86 (329) TransformationProof [EQUIVALENT, 1 ms] 125.31/76.86 (330) QDP 125.31/76.86 (331) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (332) QDP 125.31/76.86 (333) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (334) QDP 125.31/76.86 (335) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (336) QDP 125.31/76.86 (337) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (338) QDP 125.31/76.86 (339) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (340) QDP 125.31/76.86 (341) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (342) QDP 125.31/76.86 (343) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (344) QDP 125.31/76.86 (345) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (346) QDP 125.31/76.86 (347) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (348) QDP 125.31/76.86 (349) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (350) QDP 125.31/76.86 (351) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (352) QDP 125.31/76.86 (353) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (354) QDP 125.31/76.86 (355) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (356) QDP 125.31/76.86 (357) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (358) QDP 125.31/76.86 (359) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (360) QDP 125.31/76.86 (361) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (362) QDP 125.31/76.86 (363) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (364) QDP 125.31/76.86 (365) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (366) QDP 125.31/76.86 (367) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (368) QDP 125.31/76.86 (369) QDPOrderProof [EQUIVALENT, 98 ms] 125.31/76.86 (370) QDP 125.31/76.86 (371) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (372) AND 125.31/76.86 (373) QDP 125.31/76.86 (374) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (375) YES 125.31/76.86 (376) QDP 125.31/76.86 (377) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (378) YES 125.31/76.86 (379) QDP 125.31/76.86 (380) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (381) YES 125.31/76.86 (382) QDP 125.31/76.86 (383) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (384) YES 125.31/76.86 (385) QDP 125.31/76.86 (386) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (387) YES 125.31/76.86 (388) QDP 125.31/76.86 (389) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (390) YES 125.31/76.86 (391) QDP 125.31/76.86 (392) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (393) YES 125.31/76.86 (394) QDP 125.31/76.86 (395) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (396) QDP 125.31/76.86 (397) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (398) QDP 125.31/76.86 (399) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (400) QDP 125.31/76.86 (401) QReductionProof [EQUIVALENT, 0 ms] 125.31/76.86 (402) QDP 125.31/76.86 (403) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (404) QDP 125.31/76.86 (405) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (406) QDP 125.31/76.86 (407) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (408) QDP 125.31/76.86 (409) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (410) QDP 125.31/76.86 (411) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (412) QDP 125.31/76.86 (413) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (414) QDP 125.31/76.86 (415) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (416) QDP 125.31/76.86 (417) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (418) QDP 125.31/76.86 (419) QReductionProof [EQUIVALENT, 0 ms] 125.31/76.86 (420) QDP 125.31/76.86 (421) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (422) QDP 125.31/76.86 (423) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (424) QDP 125.31/76.86 (425) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (426) QDP 125.31/76.86 (427) QReductionProof [EQUIVALENT, 0 ms] 125.31/76.86 (428) QDP 125.31/76.86 (429) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (430) QDP 125.31/76.86 (431) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (432) QDP 125.31/76.86 (433) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (434) QDP 125.31/76.86 (435) QReductionProof [EQUIVALENT, 0 ms] 125.31/76.86 (436) QDP 125.31/76.86 (437) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (438) QDP 125.31/76.86 (439) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (440) QDP 125.31/76.86 (441) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (442) QDP 125.31/76.86 (443) QReductionProof [EQUIVALENT, 0 ms] 125.31/76.86 (444) QDP 125.31/76.86 (445) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (446) QDP 125.31/76.86 (447) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (448) QDP 125.31/76.86 (449) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (450) QDP 125.31/76.86 (451) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (452) QDP 125.31/76.86 (453) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (454) QDP 125.31/76.86 (455) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (456) QDP 125.31/76.86 (457) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (458) QDP 125.31/76.86 (459) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (460) QDP 125.31/76.86 (461) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (462) QDP 125.31/76.86 (463) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (464) QDP 125.31/76.86 (465) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (466) QDP 125.31/76.86 (467) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (468) QDP 125.31/76.86 (469) QReductionProof [EQUIVALENT, 0 ms] 125.31/76.86 (470) QDP 125.31/76.86 (471) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (472) QDP 125.31/76.86 (473) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (474) QDP 125.31/76.86 (475) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (476) QDP 125.31/76.86 (477) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (478) QDP 125.31/76.86 (479) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (480) QDP 125.31/76.86 (481) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (482) QDP 125.31/76.86 (483) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (484) QDP 125.31/76.86 (485) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (486) QDP 125.31/76.86 (487) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (488) QDP 125.31/76.86 (489) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (490) QDP 125.31/76.86 (491) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (492) QDP 125.31/76.86 (493) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (494) QDP 125.31/76.86 (495) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (496) QDP 125.31/76.86 (497) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (498) QDP 125.31/76.86 (499) QReductionProof [EQUIVALENT, 0 ms] 125.31/76.86 (500) QDP 125.31/76.86 (501) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (502) QDP 125.31/76.86 (503) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (504) QDP 125.31/76.86 (505) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (506) QDP 125.31/76.86 (507) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (508) QDP 125.31/76.86 (509) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (510) QDP 125.31/76.86 (511) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (512) QDP 125.31/76.86 (513) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (514) QDP 125.31/76.86 (515) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (516) QDP 125.31/76.86 (517) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (518) QDP 125.31/76.86 (519) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (520) QDP 125.31/76.86 (521) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (522) QDP 125.31/76.86 (523) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (524) QDP 125.31/76.86 (525) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (526) QDP 125.31/76.86 (527) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (528) QDP 125.31/76.86 (529) QReductionProof [EQUIVALENT, 2 ms] 125.31/76.86 (530) QDP 125.31/76.86 (531) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (532) QDP 125.31/76.86 (533) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (534) QDP 125.31/76.86 (535) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (536) QDP 125.31/76.86 (537) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (538) QDP 125.31/76.86 (539) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (540) QDP 125.31/76.86 (541) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (542) QDP 125.31/76.86 (543) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (544) QDP 125.31/76.86 (545) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (546) QDP 125.31/76.86 (547) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (548) QDP 125.31/76.86 (549) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (550) QDP 125.31/76.86 (551) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (552) QDP 125.31/76.86 (553) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (554) QDP 125.31/76.86 (555) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (556) QDP 125.31/76.86 (557) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (558) QDP 125.31/76.86 (559) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (560) QDP 125.31/76.86 (561) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (562) QDP 125.31/76.86 (563) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (564) QDP 125.31/76.86 (565) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (566) QDP 125.31/76.86 (567) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (568) QDP 125.31/76.86 (569) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (570) QDP 125.31/76.86 (571) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (572) QDP 125.31/76.86 (573) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (574) QDP 125.31/76.86 (575) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (576) QDP 125.31/76.86 (577) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (578) QDP 125.31/76.86 (579) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (580) QDP 125.31/76.86 (581) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (582) QDP 125.31/76.86 (583) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (584) QDP 125.31/76.86 (585) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (586) QDP 125.31/76.86 (587) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (588) QDP 125.31/76.86 (589) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (590) QDP 125.31/76.86 (591) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (592) QDP 125.31/76.86 (593) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (594) QDP 125.31/76.86 (595) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (596) QDP 125.31/76.86 (597) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (598) QDP 125.31/76.86 (599) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (600) QDP 125.31/76.86 (601) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (602) QDP 125.31/76.86 (603) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (604) QDP 125.31/76.86 (605) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (606) QDP 125.31/76.86 (607) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (608) QDP 125.31/76.86 (609) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (610) QDP 125.31/76.86 (611) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (612) QDP 125.31/76.86 (613) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (614) QDP 125.31/76.86 (615) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (616) QDP 125.31/76.86 (617) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (618) QDP 125.31/76.86 (619) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (620) QDP 125.31/76.86 (621) QReductionProof [EQUIVALENT, 0 ms] 125.31/76.86 (622) QDP 125.31/76.86 (623) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (624) QDP 125.31/76.86 (625) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (626) QDP 125.31/76.86 (627) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (628) QDP 125.31/76.86 (629) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (630) QDP 125.31/76.86 (631) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (632) QDP 125.31/76.86 (633) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (634) QDP 125.31/76.86 (635) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (636) QDP 125.31/76.86 (637) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (638) QDP 125.31/76.86 (639) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (640) QDP 125.31/76.86 (641) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (642) QDP 125.31/76.86 (643) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (644) QDP 125.31/76.86 (645) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (646) QDP 125.31/76.86 (647) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (648) QDP 125.31/76.86 (649) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (650) QDP 125.31/76.86 (651) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (652) QDP 125.31/76.86 (653) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (654) QDP 125.31/76.86 (655) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (656) QDP 125.31/76.86 (657) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (658) QDP 125.31/76.86 (659) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (660) QDP 125.31/76.86 (661) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (662) QDP 125.31/76.86 (663) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (664) QDP 125.31/76.86 (665) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (666) QDP 125.31/76.86 (667) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (668) QDP 125.31/76.86 (669) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (670) QDP 125.31/76.86 (671) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (672) QDP 125.31/76.86 (673) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (674) QDP 125.31/76.86 (675) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (676) QDP 125.31/76.86 (677) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (678) QDP 125.31/76.86 (679) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (680) QDP 125.31/76.86 (681) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (682) QDP 125.31/76.86 (683) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (684) QDP 125.31/76.86 (685) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (686) QDP 125.31/76.86 (687) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (688) QDP 125.31/76.86 (689) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (690) QDP 125.31/76.86 (691) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (692) QDP 125.31/76.86 (693) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (694) QDP 125.31/76.86 (695) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (696) QDP 125.31/76.86 (697) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (698) QDP 125.31/76.86 (699) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (700) QDP 125.31/76.86 (701) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (702) QDP 125.31/76.86 (703) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (704) QDP 125.31/76.86 (705) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (706) QDP 125.31/76.86 (707) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (708) QDP 125.31/76.86 (709) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (710) QDP 125.31/76.86 (711) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (712) QDP 125.31/76.86 (713) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (714) QDP 125.31/76.86 (715) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (716) QDP 125.31/76.86 (717) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (718) QDP 125.31/76.86 (719) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (720) QDP 125.31/76.86 (721) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (722) QDP 125.31/76.86 (723) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (724) QDP 125.31/76.86 (725) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (726) QDP 125.31/76.86 (727) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (728) QDP 125.31/76.86 (729) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (730) QDP 125.31/76.86 (731) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (732) QDP 125.31/76.86 (733) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (734) QDP 125.31/76.86 (735) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (736) QDP 125.31/76.86 (737) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (738) QDP 125.31/76.86 (739) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (740) QDP 125.31/76.86 (741) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (742) QDP 125.31/76.86 (743) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (744) QDP 125.31/76.86 (745) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (746) QDP 125.31/76.86 (747) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (748) QDP 125.31/76.86 (749) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (750) QDP 125.31/76.86 (751) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (752) QDP 125.31/76.86 (753) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (754) QDP 125.31/76.86 (755) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (756) QDP 125.31/76.86 (757) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (758) QDP 125.31/76.86 (759) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (760) QDP 125.31/76.86 (761) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (762) QDP 125.31/76.86 (763) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (764) QDP 125.31/76.86 (765) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (766) QDP 125.31/76.86 (767) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (768) QDP 125.31/76.86 (769) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (770) QDP 125.31/76.86 (771) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (772) QDP 125.31/76.86 (773) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (774) QDP 125.31/76.86 (775) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (776) QDP 125.31/76.86 (777) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (778) QDP 125.31/76.86 (779) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (780) QDP 125.31/76.86 (781) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (782) QDP 125.31/76.86 (783) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (784) QDP 125.31/76.86 (785) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (786) QDP 125.31/76.86 (787) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (788) QDP 125.31/76.86 (789) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (790) QDP 125.31/76.86 (791) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (792) QDP 125.31/76.86 (793) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (794) QDP 125.31/76.86 (795) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (796) QDP 125.31/76.86 (797) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (798) QDP 125.31/76.86 (799) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (800) QDP 125.31/76.86 (801) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (802) QDP 125.31/76.86 (803) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (804) QDP 125.31/76.86 (805) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (806) QDP 125.31/76.86 (807) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (808) QDP 125.31/76.86 (809) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (810) QDP 125.31/76.86 (811) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (812) QDP 125.31/76.86 (813) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (814) QDP 125.31/76.86 (815) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (816) QDP 125.31/76.86 (817) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (818) QDP 125.31/76.86 (819) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (820) QDP 125.31/76.86 (821) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (822) QDP 125.31/76.86 (823) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (824) QDP 125.31/76.86 (825) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (826) QDP 125.31/76.86 (827) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (828) QDP 125.31/76.86 (829) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (830) QDP 125.31/76.86 (831) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (832) QDP 125.31/76.86 (833) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (834) QDP 125.31/76.86 (835) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (836) QDP 125.31/76.86 (837) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (838) QDP 125.31/76.86 (839) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (840) QDP 125.31/76.86 (841) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (842) QDP 125.31/76.86 (843) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (844) QDP 125.31/76.86 (845) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (846) QDP 125.31/76.86 (847) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (848) QDP 125.31/76.86 (849) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (850) QDP 125.31/76.86 (851) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (852) QDP 125.31/76.86 (853) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (854) QDP 125.31/76.86 (855) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (856) QDP 125.31/76.86 (857) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (858) QDP 125.31/76.86 (859) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (860) QDP 125.31/76.86 (861) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (862) QDP 125.31/76.86 (863) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (864) QDP 125.31/76.86 (865) QDPOrderProof [EQUIVALENT, 93 ms] 125.31/76.86 (866) QDP 125.31/76.86 (867) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (868) AND 125.31/76.86 (869) QDP 125.31/76.86 (870) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (871) YES 125.31/76.86 (872) QDP 125.31/76.86 (873) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (874) YES 125.31/76.86 (875) QDP 125.31/76.86 (876) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (877) YES 125.31/76.86 (878) QDP 125.31/76.86 (879) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (880) YES 125.31/76.86 (881) QDP 125.31/76.86 (882) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (883) YES 125.31/76.86 (884) QDP 125.31/76.86 (885) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (886) AND 125.31/76.86 (887) QDP 125.31/76.86 (888) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (889) YES 125.31/76.86 (890) QDP 125.31/76.86 (891) QDPSizeChangeProof [EQUIVALENT, 0 ms] 125.31/76.86 (892) YES 125.31/76.86 (893) QDP 125.31/76.86 (894) DependencyGraphProof [EQUIVALENT, 0 ms] 125.31/76.86 (895) AND 125.31/76.86 (896) QDP 125.31/76.86 (897) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (898) QDP 125.31/76.86 (899) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (900) QDP 125.31/76.86 (901) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (902) QDP 125.31/76.86 (903) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (904) QDP 125.31/76.86 (905) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (906) QDP 125.31/76.86 (907) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (908) QDP 125.31/76.86 (909) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (910) QDP 125.31/76.86 (911) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (912) QDP 125.31/76.86 (913) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (914) QDP 125.31/76.86 (915) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (916) QDP 125.31/76.86 (917) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (918) QDP 125.31/76.86 (919) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (920) QDP 125.31/76.86 (921) QReductionProof [EQUIVALENT, 0 ms] 125.31/76.86 (922) QDP 125.31/76.86 (923) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (924) QDP 125.31/76.86 (925) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (926) QDP 125.31/76.86 (927) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (928) QDP 125.31/76.86 (929) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (930) QDP 125.31/76.86 (931) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (932) QDP 125.31/76.86 (933) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (934) QDP 125.31/76.86 (935) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (936) QDP 125.31/76.86 (937) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (938) QDP 125.31/76.86 (939) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (940) QDP 125.31/76.86 (941) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (942) QDP 125.31/76.86 (943) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (944) QDP 125.31/76.86 (945) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (946) QDP 125.31/76.86 (947) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (948) QDP 125.31/76.86 (949) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (950) QDP 125.31/76.86 (951) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (952) QDP 125.31/76.86 (953) UsableRulesProof [EQUIVALENT, 0 ms] 125.31/76.86 (954) QDP 125.31/76.86 (955) QReductionProof [EQUIVALENT, 7 ms] 125.31/76.86 (956) QDP 125.31/76.86 (957) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (958) QDP 125.31/76.86 (959) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (960) QDP 125.31/76.86 (961) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (962) QDP 125.31/76.86 (963) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (964) QDP 125.31/76.86 (965) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (966) QDP 125.31/76.86 (967) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (968) QDP 125.31/76.86 (969) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (970) QDP 125.31/76.86 (971) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (972) QDP 125.31/76.86 (973) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (974) QDP 125.31/76.86 (975) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (976) QDP 125.31/76.86 (977) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (978) QDP 125.31/76.86 (979) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (980) QDP 125.31/76.86 (981) TransformationProof [EQUIVALENT, 0 ms] 125.31/76.86 (982) QDP 128.02/77.61 (983) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (984) QDP 128.02/77.61 (985) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (986) QDP 128.02/77.61 (987) UsableRulesProof [EQUIVALENT, 0 ms] 128.02/77.61 (988) QDP 128.02/77.61 (989) QReductionProof [EQUIVALENT, 0 ms] 128.02/77.61 (990) QDP 128.02/77.61 (991) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (992) QDP 128.02/77.61 (993) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (994) QDP 128.02/77.61 (995) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (996) QDP 128.02/77.61 (997) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (998) QDP 128.02/77.61 (999) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1000) QDP 128.02/77.61 (1001) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1002) QDP 128.02/77.61 (1003) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1004) QDP 128.02/77.61 (1005) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1006) QDP 128.02/77.61 (1007) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1008) QDP 128.02/77.61 (1009) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1010) QDP 128.02/77.61 (1011) UsableRulesProof [EQUIVALENT, 0 ms] 128.02/77.61 (1012) QDP 128.02/77.61 (1013) QReductionProof [EQUIVALENT, 0 ms] 128.02/77.61 (1014) QDP 128.02/77.61 (1015) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1016) QDP 128.02/77.61 (1017) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1018) QDP 128.02/77.61 (1019) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1020) QDP 128.02/77.61 (1021) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1022) QDP 128.02/77.61 (1023) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1024) QDP 128.02/77.61 (1025) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1026) QDP 128.02/77.61 (1027) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1028) QDP 128.02/77.61 (1029) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1030) QDP 128.02/77.61 (1031) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1032) QDP 128.02/77.61 (1033) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1034) QDP 128.02/77.61 (1035) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1036) QDP 128.02/77.61 (1037) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1038) QDP 128.02/77.61 (1039) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1040) QDP 128.02/77.61 (1041) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1042) QDP 128.02/77.61 (1043) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1044) QDP 128.02/77.61 (1045) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1046) QDP 128.02/77.61 (1047) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1048) QDP 128.02/77.61 (1049) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1050) QDP 128.02/77.61 (1051) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1052) QDP 128.02/77.61 (1053) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1054) QDP 128.02/77.61 (1055) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1056) QDP 128.02/77.61 (1057) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1058) QDP 128.02/77.61 (1059) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1060) QDP 128.02/77.61 (1061) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1062) QDP 128.02/77.61 (1063) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1064) QDP 128.02/77.61 (1065) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1066) QDP 128.02/77.61 (1067) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1068) QDP 128.02/77.61 (1069) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1070) QDP 128.02/77.61 (1071) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1072) QDP 128.02/77.61 (1073) DependencyGraphProof [EQUIVALENT, 0 ms] 128.02/77.61 (1074) QDP 128.02/77.61 (1075) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1076) QDP 128.02/77.61 (1077) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1078) QDP 128.02/77.61 (1079) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1080) QDP 128.02/77.61 (1081) TransformationProof [EQUIVALENT, 1 ms] 128.02/77.61 (1082) QDP 128.02/77.61 (1083) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1084) QDP 128.02/77.61 (1085) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1086) QDP 128.02/77.61 (1087) QDPSizeChangeProof [EQUIVALENT, 0 ms] 128.02/77.61 (1088) YES 128.02/77.61 (1089) QDP 128.02/77.61 (1090) QDPSizeChangeProof [EQUIVALENT, 0 ms] 128.02/77.61 (1091) YES 128.02/77.61 (1092) QDP 128.02/77.61 (1093) QDPSizeChangeProof [EQUIVALENT, 0 ms] 128.02/77.61 (1094) YES 128.02/77.61 (1095) QDP 128.02/77.61 (1096) QDPSizeChangeProof [EQUIVALENT, 0 ms] 128.02/77.61 (1097) YES 128.02/77.61 (1098) QDP 128.02/77.61 (1099) QDPSizeChangeProof [EQUIVALENT, 0 ms] 128.02/77.61 (1100) YES 128.02/77.61 (1101) QDP 128.02/77.61 (1102) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1103) QDP 128.02/77.61 (1104) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1105) QDP 128.02/77.61 (1106) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1107) QDP 128.02/77.61 (1108) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1109) QDP 128.02/77.61 (1110) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1111) QDP 128.02/77.61 (1112) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1113) QDP 128.02/77.61 (1114) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1115) QDP 128.02/77.61 (1116) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1117) QDP 128.02/77.61 (1118) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1119) QDP 128.02/77.61 (1120) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1121) QDP 128.02/77.61 (1122) UsableRulesProof [EQUIVALENT, 0 ms] 128.02/77.61 (1123) QDP 128.02/77.61 (1124) QReductionProof [EQUIVALENT, 0 ms] 128.02/77.61 (1125) QDP 128.02/77.61 (1126) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1127) QDP 128.02/77.61 (1128) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1129) QDP 128.02/77.61 (1130) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1131) QDP 128.02/77.61 (1132) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1133) QDP 128.02/77.61 (1134) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1135) QDP 128.02/77.61 (1136) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1137) QDP 128.02/77.61 (1138) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1139) QDP 128.02/77.61 (1140) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1141) QDP 128.02/77.61 (1142) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1143) QDP 128.02/77.61 (1144) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1145) QDP 128.02/77.61 (1146) UsableRulesProof [EQUIVALENT, 0 ms] 128.02/77.61 (1147) QDP 128.02/77.61 (1148) QReductionProof [EQUIVALENT, 0 ms] 128.02/77.61 (1149) QDP 128.02/77.61 (1150) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1151) QDP 128.02/77.61 (1152) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1153) QDP 128.02/77.61 (1154) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1155) QDP 128.02/77.61 (1156) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1157) QDP 128.02/77.61 (1158) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1159) QDP 128.02/77.61 (1160) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1161) QDP 128.02/77.61 (1162) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1163) QDP 128.02/77.61 (1164) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1165) QDP 128.02/77.61 (1166) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1167) QDP 128.02/77.61 (1168) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1169) QDP 128.02/77.61 (1170) UsableRulesProof [EQUIVALENT, 0 ms] 128.02/77.61 (1171) QDP 128.02/77.61 (1172) QReductionProof [EQUIVALENT, 0 ms] 128.02/77.61 (1173) QDP 128.02/77.61 (1174) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1175) QDP 128.02/77.61 (1176) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1177) QDP 128.02/77.61 (1178) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1179) QDP 128.02/77.61 (1180) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1181) QDP 128.02/77.61 (1182) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1183) QDP 128.02/77.61 (1184) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1185) QDP 128.02/77.61 (1186) UsableRulesProof [EQUIVALENT, 0 ms] 128.02/77.61 (1187) QDP 128.02/77.61 (1188) QReductionProof [EQUIVALENT, 0 ms] 128.02/77.61 (1189) QDP 128.02/77.61 (1190) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1191) QDP 128.02/77.61 (1192) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1193) QDP 128.02/77.61 (1194) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1195) QDP 128.02/77.61 (1196) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1197) QDP 128.02/77.61 (1198) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1199) QDP 128.02/77.61 (1200) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1201) QDP 128.02/77.61 (1202) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1203) QDP 128.02/77.61 (1204) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1205) QDP 128.02/77.61 (1206) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1207) QDP 128.02/77.61 (1208) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1209) QDP 128.02/77.61 (1210) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1211) QDP 128.02/77.61 (1212) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1213) QDP 128.02/77.61 (1214) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1215) QDP 128.02/77.61 (1216) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1217) QDP 128.02/77.61 (1218) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1219) QDP 128.02/77.61 (1220) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1221) QDP 128.02/77.61 (1222) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1223) QDP 128.02/77.61 (1224) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1225) QDP 128.02/77.61 (1226) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1227) QDP 128.02/77.61 (1228) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1229) QDP 128.02/77.61 (1230) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1231) QDP 128.02/77.61 (1232) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1233) QDP 128.02/77.61 (1234) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1235) QDP 128.02/77.61 (1236) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1237) QDP 128.02/77.61 (1238) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1239) QDP 128.02/77.61 (1240) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1241) QDP 128.02/77.61 (1242) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1243) QDP 128.02/77.61 (1244) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1245) QDP 128.02/77.61 (1246) DependencyGraphProof [EQUIVALENT, 0 ms] 128.02/77.61 (1247) QDP 128.02/77.61 (1248) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1249) QDP 128.02/77.61 (1250) DependencyGraphProof [EQUIVALENT, 0 ms] 128.02/77.61 (1251) QDP 128.02/77.61 (1252) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1253) QDP 128.02/77.61 (1254) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1255) QDP 128.02/77.61 (1256) DependencyGraphProof [EQUIVALENT, 0 ms] 128.02/77.61 (1257) QDP 128.02/77.61 (1258) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1259) QDP 128.02/77.61 (1260) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1261) QDP 128.02/77.61 (1262) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1263) QDP 128.02/77.61 (1264) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1265) QDP 128.02/77.61 (1266) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1267) QDP 128.02/77.61 (1268) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1269) QDP 128.02/77.61 (1270) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1271) QDP 128.02/77.61 (1272) TransformationProof [EQUIVALENT, 0 ms] 128.02/77.61 (1273) QDP 128.02/77.61 (1274) QDPSizeChangeProof [EQUIVALENT, 0 ms] 128.02/77.61 (1275) YES 128.02/77.61 (1276) QDP 128.02/77.61 (1277) QDPSizeChangeProof [EQUIVALENT, 0 ms] 128.02/77.61 (1278) YES 128.02/77.61 (1279) QDP 128.02/77.61 (1280) QDPSizeChangeProof [EQUIVALENT, 0 ms] 128.02/77.61 (1281) YES 128.02/77.61 (1282) QDP 128.02/77.61 (1283) QDPSizeChangeProof [EQUIVALENT, 0 ms] 128.02/77.61 (1284) YES 128.02/77.61 (1285) QDP 128.02/77.61 (1286) DependencyGraphProof [EQUIVALENT, 0 ms] 128.02/77.61 (1287) QDP 128.02/77.61 (1288) QDPSizeChangeProof [EQUIVALENT, 0 ms] 128.02/77.61 (1289) YES 128.02/77.61 (1290) QDP 128.02/77.61 (1291) QDPSizeChangeProof [EQUIVALENT, 0 ms] 128.02/77.61 (1292) YES 128.02/77.61 (1293) QDP 128.02/77.61 (1294) QDPSizeChangeProof [EQUIVALENT, 0 ms] 128.02/77.61 (1295) YES 128.02/77.61 (1296) QDP 128.02/77.61 (1297) DependencyGraphProof [EQUIVALENT, 0 ms] 128.02/77.61 (1298) QDP 128.02/77.61 (1299) QDPSizeChangeProof [EQUIVALENT, 0 ms] 128.02/77.61 (1300) YES 128.02/77.61 128.02/77.61 128.02/77.61 ---------------------------------------- 128.02/77.61 128.02/77.61 (0) 128.02/77.61 Obligation: 128.02/77.61 mainModule Main 128.02/77.61 module FiniteMap where { 128.02/77.61 import qualified Main; 128.02/77.61 import qualified Maybe; 128.02/77.61 import qualified Prelude; 128.02/77.61 data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; 128.02/77.61 128.02/77.61 instance (Eq a, Eq b) => Eq FiniteMap b a where { 128.02/77.61 (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; 128.02/77.61 } 128.02/77.61 addToFM :: Ord a => FiniteMap a b -> a -> b -> FiniteMap a b; 128.02/77.61 addToFM fm key elt = addToFM_C (\old new ->new) fm key elt; 128.02/77.61 128.02/77.61 addToFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> a -> b -> FiniteMap a b; 128.02/77.61 addToFM_C combiner EmptyFM key elt = unitFM key elt; 128.02/77.61 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r 128.02/77.61 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt) 128.02/77.61 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r; 128.02/77.61 128.02/77.61 deleteMax :: Ord a => FiniteMap a b -> FiniteMap a b; 128.02/77.61 deleteMax (Branch key elt _ fm_l EmptyFM) = fm_l; 128.02/77.61 deleteMax (Branch key elt _ fm_l fm_r) = mkBalBranch key elt fm_l (deleteMax fm_r); 128.02/77.61 128.02/77.61 deleteMin :: Ord a => FiniteMap a b -> FiniteMap a b; 128.02/77.61 deleteMin (Branch key elt _ EmptyFM fm_r) = fm_r; 128.02/77.61 deleteMin (Branch key elt _ fm_l fm_r) = mkBalBranch key elt (deleteMin fm_l) fm_r; 128.02/77.61 128.02/77.61 emptyFM :: FiniteMap a b; 128.02/77.61 emptyFM = EmptyFM; 128.02/77.61 128.02/77.61 findMax :: FiniteMap b a -> (b,a); 128.02/77.61 findMax (Branch key elt _ _ EmptyFM) = (key,elt); 128.02/77.61 findMax (Branch key elt _ _ fm_r) = findMax fm_r; 128.02/77.61 128.02/77.61 findMin :: FiniteMap a b -> (a,b); 128.02/77.61 findMin (Branch key elt _ EmptyFM _) = (key,elt); 128.02/77.61 findMin (Branch key elt _ fm_l _) = findMin fm_l; 128.02/77.61 128.02/77.61 fmToList :: FiniteMap b a -> [(b,a)]; 128.02/77.61 fmToList fm = foldFM (\key elt rest ->(key,elt) : rest) [] fm; 128.02/77.61 128.02/77.61 foldFM :: (a -> b -> c -> c) -> c -> FiniteMap a b -> c; 128.02/77.61 foldFM k z EmptyFM = z; 128.02/77.61 foldFM k z (Branch key elt _ fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; 128.02/77.61 128.02/77.61 glueBal :: Ord a => FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 128.02/77.61 glueBal EmptyFM fm2 = fm2; 128.02/77.61 glueBal fm1 EmptyFM = fm1; 128.02/77.61 glueBal fm1 fm2 | sizeFM fm2 > sizeFM fm1 = mkBalBranch mid_key2 mid_elt2 fm1 (deleteMin fm2) 128.02/77.61 | otherwise = mkBalBranch mid_key1 mid_elt1 (deleteMax fm1) fm2 where { 128.02/77.61 mid_elt1 = (\(_,mid_elt1) ->mid_elt1) vv2; 128.02/77.61 mid_elt2 = (\(_,mid_elt2) ->mid_elt2) vv3; 128.02/77.61 mid_key1 = (\(mid_key1,_) ->mid_key1) vv2; 128.02/77.61 mid_key2 = (\(mid_key2,_) ->mid_key2) vv3; 128.02/77.61 vv2 = findMax fm1; 128.02/77.61 vv3 = findMin fm2; 128.02/77.61 }; 128.02/77.61 128.02/77.61 glueVBal :: Ord a => FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 128.02/77.61 glueVBal EmptyFM fm2 = fm2; 128.02/77.61 glueVBal fm1 EmptyFM = fm1; 128.02/77.61 glueVBal fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) | sIZE_RATIO * size_l < size_r = mkBalBranch key_r elt_r (glueVBal fm_l fm_rl) fm_rr 128.35/77.65 | sIZE_RATIO * size_r < size_l = mkBalBranch key_l elt_l fm_ll (glueVBal fm_lr fm_r) 128.35/77.65 | otherwise = glueBal fm_l fm_r where { 128.35/77.65 size_l = sizeFM fm_l; 128.35/77.65 size_r = sizeFM fm_r; 128.35/77.65 }; 128.35/77.65 128.35/77.65 intersectFM :: Ord a => FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 128.35/77.65 intersectFM fm1 fm2 = intersectFM_C (\left right ->right) fm1 fm2; 128.35/77.65 128.35/77.65 intersectFM_C :: Ord b => (a -> d -> c) -> FiniteMap b a -> FiniteMap b d -> FiniteMap b c; 128.35/77.65 intersectFM_C combiner fm1 EmptyFM = emptyFM; 128.35/77.65 intersectFM_C combiner EmptyFM fm2 = emptyFM; 128.35/77.65 intersectFM_C combiner fm1 (Branch split_key elt2 _ left right) | Maybe.isJust maybe_elt1 = mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) 128.35/77.65 | otherwise = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) where { 128.35/77.65 elt1 = (\(Just elt1) ->elt1) vv1; 128.35/77.65 gts = splitGT fm1 split_key; 128.35/77.65 lts = splitLT fm1 split_key; 128.35/77.65 maybe_elt1 = lookupFM fm1 split_key; 128.35/77.65 vv1 = maybe_elt1; 128.35/77.65 }; 128.35/77.65 128.35/77.65 lookupFM :: Ord b => FiniteMap b a -> b -> Maybe a; 128.35/77.66 lookupFM EmptyFM key = Nothing; 128.35/77.66 lookupFM (Branch key elt _ fm_l fm_r) key_to_find | key_to_find < key = lookupFM fm_l key_to_find 128.35/77.66 | key_to_find > key = lookupFM fm_r key_to_find 128.35/77.66 | otherwise = Just elt; 128.35/77.66 128.35/77.66 mkBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 128.35/77.66 mkBalBranch key elt fm_L fm_R | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R 128.35/77.66 | size_r > sIZE_RATIO * size_l = case fm_R of { 128.35/77.66 Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R 128.35/77.66 | otherwise -> double_L fm_L fm_R; 128.35/77.66 } 128.35/77.66 | size_l > sIZE_RATIO * size_r = case fm_L of { 128.35/77.66 Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R 128.35/77.66 | otherwise -> double_R fm_L fm_R; 128.35/77.66 } 128.35/77.66 | otherwise = mkBranch 2 key elt fm_L fm_R where { 128.35/77.66 double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 128.35/77.66 double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); 128.35/77.66 single_L fm_l (Branch key_r elt_r _ fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 128.35/77.66 single_R (Branch key_l elt_l _ fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 128.35/77.66 size_l = sizeFM fm_L; 128.35/77.66 size_r = sizeFM fm_R; 128.35/77.66 }; 128.35/77.66 128.35/77.66 mkBranch :: Ord b => Int -> b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 128.35/77.66 mkBranch which key elt fm_l fm_r = let { 128.35/77.66 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 128.35/77.66 } in result where { 128.35/77.66 balance_ok = True; 128.35/77.66 left_ok = case fm_l of { 128.35/77.66 EmptyFM-> True; 128.35/77.66 Branch left_key _ _ _ _-> let { 128.35/77.66 biggest_left_key = fst (findMax fm_l); 128.35/77.66 } in biggest_left_key < key; 128.35/77.66 } ; 128.35/77.66 left_size = sizeFM fm_l; 128.35/77.66 right_ok = case fm_r of { 128.35/77.66 EmptyFM-> True; 128.35/77.66 Branch right_key _ _ _ _-> let { 128.35/77.66 smallest_right_key = fst (findMin fm_r); 128.35/77.66 } in key < smallest_right_key; 128.35/77.66 } ; 128.35/77.66 right_size = sizeFM fm_r; 128.35/77.66 unbox :: Int -> Int; 128.35/77.66 unbox x = x; 128.35/77.66 }; 128.35/77.66 128.35/77.66 mkVBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 128.35/77.66 mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt; 128.35/77.66 mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt; 128.35/77.66 mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) | sIZE_RATIO * size_l < size_r = mkBalBranch key_r elt_r (mkVBalBranch key elt fm_l fm_rl) fm_rr 128.35/77.66 | sIZE_RATIO * size_r < size_l = mkBalBranch key_l elt_l fm_ll (mkVBalBranch key elt fm_lr fm_r) 128.35/77.66 | otherwise = mkBranch 13 key elt fm_l fm_r where { 128.35/77.66 size_l = sizeFM fm_l; 128.35/77.66 size_r = sizeFM fm_r; 128.35/77.66 }; 128.35/77.66 128.35/77.66 sIZE_RATIO :: Int; 128.35/77.66 sIZE_RATIO = 5; 128.35/77.66 128.35/77.66 sizeFM :: FiniteMap a b -> Int; 128.35/77.66 sizeFM EmptyFM = 0; 128.35/77.66 sizeFM (Branch _ _ size _ _) = size; 128.35/77.66 128.35/77.66 splitGT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; 128.35/77.66 splitGT EmptyFM split_key = emptyFM; 128.35/77.66 splitGT (Branch key elt _ fm_l fm_r) split_key | split_key > key = splitGT fm_r split_key 128.35/77.66 | split_key < key = mkVBalBranch key elt (splitGT fm_l split_key) fm_r 128.35/77.66 | otherwise = fm_r; 128.35/77.66 128.35/77.66 splitLT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; 128.35/77.66 splitLT EmptyFM split_key = emptyFM; 128.35/77.66 splitLT (Branch key elt _ fm_l fm_r) split_key | split_key < key = splitLT fm_l split_key 128.35/77.66 | split_key > key = mkVBalBranch key elt fm_l (splitLT fm_r split_key) 128.35/77.66 | otherwise = fm_l; 128.35/77.66 128.35/77.66 unitFM :: b -> a -> FiniteMap b a; 128.35/77.66 unitFM key elt = Branch key elt 1 emptyFM emptyFM; 128.35/77.66 128.35/77.66 } 128.35/77.66 module Maybe where { 128.35/77.66 import qualified FiniteMap; 128.35/77.66 import qualified Main; 128.35/77.66 import qualified Prelude; 128.35/77.66 isJust :: Maybe a -> Bool; 128.35/77.66 isJust Nothing = False; 128.35/77.66 isJust _ = True; 128.35/77.66 128.35/77.66 } 128.35/77.66 module Main where { 128.35/77.66 import qualified FiniteMap; 128.35/77.66 import qualified Maybe; 128.35/77.66 import qualified Prelude; 128.35/77.66 } 128.35/77.66 128.35/77.66 ---------------------------------------- 128.35/77.66 128.35/77.66 (1) LR (EQUIVALENT) 128.35/77.66 Lambda Reductions: 128.35/77.66 The following Lambda expression 128.35/77.66 "\oldnew->new" 128.35/77.66 is transformed to 128.35/77.66 "addToFM0 old new = new; 128.35/77.66 " 128.35/77.66 The following Lambda expression 128.35/77.66 "\leftright->right" 128.35/77.66 is transformed to 128.35/77.66 "intersectFM0 left right = right; 128.35/77.66 " 128.35/77.66 The following Lambda expression 128.35/77.66 "\(_,mid_elt2)->mid_elt2" 128.35/77.66 is transformed to 128.35/77.66 "mid_elt20 (_,mid_elt2) = mid_elt2; 128.35/77.66 " 128.35/77.66 The following Lambda expression 128.35/77.66 "\(mid_key2,_)->mid_key2" 128.35/77.66 is transformed to 128.35/77.66 "mid_key20 (mid_key2,_) = mid_key2; 128.35/77.66 " 128.35/77.66 The following Lambda expression 128.35/77.66 "\(mid_key1,_)->mid_key1" 128.35/77.66 is transformed to 128.35/77.66 "mid_key10 (mid_key1,_) = mid_key1; 128.35/77.66 " 128.35/77.66 The following Lambda expression 128.35/77.66 "\(_,mid_elt1)->mid_elt1" 128.35/77.66 is transformed to 128.35/77.66 "mid_elt10 (_,mid_elt1) = mid_elt1; 128.35/77.66 " 128.35/77.66 The following Lambda expression 128.35/77.66 "\keyeltrest->(key,elt) : rest" 128.35/77.66 is transformed to 128.35/77.66 "fmToList0 key elt rest = (key,elt) : rest; 128.35/77.66 " 128.35/77.66 The following Lambda expression 128.35/77.66 "\(Just elt1)->elt1" 128.35/77.66 is transformed to 128.35/77.66 "elt10 (Just elt1) = elt1; 128.35/77.66 " 128.35/77.66 128.35/77.66 ---------------------------------------- 128.35/77.66 128.35/77.66 (2) 128.35/77.66 Obligation: 128.35/77.66 mainModule Main 128.35/77.66 module FiniteMap where { 128.35/77.66 import qualified Main; 128.35/77.66 import qualified Maybe; 128.35/77.66 import qualified Prelude; 128.35/77.66 data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; 128.35/77.66 128.35/77.66 instance (Eq a, Eq b) => Eq FiniteMap a b where { 128.35/77.66 (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; 128.35/77.66 } 128.35/77.66 addToFM :: Ord a => FiniteMap a b -> a -> b -> FiniteMap a b; 128.35/77.66 addToFM fm key elt = addToFM_C addToFM0 fm key elt; 128.35/77.66 128.35/77.66 addToFM0 old new = new; 128.35/77.66 128.35/77.66 addToFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> b -> a -> FiniteMap b a; 128.35/77.66 addToFM_C combiner EmptyFM key elt = unitFM key elt; 128.35/77.66 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r 128.35/77.66 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt) 128.35/77.66 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r; 128.35/77.66 128.35/77.66 deleteMax :: Ord a => FiniteMap a b -> FiniteMap a b; 128.35/77.66 deleteMax (Branch key elt _ fm_l EmptyFM) = fm_l; 128.35/77.66 deleteMax (Branch key elt _ fm_l fm_r) = mkBalBranch key elt fm_l (deleteMax fm_r); 128.35/77.66 128.35/77.66 deleteMin :: Ord b => FiniteMap b a -> FiniteMap b a; 128.35/77.66 deleteMin (Branch key elt _ EmptyFM fm_r) = fm_r; 128.35/77.66 deleteMin (Branch key elt _ fm_l fm_r) = mkBalBranch key elt (deleteMin fm_l) fm_r; 128.35/77.66 128.35/77.66 emptyFM :: FiniteMap a b; 128.35/77.66 emptyFM = EmptyFM; 128.35/77.66 128.35/77.66 findMax :: FiniteMap b a -> (b,a); 128.35/77.66 findMax (Branch key elt _ _ EmptyFM) = (key,elt); 128.35/77.66 findMax (Branch key elt _ _ fm_r) = findMax fm_r; 128.35/77.66 128.35/77.66 findMin :: FiniteMap b a -> (b,a); 128.35/77.66 findMin (Branch key elt _ EmptyFM _) = (key,elt); 128.35/77.66 findMin (Branch key elt _ fm_l _) = findMin fm_l; 128.35/77.66 128.35/77.66 fmToList :: FiniteMap a b -> [(a,b)]; 128.35/77.66 fmToList fm = foldFM fmToList0 [] fm; 128.35/77.66 128.35/77.66 fmToList0 key elt rest = (key,elt) : rest; 128.35/77.66 128.35/77.66 foldFM :: (a -> c -> b -> b) -> b -> FiniteMap a c -> b; 128.35/77.66 foldFM k z EmptyFM = z; 128.35/77.66 foldFM k z (Branch key elt _ fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; 128.35/77.66 128.35/77.66 glueBal :: Ord b => FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 128.35/77.66 glueBal EmptyFM fm2 = fm2; 128.35/77.66 glueBal fm1 EmptyFM = fm1; 128.35/77.66 glueBal fm1 fm2 | sizeFM fm2 > sizeFM fm1 = mkBalBranch mid_key2 mid_elt2 fm1 (deleteMin fm2) 128.35/77.66 | otherwise = mkBalBranch mid_key1 mid_elt1 (deleteMax fm1) fm2 where { 128.35/77.66 mid_elt1 = mid_elt10 vv2; 128.35/77.66 mid_elt10 (_,mid_elt1) = mid_elt1; 128.35/77.66 mid_elt2 = mid_elt20 vv3; 128.35/77.66 mid_elt20 (_,mid_elt2) = mid_elt2; 128.35/77.66 mid_key1 = mid_key10 vv2; 128.35/77.66 mid_key10 (mid_key1,_) = mid_key1; 128.35/77.66 mid_key2 = mid_key20 vv3; 128.35/77.66 mid_key20 (mid_key2,_) = mid_key2; 128.35/77.66 vv2 = findMax fm1; 128.35/77.66 vv3 = findMin fm2; 128.35/77.66 }; 128.35/77.66 128.35/77.66 glueVBal :: Ord b => FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 128.35/77.66 glueVBal EmptyFM fm2 = fm2; 128.35/77.66 glueVBal fm1 EmptyFM = fm1; 128.35/77.66 glueVBal fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) | sIZE_RATIO * size_l < size_r = mkBalBranch key_r elt_r (glueVBal fm_l fm_rl) fm_rr 128.35/77.66 | sIZE_RATIO * size_r < size_l = mkBalBranch key_l elt_l fm_ll (glueVBal fm_lr fm_r) 128.35/77.66 | otherwise = glueBal fm_l fm_r where { 128.35/77.66 size_l = sizeFM fm_l; 128.35/77.66 size_r = sizeFM fm_r; 128.35/77.66 }; 128.35/77.66 128.35/77.66 intersectFM :: Ord b => FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 128.35/77.66 intersectFM fm1 fm2 = intersectFM_C intersectFM0 fm1 fm2; 128.35/77.66 128.35/77.66 intersectFM0 left right = right; 128.35/77.66 128.35/77.66 intersectFM_C :: Ord d => (b -> a -> c) -> FiniteMap d b -> FiniteMap d a -> FiniteMap d c; 128.35/77.66 intersectFM_C combiner fm1 EmptyFM = emptyFM; 128.35/77.66 intersectFM_C combiner EmptyFM fm2 = emptyFM; 128.35/77.66 intersectFM_C combiner fm1 (Branch split_key elt2 _ left right) | Maybe.isJust maybe_elt1 = mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) 128.35/77.66 | otherwise = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) where { 128.35/77.66 elt1 = elt10 vv1; 128.35/77.66 elt10 (Just elt1) = elt1; 128.35/77.66 gts = splitGT fm1 split_key; 128.35/77.66 lts = splitLT fm1 split_key; 128.35/77.66 maybe_elt1 = lookupFM fm1 split_key; 128.35/77.66 vv1 = maybe_elt1; 128.35/77.66 }; 128.35/77.66 128.35/77.66 lookupFM :: Ord a => FiniteMap a b -> a -> Maybe b; 128.35/77.66 lookupFM EmptyFM key = Nothing; 128.35/77.66 lookupFM (Branch key elt _ fm_l fm_r) key_to_find | key_to_find < key = lookupFM fm_l key_to_find 128.35/77.66 | key_to_find > key = lookupFM fm_r key_to_find 128.35/77.66 | otherwise = Just elt; 128.35/77.66 128.35/77.66 mkBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 128.35/77.66 mkBalBranch key elt fm_L fm_R | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R 128.35/77.66 | size_r > sIZE_RATIO * size_l = case fm_R of { 128.35/77.66 Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R 128.35/77.66 | otherwise -> double_L fm_L fm_R; 128.35/77.66 } 128.35/77.66 | size_l > sIZE_RATIO * size_r = case fm_L of { 128.35/77.66 Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R 128.35/77.66 | otherwise -> double_R fm_L fm_R; 128.35/77.66 } 128.35/77.66 | otherwise = mkBranch 2 key elt fm_L fm_R where { 128.35/77.66 double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 128.35/77.66 double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); 128.35/77.66 single_L fm_l (Branch key_r elt_r _ fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 128.35/77.66 single_R (Branch key_l elt_l _ fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 128.35/77.66 size_l = sizeFM fm_L; 128.35/77.66 size_r = sizeFM fm_R; 128.35/77.66 }; 128.35/77.66 128.35/77.66 mkBranch :: Ord b => Int -> b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 128.35/77.66 mkBranch which key elt fm_l fm_r = let { 128.35/77.66 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 128.35/77.66 } in result where { 128.35/77.66 balance_ok = True; 128.35/77.66 left_ok = case fm_l of { 128.35/77.66 EmptyFM-> True; 128.35/77.66 Branch left_key _ _ _ _-> let { 128.35/77.66 biggest_left_key = fst (findMax fm_l); 128.35/77.66 } in biggest_left_key < key; 128.35/77.66 } ; 128.35/77.66 left_size = sizeFM fm_l; 128.35/77.66 right_ok = case fm_r of { 128.35/77.66 EmptyFM-> True; 128.35/77.66 Branch right_key _ _ _ _-> let { 128.35/77.66 smallest_right_key = fst (findMin fm_r); 128.35/77.66 } in key < smallest_right_key; 128.35/77.66 } ; 128.35/77.66 right_size = sizeFM fm_r; 128.35/77.66 unbox :: Int -> Int; 128.35/77.66 unbox x = x; 128.35/77.66 }; 128.35/77.66 128.35/77.66 mkVBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 128.35/77.66 mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt; 128.35/77.66 mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt; 128.35/77.66 mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) | sIZE_RATIO * size_l < size_r = mkBalBranch key_r elt_r (mkVBalBranch key elt fm_l fm_rl) fm_rr 128.35/77.66 | sIZE_RATIO * size_r < size_l = mkBalBranch key_l elt_l fm_ll (mkVBalBranch key elt fm_lr fm_r) 128.35/77.66 | otherwise = mkBranch 13 key elt fm_l fm_r where { 128.35/77.66 size_l = sizeFM fm_l; 128.35/77.66 size_r = sizeFM fm_r; 128.35/77.66 }; 128.35/77.66 128.35/77.66 sIZE_RATIO :: Int; 128.35/77.66 sIZE_RATIO = 5; 128.35/77.66 128.35/77.66 sizeFM :: FiniteMap b a -> Int; 128.35/77.66 sizeFM EmptyFM = 0; 128.35/77.66 sizeFM (Branch _ _ size _ _) = size; 128.35/77.66 128.35/77.66 splitGT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; 128.35/77.66 splitGT EmptyFM split_key = emptyFM; 128.35/77.66 splitGT (Branch key elt _ fm_l fm_r) split_key | split_key > key = splitGT fm_r split_key 128.35/77.66 | split_key < key = mkVBalBranch key elt (splitGT fm_l split_key) fm_r 128.35/77.66 | otherwise = fm_r; 128.35/77.66 128.35/77.66 splitLT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; 128.35/77.66 splitLT EmptyFM split_key = emptyFM; 128.35/77.66 splitLT (Branch key elt _ fm_l fm_r) split_key | split_key < key = splitLT fm_l split_key 128.35/77.66 | split_key > key = mkVBalBranch key elt fm_l (splitLT fm_r split_key) 128.35/77.66 | otherwise = fm_l; 128.35/77.66 128.35/77.66 unitFM :: a -> b -> FiniteMap a b; 128.35/77.66 unitFM key elt = Branch key elt 1 emptyFM emptyFM; 128.35/77.66 128.35/77.66 } 128.35/77.66 module Maybe where { 128.35/77.66 import qualified FiniteMap; 128.35/77.66 import qualified Main; 128.35/77.66 import qualified Prelude; 128.35/77.66 isJust :: Maybe a -> Bool; 128.35/77.66 isJust Nothing = False; 128.35/77.66 isJust _ = True; 128.35/77.66 128.35/77.66 } 128.35/77.66 module Main where { 128.35/77.66 import qualified FiniteMap; 128.35/77.66 import qualified Maybe; 128.35/77.66 import qualified Prelude; 128.35/77.66 } 128.35/77.66 128.35/77.66 ---------------------------------------- 128.35/77.66 128.35/77.66 (3) CR (EQUIVALENT) 128.35/77.66 Case Reductions: 128.35/77.66 The following Case expression 128.35/77.66 "case compare x y of { 128.35/77.66 EQ -> o; 128.35/77.66 LT -> LT; 128.35/77.66 GT -> GT} 128.35/77.66 " 128.35/77.66 is transformed to 128.35/77.66 "primCompAux0 o EQ = o; 128.35/77.66 primCompAux0 o LT = LT; 128.35/77.66 primCompAux0 o GT = GT; 128.35/77.66 " 128.35/77.66 The following Case expression 128.35/77.66 "case fm_r of { 128.35/77.66 EmptyFM -> True; 128.35/77.66 Branch right_key _ _ _ _ -> let { 128.35/77.66 smallest_right_key = fst (findMin fm_r); 128.35/77.66 } in key < smallest_right_key} 128.35/77.66 " 128.35/77.66 is transformed to 128.35/77.66 "right_ok0 fm_r key EmptyFM = True; 128.35/77.66 right_ok0 fm_r key (Branch right_key _ _ _ _) = let { 128.35/77.66 smallest_right_key = fst (findMin fm_r); 128.35/77.66 } in key < smallest_right_key; 128.35/77.66 " 128.35/77.66 The following Case expression 128.35/77.66 "case fm_l of { 128.35/77.66 EmptyFM -> True; 128.35/77.66 Branch left_key _ _ _ _ -> let { 128.35/77.66 biggest_left_key = fst (findMax fm_l); 128.35/77.66 } in biggest_left_key < key} 128.35/77.66 " 128.35/77.66 is transformed to 128.35/77.66 "left_ok0 fm_l key EmptyFM = True; 128.35/77.66 left_ok0 fm_l key (Branch left_key _ _ _ _) = let { 128.35/77.66 biggest_left_key = fst (findMax fm_l); 128.35/77.66 } in biggest_left_key < key; 128.35/77.66 " 128.35/77.66 The following Case expression 128.35/77.66 "case fm_R of { 128.35/77.66 Branch _ _ _ fm_rl fm_rr |sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R} 128.35/77.66 " 128.35/77.66 is transformed to 128.35/77.66 "mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr)|sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R; 128.35/77.66 " 128.35/77.66 The following Case expression 128.35/77.66 "case fm_L of { 128.35/77.66 Branch _ _ _ fm_ll fm_lr |sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R} 128.35/77.66 " 128.35/77.66 is transformed to 128.35/77.66 "mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr)|sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R; 128.35/77.66 " 128.35/77.66 128.35/77.66 ---------------------------------------- 128.35/77.66 128.35/77.66 (4) 128.35/77.66 Obligation: 128.35/77.66 mainModule Main 128.35/77.66 module FiniteMap where { 128.35/77.66 import qualified Main; 128.35/77.66 import qualified Maybe; 128.35/77.66 import qualified Prelude; 128.35/77.66 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 128.35/77.66 128.35/77.66 instance (Eq a, Eq b) => Eq FiniteMap b a where { 128.35/77.66 (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; 128.35/77.66 } 128.35/77.66 addToFM :: Ord a => FiniteMap a b -> a -> b -> FiniteMap a b; 128.35/77.66 addToFM fm key elt = addToFM_C addToFM0 fm key elt; 128.35/77.66 128.35/77.66 addToFM0 old new = new; 128.35/77.66 128.35/77.66 addToFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> b -> a -> FiniteMap b a; 128.35/77.66 addToFM_C combiner EmptyFM key elt = unitFM key elt; 128.35/77.66 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r 128.35/77.66 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt) 128.35/77.66 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r; 128.35/77.66 128.35/77.66 deleteMax :: Ord a => FiniteMap a b -> FiniteMap a b; 128.35/77.66 deleteMax (Branch key elt _ fm_l EmptyFM) = fm_l; 128.35/77.66 deleteMax (Branch key elt _ fm_l fm_r) = mkBalBranch key elt fm_l (deleteMax fm_r); 128.35/77.66 128.35/77.66 deleteMin :: Ord b => FiniteMap b a -> FiniteMap b a; 128.35/77.66 deleteMin (Branch key elt _ EmptyFM fm_r) = fm_r; 128.35/77.66 deleteMin (Branch key elt _ fm_l fm_r) = mkBalBranch key elt (deleteMin fm_l) fm_r; 128.35/77.66 128.35/77.66 emptyFM :: FiniteMap a b; 129.11/77.83 emptyFM = EmptyFM; 129.11/77.83 129.11/77.83 findMax :: FiniteMap b a -> (b,a); 129.11/77.83 findMax (Branch key elt _ _ EmptyFM) = (key,elt); 129.11/77.83 findMax (Branch key elt _ _ fm_r) = findMax fm_r; 129.11/77.83 129.11/77.83 findMin :: FiniteMap a b -> (a,b); 129.11/77.83 findMin (Branch key elt _ EmptyFM _) = (key,elt); 129.11/77.83 findMin (Branch key elt _ fm_l _) = findMin fm_l; 129.11/77.83 129.11/77.83 fmToList :: FiniteMap a b -> [(a,b)]; 129.11/77.83 fmToList fm = foldFM fmToList0 [] fm; 129.11/77.83 129.11/77.83 fmToList0 key elt rest = (key,elt) : rest; 129.11/77.83 129.11/77.83 foldFM :: (a -> b -> c -> c) -> c -> FiniteMap a b -> c; 129.11/77.83 foldFM k z EmptyFM = z; 129.11/77.83 foldFM k z (Branch key elt _ fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; 129.11/77.83 129.11/77.83 glueBal :: Ord a => FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 129.11/77.83 glueBal EmptyFM fm2 = fm2; 129.11/77.83 glueBal fm1 EmptyFM = fm1; 129.11/77.83 glueBal fm1 fm2 | sizeFM fm2 > sizeFM fm1 = mkBalBranch mid_key2 mid_elt2 fm1 (deleteMin fm2) 129.11/77.83 | otherwise = mkBalBranch mid_key1 mid_elt1 (deleteMax fm1) fm2 where { 129.11/77.83 mid_elt1 = mid_elt10 vv2; 129.11/77.83 mid_elt10 (_,mid_elt1) = mid_elt1; 129.11/77.83 mid_elt2 = mid_elt20 vv3; 129.11/77.83 mid_elt20 (_,mid_elt2) = mid_elt2; 129.11/77.83 mid_key1 = mid_key10 vv2; 129.11/77.83 mid_key10 (mid_key1,_) = mid_key1; 129.11/77.83 mid_key2 = mid_key20 vv3; 129.11/77.83 mid_key20 (mid_key2,_) = mid_key2; 129.11/77.83 vv2 = findMax fm1; 129.11/77.83 vv3 = findMin fm2; 129.11/77.83 }; 129.11/77.83 129.11/77.83 glueVBal :: Ord a => FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 129.11/77.83 glueVBal EmptyFM fm2 = fm2; 129.11/77.83 glueVBal fm1 EmptyFM = fm1; 129.11/77.83 glueVBal fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) | sIZE_RATIO * size_l < size_r = mkBalBranch key_r elt_r (glueVBal fm_l fm_rl) fm_rr 129.11/77.83 | sIZE_RATIO * size_r < size_l = mkBalBranch key_l elt_l fm_ll (glueVBal fm_lr fm_r) 129.11/77.83 | otherwise = glueBal fm_l fm_r where { 129.11/77.83 size_l = sizeFM fm_l; 129.11/77.83 size_r = sizeFM fm_r; 129.11/77.83 }; 129.11/77.83 129.11/77.83 intersectFM :: Ord b => FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 129.11/77.83 intersectFM fm1 fm2 = intersectFM_C intersectFM0 fm1 fm2; 129.11/77.83 129.11/77.83 intersectFM0 left right = right; 129.11/77.83 129.11/77.83 intersectFM_C :: Ord d => (a -> b -> c) -> FiniteMap d a -> FiniteMap d b -> FiniteMap d c; 129.11/77.83 intersectFM_C combiner fm1 EmptyFM = emptyFM; 129.11/77.83 intersectFM_C combiner EmptyFM fm2 = emptyFM; 129.11/77.83 intersectFM_C combiner fm1 (Branch split_key elt2 _ left right) | Maybe.isJust maybe_elt1 = mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) 129.11/77.83 | otherwise = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) where { 129.11/77.83 elt1 = elt10 vv1; 129.11/77.83 elt10 (Just elt1) = elt1; 129.11/77.83 gts = splitGT fm1 split_key; 129.11/77.83 lts = splitLT fm1 split_key; 129.11/77.83 maybe_elt1 = lookupFM fm1 split_key; 129.11/77.83 vv1 = maybe_elt1; 129.11/77.83 }; 129.11/77.83 129.11/77.83 lookupFM :: Ord a => FiniteMap a b -> a -> Maybe b; 129.11/77.83 lookupFM EmptyFM key = Nothing; 129.11/77.83 lookupFM (Branch key elt _ fm_l fm_r) key_to_find | key_to_find < key = lookupFM fm_l key_to_find 129.11/77.83 | key_to_find > key = lookupFM fm_r key_to_find 129.11/77.83 | otherwise = Just elt; 129.11/77.83 129.11/77.83 mkBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 129.11/77.83 mkBalBranch key elt fm_L fm_R | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R 129.11/77.83 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R 129.11/77.83 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L 129.11/77.83 | otherwise = mkBranch 2 key elt fm_L fm_R where { 129.11/77.83 double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 129.11/77.83 double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); 129.11/77.83 mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr) | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R 129.11/77.83 | otherwise = double_L fm_L fm_R; 129.11/77.83 mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr) | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R 129.11/77.83 | otherwise = double_R fm_L fm_R; 129.11/77.83 single_L fm_l (Branch key_r elt_r _ fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 129.11/77.83 single_R (Branch key_l elt_l _ fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 129.11/77.83 size_l = sizeFM fm_L; 129.11/77.83 size_r = sizeFM fm_R; 129.11/77.83 }; 129.11/77.83 129.11/77.83 mkBranch :: Ord a => Int -> a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 129.11/77.83 mkBranch which key elt fm_l fm_r = let { 129.11/77.83 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 129.11/77.83 } in result where { 129.11/77.83 balance_ok = True; 129.11/77.83 left_ok = left_ok0 fm_l key fm_l; 129.11/77.83 left_ok0 fm_l key EmptyFM = True; 129.11/77.83 left_ok0 fm_l key (Branch left_key _ _ _ _) = let { 129.11/77.83 biggest_left_key = fst (findMax fm_l); 129.11/77.83 } in biggest_left_key < key; 129.11/77.83 left_size = sizeFM fm_l; 129.11/77.83 right_ok = right_ok0 fm_r key fm_r; 129.11/77.83 right_ok0 fm_r key EmptyFM = True; 129.11/77.83 right_ok0 fm_r key (Branch right_key _ _ _ _) = let { 129.11/77.83 smallest_right_key = fst (findMin fm_r); 129.11/77.83 } in key < smallest_right_key; 129.11/77.83 right_size = sizeFM fm_r; 129.11/77.83 unbox :: Int -> Int; 129.11/77.83 unbox x = x; 129.11/77.83 }; 129.11/77.83 129.11/77.83 mkVBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 129.11/77.83 mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt; 129.11/77.83 mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt; 129.11/77.83 mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) | sIZE_RATIO * size_l < size_r = mkBalBranch key_r elt_r (mkVBalBranch key elt fm_l fm_rl) fm_rr 129.11/77.83 | sIZE_RATIO * size_r < size_l = mkBalBranch key_l elt_l fm_ll (mkVBalBranch key elt fm_lr fm_r) 129.11/77.83 | otherwise = mkBranch 13 key elt fm_l fm_r where { 129.11/77.83 size_l = sizeFM fm_l; 129.11/77.83 size_r = sizeFM fm_r; 129.11/77.83 }; 129.11/77.83 129.11/77.83 sIZE_RATIO :: Int; 129.11/77.83 sIZE_RATIO = 5; 129.11/77.83 129.11/77.83 sizeFM :: FiniteMap b a -> Int; 129.11/77.83 sizeFM EmptyFM = 0; 129.11/77.83 sizeFM (Branch _ _ size _ _) = size; 129.11/77.83 129.11/77.83 splitGT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; 129.11/77.83 splitGT EmptyFM split_key = emptyFM; 129.11/77.83 splitGT (Branch key elt _ fm_l fm_r) split_key | split_key > key = splitGT fm_r split_key 129.11/77.83 | split_key < key = mkVBalBranch key elt (splitGT fm_l split_key) fm_r 129.11/77.83 | otherwise = fm_r; 129.11/77.83 129.11/77.83 splitLT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; 129.11/77.83 splitLT EmptyFM split_key = emptyFM; 129.11/77.83 splitLT (Branch key elt _ fm_l fm_r) split_key | split_key < key = splitLT fm_l split_key 129.11/77.83 | split_key > key = mkVBalBranch key elt fm_l (splitLT fm_r split_key) 129.11/77.83 | otherwise = fm_l; 129.11/77.83 129.11/77.83 unitFM :: a -> b -> FiniteMap a b; 129.11/77.83 unitFM key elt = Branch key elt 1 emptyFM emptyFM; 129.11/77.83 129.11/77.83 } 129.11/77.83 module Maybe where { 129.11/77.83 import qualified FiniteMap; 129.11/77.83 import qualified Main; 129.11/77.83 import qualified Prelude; 129.11/77.83 isJust :: Maybe a -> Bool; 129.11/77.83 isJust Nothing = False; 129.11/77.83 isJust _ = True; 129.11/77.83 129.11/77.83 } 129.11/77.83 module Main where { 129.11/77.83 import qualified FiniteMap; 129.11/77.83 import qualified Maybe; 129.11/77.83 import qualified Prelude; 129.11/77.83 } 129.11/77.83 129.11/77.83 ---------------------------------------- 129.11/77.83 129.11/77.83 (5) IFR (EQUIVALENT) 129.11/77.83 If Reductions: 129.11/77.83 The following If expression 129.11/77.83 "if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero" 129.11/77.83 is transformed to 129.11/77.83 "primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y)); 129.11/77.83 primDivNatS0 x y False = Zero; 129.11/77.83 " 129.11/77.83 The following If expression 129.11/77.83 "if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x" 129.11/77.83 is transformed to 129.11/77.83 "primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y); 129.11/77.83 primModNatS0 x y False = Succ x; 129.11/77.83 " 129.11/77.83 129.11/77.83 ---------------------------------------- 129.11/77.83 129.11/77.83 (6) 129.11/77.83 Obligation: 129.11/77.83 mainModule Main 129.11/77.83 module FiniteMap where { 129.11/77.83 import qualified Main; 129.11/77.83 import qualified Maybe; 129.11/77.83 import qualified Prelude; 129.11/77.83 data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; 129.11/77.83 129.11/77.83 instance (Eq a, Eq b) => Eq FiniteMap b a where { 129.11/77.83 (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; 129.11/77.83 } 129.11/77.83 addToFM :: Ord b => FiniteMap b a -> b -> a -> FiniteMap b a; 129.11/77.83 addToFM fm key elt = addToFM_C addToFM0 fm key elt; 129.11/77.83 129.11/77.83 addToFM0 old new = new; 129.11/77.83 129.11/77.83 addToFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> a -> b -> FiniteMap a b; 129.11/77.83 addToFM_C combiner EmptyFM key elt = unitFM key elt; 129.11/77.83 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r 129.11/77.83 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt) 129.11/77.83 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r; 129.11/77.83 129.11/77.83 deleteMax :: Ord a => FiniteMap a b -> FiniteMap a b; 129.11/77.83 deleteMax (Branch key elt _ fm_l EmptyFM) = fm_l; 129.11/77.83 deleteMax (Branch key elt _ fm_l fm_r) = mkBalBranch key elt fm_l (deleteMax fm_r); 129.11/77.83 129.11/77.83 deleteMin :: Ord b => FiniteMap b a -> FiniteMap b a; 129.11/77.83 deleteMin (Branch key elt _ EmptyFM fm_r) = fm_r; 129.11/77.83 deleteMin (Branch key elt _ fm_l fm_r) = mkBalBranch key elt (deleteMin fm_l) fm_r; 129.11/77.83 129.11/77.83 emptyFM :: FiniteMap a b; 129.11/77.83 emptyFM = EmptyFM; 129.11/77.83 129.11/77.83 findMax :: FiniteMap b a -> (b,a); 129.11/77.83 findMax (Branch key elt _ _ EmptyFM) = (key,elt); 129.11/77.83 findMax (Branch key elt _ _ fm_r) = findMax fm_r; 129.11/77.83 129.11/77.83 findMin :: FiniteMap b a -> (b,a); 129.11/77.83 findMin (Branch key elt _ EmptyFM _) = (key,elt); 129.11/77.83 findMin (Branch key elt _ fm_l _) = findMin fm_l; 129.11/77.83 129.11/77.83 fmToList :: FiniteMap a b -> [(a,b)]; 129.11/77.83 fmToList fm = foldFM fmToList0 [] fm; 129.11/77.83 129.11/77.83 fmToList0 key elt rest = (key,elt) : rest; 129.11/77.83 129.11/77.83 foldFM :: (b -> c -> a -> a) -> a -> FiniteMap b c -> a; 129.11/77.83 foldFM k z EmptyFM = z; 129.11/77.83 foldFM k z (Branch key elt _ fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; 129.11/77.83 129.11/77.83 glueBal :: Ord a => FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 129.11/77.83 glueBal EmptyFM fm2 = fm2; 129.11/77.83 glueBal fm1 EmptyFM = fm1; 129.11/77.83 glueBal fm1 fm2 | sizeFM fm2 > sizeFM fm1 = mkBalBranch mid_key2 mid_elt2 fm1 (deleteMin fm2) 129.11/77.83 | otherwise = mkBalBranch mid_key1 mid_elt1 (deleteMax fm1) fm2 where { 129.11/77.83 mid_elt1 = mid_elt10 vv2; 129.11/77.83 mid_elt10 (_,mid_elt1) = mid_elt1; 129.11/77.83 mid_elt2 = mid_elt20 vv3; 129.11/77.83 mid_elt20 (_,mid_elt2) = mid_elt2; 129.11/77.83 mid_key1 = mid_key10 vv2; 129.11/77.83 mid_key10 (mid_key1,_) = mid_key1; 129.11/77.83 mid_key2 = mid_key20 vv3; 129.11/77.83 mid_key20 (mid_key2,_) = mid_key2; 129.11/77.83 vv2 = findMax fm1; 129.11/77.83 vv3 = findMin fm2; 129.11/77.83 }; 129.11/77.83 129.11/77.83 glueVBal :: Ord b => FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 129.11/77.83 glueVBal EmptyFM fm2 = fm2; 129.11/77.83 glueVBal fm1 EmptyFM = fm1; 129.11/77.83 glueVBal fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) | sIZE_RATIO * size_l < size_r = mkBalBranch key_r elt_r (glueVBal fm_l fm_rl) fm_rr 129.11/77.83 | sIZE_RATIO * size_r < size_l = mkBalBranch key_l elt_l fm_ll (glueVBal fm_lr fm_r) 129.11/77.83 | otherwise = glueBal fm_l fm_r where { 129.11/77.83 size_l = sizeFM fm_l; 129.11/77.83 size_r = sizeFM fm_r; 129.11/77.83 }; 129.11/77.83 129.11/77.83 intersectFM :: Ord b => FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 129.11/77.83 intersectFM fm1 fm2 = intersectFM_C intersectFM0 fm1 fm2; 129.11/77.83 129.11/77.83 intersectFM0 left right = right; 129.11/77.83 129.11/77.83 intersectFM_C :: Ord b => (d -> c -> a) -> FiniteMap b d -> FiniteMap b c -> FiniteMap b a; 129.11/77.83 intersectFM_C combiner fm1 EmptyFM = emptyFM; 129.11/77.83 intersectFM_C combiner EmptyFM fm2 = emptyFM; 129.11/77.83 intersectFM_C combiner fm1 (Branch split_key elt2 _ left right) | Maybe.isJust maybe_elt1 = mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) 129.11/77.83 | otherwise = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) where { 129.11/77.83 elt1 = elt10 vv1; 129.11/77.83 elt10 (Just elt1) = elt1; 129.11/77.83 gts = splitGT fm1 split_key; 129.11/77.83 lts = splitLT fm1 split_key; 129.11/77.83 maybe_elt1 = lookupFM fm1 split_key; 129.11/77.83 vv1 = maybe_elt1; 129.11/77.83 }; 129.11/77.83 129.11/77.83 lookupFM :: Ord b => FiniteMap b a -> b -> Maybe a; 129.11/77.83 lookupFM EmptyFM key = Nothing; 129.11/77.83 lookupFM (Branch key elt _ fm_l fm_r) key_to_find | key_to_find < key = lookupFM fm_l key_to_find 129.11/77.83 | key_to_find > key = lookupFM fm_r key_to_find 129.11/77.83 | otherwise = Just elt; 129.11/77.83 129.11/77.83 mkBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 129.11/77.83 mkBalBranch key elt fm_L fm_R | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R 129.11/77.83 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R 129.11/77.83 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L 129.11/77.83 | otherwise = mkBranch 2 key elt fm_L fm_R where { 129.11/77.83 double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 129.11/77.83 double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); 129.11/77.83 mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr) | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R 129.11/77.83 | otherwise = double_L fm_L fm_R; 129.11/77.83 mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr) | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R 129.11/77.83 | otherwise = double_R fm_L fm_R; 129.11/77.83 single_L fm_l (Branch key_r elt_r _ fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 129.11/77.83 single_R (Branch key_l elt_l _ fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 129.11/77.83 size_l = sizeFM fm_L; 129.11/77.83 size_r = sizeFM fm_R; 129.11/77.83 }; 129.11/77.83 129.11/77.83 mkBranch :: Ord b => Int -> b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 129.11/77.83 mkBranch which key elt fm_l fm_r = let { 129.11/77.83 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 129.11/77.83 } in result where { 129.11/77.83 balance_ok = True; 129.11/77.83 left_ok = left_ok0 fm_l key fm_l; 129.11/77.83 left_ok0 fm_l key EmptyFM = True; 129.11/77.83 left_ok0 fm_l key (Branch left_key _ _ _ _) = let { 129.11/77.83 biggest_left_key = fst (findMax fm_l); 129.11/77.83 } in biggest_left_key < key; 129.11/77.83 left_size = sizeFM fm_l; 129.11/77.83 right_ok = right_ok0 fm_r key fm_r; 129.11/77.83 right_ok0 fm_r key EmptyFM = True; 129.11/77.83 right_ok0 fm_r key (Branch right_key _ _ _ _) = let { 129.11/77.83 smallest_right_key = fst (findMin fm_r); 129.11/77.83 } in key < smallest_right_key; 129.11/77.83 right_size = sizeFM fm_r; 129.11/77.83 unbox :: Int -> Int; 129.11/77.83 unbox x = x; 129.11/77.83 }; 129.11/77.83 129.11/77.83 mkVBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 129.11/77.83 mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt; 129.11/77.83 mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt; 129.11/77.83 mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) | sIZE_RATIO * size_l < size_r = mkBalBranch key_r elt_r (mkVBalBranch key elt fm_l fm_rl) fm_rr 129.11/77.83 | sIZE_RATIO * size_r < size_l = mkBalBranch key_l elt_l fm_ll (mkVBalBranch key elt fm_lr fm_r) 129.11/77.83 | otherwise = mkBranch 13 key elt fm_l fm_r where { 129.11/77.83 size_l = sizeFM fm_l; 129.11/77.83 size_r = sizeFM fm_r; 129.11/77.83 }; 129.11/77.83 129.11/77.83 sIZE_RATIO :: Int; 129.11/77.83 sIZE_RATIO = 5; 129.11/77.83 129.11/77.83 sizeFM :: FiniteMap a b -> Int; 129.11/77.83 sizeFM EmptyFM = 0; 129.11/77.83 sizeFM (Branch _ _ size _ _) = size; 129.11/77.83 129.11/77.83 splitGT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; 129.11/77.83 splitGT EmptyFM split_key = emptyFM; 129.11/77.83 splitGT (Branch key elt _ fm_l fm_r) split_key | split_key > key = splitGT fm_r split_key 129.11/77.83 | split_key < key = mkVBalBranch key elt (splitGT fm_l split_key) fm_r 129.11/77.83 | otherwise = fm_r; 129.11/77.83 129.11/77.83 splitLT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; 129.11/77.83 splitLT EmptyFM split_key = emptyFM; 129.11/77.83 splitLT (Branch key elt _ fm_l fm_r) split_key | split_key < key = splitLT fm_l split_key 129.15/77.83 | split_key > key = mkVBalBranch key elt fm_l (splitLT fm_r split_key) 129.15/77.83 | otherwise = fm_l; 129.15/77.83 129.15/77.83 unitFM :: a -> b -> FiniteMap a b; 129.15/77.83 unitFM key elt = Branch key elt 1 emptyFM emptyFM; 129.15/77.83 129.15/77.83 } 129.15/77.83 module Maybe where { 129.15/77.83 import qualified FiniteMap; 129.15/77.83 import qualified Main; 129.15/77.83 import qualified Prelude; 129.15/77.83 isJust :: Maybe a -> Bool; 129.15/77.83 isJust Nothing = False; 129.15/77.83 isJust _ = True; 129.15/77.83 129.15/77.83 } 129.15/77.83 module Main where { 129.15/77.83 import qualified FiniteMap; 129.15/77.83 import qualified Maybe; 129.15/77.83 import qualified Prelude; 129.15/77.83 } 129.15/77.83 129.15/77.83 ---------------------------------------- 129.15/77.83 129.15/77.83 (7) BR (EQUIVALENT) 129.15/77.83 Replaced joker patterns by fresh variables and removed binding patterns. 129.15/77.83 129.15/77.83 Binding Reductions: 129.15/77.83 The bind variable of the following binding Pattern 129.15/77.83 "fm_l@(Branch vwz vxu vxv vxw vxx)" 129.15/77.83 is replaced by the following term 129.15/77.83 "Branch vwz vxu vxv vxw vxx" 129.15/77.83 The bind variable of the following binding Pattern 129.15/77.83 "fm_r@(Branch vxz vyu vyv vyw vyx)" 129.15/77.83 is replaced by the following term 129.15/77.83 "Branch vxz vyu vyv vyw vyx" 129.15/77.83 The bind variable of the following binding Pattern 129.15/77.83 "fm_l@(Branch vzv vzw vzx vzy vzz)" 129.15/77.83 is replaced by the following term 129.15/77.83 "Branch vzv vzw vzx vzy vzz" 129.15/77.83 The bind variable of the following binding Pattern 129.15/77.83 "fm_r@(Branch wuv wuw wux wuy wuz)" 129.15/77.83 is replaced by the following term 129.15/77.83 "Branch wuv wuw wux wuy wuz" 129.15/77.83 129.15/77.83 ---------------------------------------- 129.15/77.83 129.15/77.83 (8) 129.15/77.83 Obligation: 129.15/77.83 mainModule Main 129.15/77.83 module FiniteMap where { 129.15/77.83 import qualified Main; 129.15/77.83 import qualified Maybe; 129.15/77.83 import qualified Prelude; 129.15/77.83 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 129.15/77.83 129.15/77.83 instance (Eq a, Eq b) => Eq FiniteMap a b where { 129.15/77.83 (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; 129.15/77.83 } 129.15/77.83 addToFM :: Ord a => FiniteMap a b -> a -> b -> FiniteMap a b; 129.15/77.83 addToFM fm key elt = addToFM_C addToFM0 fm key elt; 129.15/77.83 129.15/77.83 addToFM0 old new = new; 129.15/77.83 129.15/77.83 addToFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> a -> b -> FiniteMap a b; 129.15/77.83 addToFM_C combiner EmptyFM key elt = unitFM key elt; 129.15/77.83 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r 129.15/77.83 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt) 129.15/77.83 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r; 129.15/77.83 129.15/77.83 deleteMax :: Ord a => FiniteMap a b -> FiniteMap a b; 129.15/77.83 deleteMax (Branch key elt wvu fm_l EmptyFM) = fm_l; 129.15/77.83 deleteMax (Branch key elt wvv fm_l fm_r) = mkBalBranch key elt fm_l (deleteMax fm_r); 129.15/77.83 129.15/77.83 deleteMin :: Ord b => FiniteMap b a -> FiniteMap b a; 129.15/77.83 deleteMin (Branch key elt wyv EmptyFM fm_r) = fm_r; 129.15/77.83 deleteMin (Branch key elt wyw fm_l fm_r) = mkBalBranch key elt (deleteMin fm_l) fm_r; 129.15/77.83 129.15/77.83 emptyFM :: FiniteMap b a; 129.15/77.83 emptyFM = EmptyFM; 129.15/77.83 129.15/77.83 findMax :: FiniteMap a b -> (a,b); 129.15/77.83 findMax (Branch key elt vvw vvx EmptyFM) = (key,elt); 129.15/77.83 findMax (Branch key elt vvy vvz fm_r) = findMax fm_r; 129.15/77.83 129.15/77.83 findMin :: FiniteMap b a -> (b,a); 129.15/77.83 findMin (Branch key elt wyy EmptyFM wyz) = (key,elt); 129.15/77.83 findMin (Branch key elt wzu fm_l wzv) = findMin fm_l; 129.15/77.83 129.15/77.83 fmToList :: FiniteMap a b -> [(a,b)]; 129.15/77.83 fmToList fm = foldFM fmToList0 [] fm; 129.15/77.83 129.15/77.83 fmToList0 key elt rest = (key,elt) : rest; 129.15/77.83 129.15/77.83 foldFM :: (c -> b -> a -> a) -> a -> FiniteMap c b -> a; 129.15/77.83 foldFM k z EmptyFM = z; 129.15/77.83 foldFM k z (Branch key elt vyy fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; 129.15/77.83 129.15/77.83 glueBal :: Ord a => FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 129.15/77.83 glueBal EmptyFM fm2 = fm2; 129.15/77.83 glueBal fm1 EmptyFM = fm1; 129.15/77.83 glueBal fm1 fm2 | sizeFM fm2 > sizeFM fm1 = mkBalBranch mid_key2 mid_elt2 fm1 (deleteMin fm2) 129.15/77.83 | otherwise = mkBalBranch mid_key1 mid_elt1 (deleteMax fm1) fm2 where { 129.15/77.83 mid_elt1 = mid_elt10 vv2; 129.15/77.83 mid_elt10 (vwv,mid_elt1) = mid_elt1; 129.15/77.83 mid_elt2 = mid_elt20 vv3; 129.15/77.83 mid_elt20 (vwu,mid_elt2) = mid_elt2; 129.15/77.83 mid_key1 = mid_key10 vv2; 129.15/77.83 mid_key10 (mid_key1,vww) = mid_key1; 129.15/77.83 mid_key2 = mid_key20 vv3; 129.15/77.83 mid_key20 (mid_key2,vwx) = mid_key2; 129.15/77.83 vv2 = findMax fm1; 129.15/77.83 vv3 = findMin fm2; 129.15/77.83 }; 129.15/77.83 129.15/77.83 glueVBal :: Ord b => FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 129.15/77.83 glueVBal EmptyFM fm2 = fm2; 129.15/77.83 glueVBal fm1 EmptyFM = fm1; 129.15/77.83 glueVBal (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx) | sIZE_RATIO * size_l < size_r = mkBalBranch vxz vyu (glueVBal (Branch vwz vxu vxv vxw vxx) vyw) vyx 129.15/77.83 | sIZE_RATIO * size_r < size_l = mkBalBranch vwz vxu vxw (glueVBal vxx (Branch vxz vyu vyv vyw vyx)) 129.15/77.83 | otherwise = glueBal (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx) where { 129.15/77.83 size_l = sizeFM (Branch vwz vxu vxv vxw vxx); 129.15/77.83 size_r = sizeFM (Branch vxz vyu vyv vyw vyx); 129.15/77.83 }; 129.15/77.83 129.15/77.83 intersectFM :: Ord b => FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 129.15/77.83 intersectFM fm1 fm2 = intersectFM_C intersectFM0 fm1 fm2; 129.15/77.83 129.15/77.83 intersectFM0 left right = right; 129.15/77.83 129.15/77.83 intersectFM_C :: Ord a => (c -> d -> b) -> FiniteMap a c -> FiniteMap a d -> FiniteMap a b; 129.15/77.83 intersectFM_C combiner fm1 EmptyFM = emptyFM; 129.15/77.83 intersectFM_C combiner EmptyFM fm2 = emptyFM; 129.15/77.83 intersectFM_C combiner fm1 (Branch split_key elt2 wyx left right) | Maybe.isJust maybe_elt1 = mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) 129.15/77.83 | otherwise = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) where { 129.15/77.83 elt1 = elt10 vv1; 129.15/77.83 elt10 (Just elt1) = elt1; 129.15/77.83 gts = splitGT fm1 split_key; 129.15/77.83 lts = splitLT fm1 split_key; 129.15/77.83 maybe_elt1 = lookupFM fm1 split_key; 129.15/77.83 vv1 = maybe_elt1; 129.15/77.83 }; 129.15/77.83 129.15/77.83 lookupFM :: Ord a => FiniteMap a b -> a -> Maybe b; 129.15/77.83 lookupFM EmptyFM key = Nothing; 129.15/77.83 lookupFM (Branch key elt vyz fm_l fm_r) key_to_find | key_to_find < key = lookupFM fm_l key_to_find 129.15/77.83 | key_to_find > key = lookupFM fm_r key_to_find 129.15/77.83 | otherwise = Just elt; 129.15/77.83 129.15/77.83 mkBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 129.15/77.83 mkBalBranch key elt fm_L fm_R | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R 129.15/77.83 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R 129.15/77.83 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L 129.15/77.83 | otherwise = mkBranch 2 key elt fm_L fm_R where { 129.15/77.83 double_L fm_l (Branch key_r elt_r wwx (Branch key_rl elt_rl wwy fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 129.15/77.83 double_R (Branch key_l elt_l wvy fm_ll (Branch key_lr elt_lr wvz fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); 129.15/77.83 mkBalBranch0 fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr) | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R 129.15/77.83 | otherwise = double_L fm_L fm_R; 129.15/77.83 mkBalBranch1 fm_L fm_R (Branch wwu wwv www fm_ll fm_lr) | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R 129.15/77.83 | otherwise = double_R fm_L fm_R; 129.15/77.83 single_L fm_l (Branch key_r elt_r wxw fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 129.15/77.83 single_R (Branch key_l elt_l wvx fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 129.15/77.83 size_l = sizeFM fm_L; 129.15/77.83 size_r = sizeFM fm_R; 129.15/77.83 }; 129.15/77.83 129.15/77.83 mkBranch :: Ord a => Int -> a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 129.15/77.83 mkBranch which key elt fm_l fm_r = let { 129.15/77.83 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 129.15/77.83 } in result where { 129.15/77.83 balance_ok = True; 129.15/77.83 left_ok = left_ok0 fm_l key fm_l; 129.15/77.83 left_ok0 fm_l key EmptyFM = True; 129.15/77.83 left_ok0 fm_l key (Branch left_key vuu vuv vuw vux) = let { 129.15/77.83 biggest_left_key = fst (findMax fm_l); 129.15/77.83 } in biggest_left_key < key; 129.15/77.83 left_size = sizeFM fm_l; 129.15/77.83 right_ok = right_ok0 fm_r key fm_r; 129.15/77.83 right_ok0 fm_r key EmptyFM = True; 129.15/77.83 right_ok0 fm_r key (Branch right_key vuy vuz vvu vvv) = let { 129.15/77.83 smallest_right_key = fst (findMin fm_r); 129.15/77.83 } in key < smallest_right_key; 129.15/77.83 right_size = sizeFM fm_r; 129.15/77.83 unbox :: Int -> Int; 129.15/77.83 unbox x = x; 129.15/77.83 }; 129.15/77.83 129.15/77.83 mkVBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 129.15/77.83 mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt; 129.15/77.83 mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt; 129.15/77.83 mkVBalBranch key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz) | sIZE_RATIO * size_l < size_r = mkBalBranch wuv wuw (mkVBalBranch key elt (Branch vzv vzw vzx vzy vzz) wuy) wuz 129.15/77.83 | sIZE_RATIO * size_r < size_l = mkBalBranch vzv vzw vzy (mkVBalBranch key elt vzz (Branch wuv wuw wux wuy wuz)) 129.15/77.83 | otherwise = mkBranch 13 key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz) where { 129.15/77.83 size_l = sizeFM (Branch vzv vzw vzx vzy vzz); 129.15/77.83 size_r = sizeFM (Branch wuv wuw wux wuy wuz); 129.15/77.83 }; 129.15/77.83 129.15/77.83 sIZE_RATIO :: Int; 129.15/77.83 sIZE_RATIO = 5; 129.15/77.83 129.15/77.83 sizeFM :: FiniteMap b a -> Int; 129.15/77.83 sizeFM EmptyFM = 0; 129.15/77.83 sizeFM (Branch wxx wxy size wxz wyu) = size; 129.15/77.83 129.15/77.83 splitGT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; 129.15/77.83 splitGT EmptyFM split_key = emptyFM; 129.15/77.83 splitGT (Branch key elt wvw fm_l fm_r) split_key | split_key > key = splitGT fm_r split_key 129.15/77.83 | split_key < key = mkVBalBranch key elt (splitGT fm_l split_key) fm_r 129.15/77.83 | otherwise = fm_r; 129.15/77.83 129.15/77.83 splitLT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; 129.15/77.83 splitLT EmptyFM split_key = emptyFM; 129.15/77.83 splitLT (Branch key elt zz fm_l fm_r) split_key | split_key < key = splitLT fm_l split_key 129.15/77.83 | split_key > key = mkVBalBranch key elt fm_l (splitLT fm_r split_key) 129.15/77.83 | otherwise = fm_l; 129.15/77.83 129.15/77.83 unitFM :: a -> b -> FiniteMap a b; 129.15/77.83 unitFM key elt = Branch key elt 1 emptyFM emptyFM; 129.15/77.83 129.15/77.83 } 129.15/77.83 module Maybe where { 129.15/77.83 import qualified FiniteMap; 129.15/77.83 import qualified Main; 129.15/77.83 import qualified Prelude; 129.15/77.83 isJust :: Maybe a -> Bool; 129.15/77.83 isJust Nothing = False; 129.15/77.83 isJust wzw = True; 129.15/77.83 129.15/77.83 } 129.15/77.83 module Main where { 129.15/77.83 import qualified FiniteMap; 129.15/77.83 import qualified Maybe; 129.15/77.83 import qualified Prelude; 129.15/77.83 } 129.15/77.83 129.15/77.83 ---------------------------------------- 129.15/77.83 129.15/77.83 (9) COR (EQUIVALENT) 129.15/77.83 Cond Reductions: 129.15/77.83 The following Function with conditions 129.15/77.83 "compare x y|x == yEQ|x <= yLT|otherwiseGT; 129.15/77.83 " 129.15/77.83 is transformed to 129.15/77.83 "compare x y = compare3 x y; 129.15/77.83 " 129.15/77.83 "compare2 x y True = EQ; 129.15/77.83 compare2 x y False = compare1 x y (x <= y); 129.15/77.83 " 129.15/77.83 "compare0 x y True = GT; 129.15/77.83 " 129.15/77.83 "compare1 x y True = LT; 129.15/77.83 compare1 x y False = compare0 x y otherwise; 129.15/77.83 " 129.15/77.83 "compare3 x y = compare2 x y (x == y); 129.15/77.83 " 129.15/77.83 The following Function with conditions 129.15/77.83 "absReal x|x >= 0x|otherwise`negate` x; 129.15/77.83 " 129.15/77.83 is transformed to 129.15/77.83 "absReal x = absReal2 x; 129.15/77.83 " 129.15/77.83 "absReal1 x True = x; 129.15/77.83 absReal1 x False = absReal0 x otherwise; 129.15/77.83 " 129.15/77.83 "absReal0 x True = `negate` x; 129.15/77.83 " 129.15/77.83 "absReal2 x = absReal1 x (x >= 0); 129.15/77.83 " 129.15/77.83 The following Function with conditions 129.15/77.83 "gcd' x 0 = x; 129.15/77.83 gcd' x y = gcd' y (x `rem` y); 129.15/77.83 " 129.15/77.83 is transformed to 129.15/77.83 "gcd' x wzx = gcd'2 x wzx; 129.15/77.83 gcd' x y = gcd'0 x y; 129.15/77.83 " 129.15/77.83 "gcd'0 x y = gcd' y (x `rem` y); 129.15/77.83 " 129.15/77.83 "gcd'1 True x wzx = x; 129.15/77.83 gcd'1 wzy wzz xuu = gcd'0 wzz xuu; 129.15/77.83 " 129.15/77.83 "gcd'2 x wzx = gcd'1 (wzx == 0) x wzx; 129.15/77.83 gcd'2 xuv xuw = gcd'0 xuv xuw; 129.15/77.83 " 129.15/77.83 The following Function with conditions 129.15/77.83 "gcd 0 0 = error []; 129.15/77.83 gcd x y = gcd' (abs x) (abs y) where { 129.15/77.83 gcd' x 0 = x; 129.15/77.83 gcd' x y = gcd' y (x `rem` y); 129.15/77.83 } 129.15/77.83 ; 129.15/77.83 " 129.15/77.83 is transformed to 129.15/77.83 "gcd xux xuy = gcd3 xux xuy; 129.15/77.83 gcd x y = gcd0 x y; 129.15/77.83 " 129.15/77.83 "gcd0 x y = gcd' (abs x) (abs y) where { 129.15/77.83 gcd' x wzx = gcd'2 x wzx; 129.15/77.83 gcd' x y = gcd'0 x y; 129.15/77.83 ; 129.15/77.83 gcd'0 x y = gcd' y (x `rem` y); 129.15/77.83 ; 129.15/77.83 gcd'1 True x wzx = x; 129.15/77.83 gcd'1 wzy wzz xuu = gcd'0 wzz xuu; 129.15/77.83 ; 129.15/77.83 gcd'2 x wzx = gcd'1 (wzx == 0) x wzx; 129.15/77.83 gcd'2 xuv xuw = gcd'0 xuv xuw; 129.15/77.83 } 129.15/77.83 ; 129.15/77.83 " 129.15/77.83 "gcd1 True xux xuy = error []; 129.15/77.83 gcd1 xuz xvu xvv = gcd0 xvu xvv; 129.15/77.83 " 129.15/77.83 "gcd2 True xux xuy = gcd1 (xuy == 0) xux xuy; 129.15/77.83 gcd2 xvw xvx xvy = gcd0 xvx xvy; 129.15/77.83 " 129.15/77.83 "gcd3 xux xuy = gcd2 (xux == 0) xux xuy; 129.15/77.83 gcd3 xvz xwu = gcd0 xvz xwu; 129.15/77.83 " 129.15/77.83 The following Function with conditions 129.15/77.83 "undefined |Falseundefined; 129.15/77.83 " 129.15/77.83 is transformed to 129.15/77.83 "undefined = undefined1; 129.15/77.83 " 129.15/77.83 "undefined0 True = undefined; 129.15/77.83 " 129.15/77.83 "undefined1 = undefined0 False; 129.15/77.83 " 129.15/77.83 The following Function with conditions 129.15/77.83 "reduce x y|y == 0error []|otherwisex `quot` d :% (y `quot` d) where { 129.15/77.83 d = gcd x y; 129.15/77.83 } 129.15/77.83 ; 129.15/77.83 " 129.15/77.83 is transformed to 129.15/77.83 "reduce x y = reduce2 x y; 129.15/77.83 " 129.15/77.83 "reduce2 x y = reduce1 x y (y == 0) where { 129.15/77.83 d = gcd x y; 129.15/77.83 ; 129.15/77.83 reduce0 x y True = x `quot` d :% (y `quot` d); 129.15/77.83 ; 129.15/77.83 reduce1 x y True = error []; 129.15/77.83 reduce1 x y False = reduce0 x y otherwise; 129.15/77.83 } 129.15/77.83 ; 129.15/77.83 " 129.15/77.83 The following Function with conditions 129.15/77.83 "splitLT EmptyFM split_key = emptyFM; 129.15/77.83 splitLT (Branch key elt zz fm_l fm_r) split_key|split_key < keysplitLT fm_l split_key|split_key > keymkVBalBranch key elt fm_l (splitLT fm_r split_key)|otherwisefm_l; 129.15/77.83 " 129.15/77.83 is transformed to 129.15/77.83 "splitLT EmptyFM split_key = splitLT4 EmptyFM split_key; 129.15/77.83 splitLT (Branch key elt zz fm_l fm_r) split_key = splitLT3 (Branch key elt zz fm_l fm_r) split_key; 129.15/77.83 " 129.15/77.83 "splitLT1 key elt zz fm_l fm_r split_key True = mkVBalBranch key elt fm_l (splitLT fm_r split_key); 129.15/77.83 splitLT1 key elt zz fm_l fm_r split_key False = splitLT0 key elt zz fm_l fm_r split_key otherwise; 129.15/77.83 " 129.15/77.83 "splitLT2 key elt zz fm_l fm_r split_key True = splitLT fm_l split_key; 129.15/77.83 splitLT2 key elt zz fm_l fm_r split_key False = splitLT1 key elt zz fm_l fm_r split_key (split_key > key); 129.15/77.83 " 129.15/77.83 "splitLT0 key elt zz fm_l fm_r split_key True = fm_l; 129.15/77.83 " 129.15/77.83 "splitLT3 (Branch key elt zz fm_l fm_r) split_key = splitLT2 key elt zz fm_l fm_r split_key (split_key < key); 129.15/77.83 " 129.15/77.83 "splitLT4 EmptyFM split_key = emptyFM; 129.15/77.83 splitLT4 xwx xwy = splitLT3 xwx xwy; 129.15/77.83 " 129.15/77.83 The following Function with conditions 129.15/77.83 "glueBal EmptyFM fm2 = fm2; 129.15/77.83 glueBal fm1 EmptyFM = fm1; 129.15/77.83 glueBal fm1 fm2|sizeFM fm2 > sizeFM fm1mkBalBranch mid_key2 mid_elt2 fm1 (deleteMin fm2)|otherwisemkBalBranch mid_key1 mid_elt1 (deleteMax fm1) fm2 where { 129.15/77.83 mid_elt1 = mid_elt10 vv2; 129.15/77.83 ; 129.15/77.83 mid_elt10 (vwv,mid_elt1) = mid_elt1; 129.15/77.83 ; 129.15/77.83 mid_elt2 = mid_elt20 vv3; 129.15/77.83 ; 129.15/77.83 mid_elt20 (vwu,mid_elt2) = mid_elt2; 129.15/77.83 ; 129.15/77.83 mid_key1 = mid_key10 vv2; 129.15/77.83 ; 129.15/77.83 mid_key10 (mid_key1,vww) = mid_key1; 129.15/77.83 ; 129.15/77.83 mid_key2 = mid_key20 vv3; 129.15/77.83 ; 129.15/77.83 mid_key20 (mid_key2,vwx) = mid_key2; 129.15/77.83 ; 129.15/77.83 vv2 = findMax fm1; 129.15/77.83 ; 129.15/77.83 vv3 = findMin fm2; 129.15/77.83 } 129.15/77.83 ; 129.15/77.83 " 129.15/77.83 is transformed to 129.15/77.83 "glueBal EmptyFM fm2 = glueBal4 EmptyFM fm2; 129.15/77.83 glueBal fm1 EmptyFM = glueBal3 fm1 EmptyFM; 129.15/77.83 glueBal fm1 fm2 = glueBal2 fm1 fm2; 129.15/77.83 " 129.15/77.83 "glueBal2 fm1 fm2 = glueBal1 fm1 fm2 (sizeFM fm2 > sizeFM fm1) where { 129.15/77.83 glueBal0 fm1 fm2 True = mkBalBranch mid_key1 mid_elt1 (deleteMax fm1) fm2; 129.15/77.83 ; 129.15/77.83 glueBal1 fm1 fm2 True = mkBalBranch mid_key2 mid_elt2 fm1 (deleteMin fm2); 129.15/77.83 glueBal1 fm1 fm2 False = glueBal0 fm1 fm2 otherwise; 129.15/77.83 ; 129.15/77.83 mid_elt1 = mid_elt10 vv2; 129.15/77.83 ; 129.15/77.83 mid_elt10 (vwv,mid_elt1) = mid_elt1; 129.15/77.83 ; 129.15/77.83 mid_elt2 = mid_elt20 vv3; 129.15/77.83 ; 129.15/77.83 mid_elt20 (vwu,mid_elt2) = mid_elt2; 129.15/77.83 ; 129.15/77.83 mid_key1 = mid_key10 vv2; 129.15/77.83 ; 129.15/77.83 mid_key10 (mid_key1,vww) = mid_key1; 129.15/77.83 ; 129.15/77.83 mid_key2 = mid_key20 vv3; 129.15/77.83 ; 129.15/77.83 mid_key20 (mid_key2,vwx) = mid_key2; 129.15/77.83 ; 129.15/77.83 vv2 = findMax fm1; 129.15/77.83 ; 129.15/77.83 vv3 = findMin fm2; 129.15/77.83 } 129.15/77.83 ; 129.15/77.83 " 129.15/77.83 "glueBal3 fm1 EmptyFM = fm1; 129.15/77.83 glueBal3 xxu xxv = glueBal2 xxu xxv; 129.15/77.83 " 129.15/77.83 "glueBal4 EmptyFM fm2 = fm2; 129.15/77.83 glueBal4 xxx xxy = glueBal3 xxx xxy; 129.15/77.83 " 129.15/77.83 The following Function with conditions 129.15/77.83 "glueVBal EmptyFM fm2 = fm2; 129.15/77.83 glueVBal fm1 EmptyFM = fm1; 129.15/77.83 glueVBal (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx)|sIZE_RATIO * size_l < size_rmkBalBranch vxz vyu (glueVBal (Branch vwz vxu vxv vxw vxx) vyw) vyx|sIZE_RATIO * size_r < size_lmkBalBranch vwz vxu vxw (glueVBal vxx (Branch vxz vyu vyv vyw vyx))|otherwiseglueBal (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx) where { 129.15/77.83 size_l = sizeFM (Branch vwz vxu vxv vxw vxx); 129.15/77.83 ; 129.15/77.83 size_r = sizeFM (Branch vxz vyu vyv vyw vyx); 129.15/77.83 } 129.15/77.83 ; 129.15/77.83 " 129.15/77.83 is transformed to 129.15/77.83 "glueVBal EmptyFM fm2 = glueVBal5 EmptyFM fm2; 129.15/77.83 glueVBal fm1 EmptyFM = glueVBal4 fm1 EmptyFM; 129.15/77.83 glueVBal (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx) = glueVBal3 (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx); 129.15/77.83 " 129.15/77.83 "glueVBal3 (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx) = glueVBal2 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx (sIZE_RATIO * size_l < size_r) where { 129.15/77.83 glueVBal0 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx True = glueBal (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx); 129.15/77.83 ; 129.15/77.83 glueVBal1 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx True = mkBalBranch vwz vxu vxw (glueVBal vxx (Branch vxz vyu vyv vyw vyx)); 129.15/77.83 glueVBal1 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx False = glueVBal0 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx otherwise; 129.15/77.83 ; 129.15/77.83 glueVBal2 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx True = mkBalBranch vxz vyu (glueVBal (Branch vwz vxu vxv vxw vxx) vyw) vyx; 129.15/77.83 glueVBal2 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx False = glueVBal1 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx (sIZE_RATIO * size_r < size_l); 129.15/77.83 ; 129.15/77.83 size_l = sizeFM (Branch vwz vxu vxv vxw vxx); 129.15/77.83 ; 129.15/77.83 size_r = sizeFM (Branch vxz vyu vyv vyw vyx); 129.15/77.83 } 129.15/77.83 ; 129.15/77.83 " 129.15/77.83 "glueVBal4 fm1 EmptyFM = fm1; 129.15/77.83 glueVBal4 xyw xyx = glueVBal3 xyw xyx; 129.15/77.83 " 129.15/77.83 "glueVBal5 EmptyFM fm2 = fm2; 129.15/77.83 glueVBal5 xyz xzu = glueVBal4 xyz xzu; 129.15/77.83 " 129.15/77.83 The following Function with conditions 129.15/77.83 "lookupFM EmptyFM key = Nothing; 129.15/77.83 lookupFM (Branch key elt vyz fm_l fm_r) key_to_find|key_to_find < keylookupFM fm_l key_to_find|key_to_find > keylookupFM fm_r key_to_find|otherwiseJust elt; 129.15/77.83 " 129.15/77.83 is transformed to 129.15/77.83 "lookupFM EmptyFM key = lookupFM4 EmptyFM key; 129.15/77.83 lookupFM (Branch key elt vyz fm_l fm_r) key_to_find = lookupFM3 (Branch key elt vyz fm_l fm_r) key_to_find; 129.15/77.83 " 129.15/77.83 "lookupFM1 key elt vyz fm_l fm_r key_to_find True = lookupFM fm_r key_to_find; 129.15/77.83 lookupFM1 key elt vyz fm_l fm_r key_to_find False = lookupFM0 key elt vyz fm_l fm_r key_to_find otherwise; 129.15/77.83 " 129.15/77.83 "lookupFM0 key elt vyz fm_l fm_r key_to_find True = Just elt; 129.15/77.83 " 129.15/77.83 "lookupFM2 key elt vyz fm_l fm_r key_to_find True = lookupFM fm_l key_to_find; 129.15/77.83 lookupFM2 key elt vyz fm_l fm_r key_to_find False = lookupFM1 key elt vyz fm_l fm_r key_to_find (key_to_find > key); 129.15/77.83 " 129.15/77.83 "lookupFM3 (Branch key elt vyz fm_l fm_r) key_to_find = lookupFM2 key elt vyz fm_l fm_r key_to_find (key_to_find < key); 129.15/77.83 " 129.15/77.83 "lookupFM4 EmptyFM key = Nothing; 129.15/77.83 lookupFM4 xzx xzy = lookupFM3 xzx xzy; 129.15/77.83 " 129.15/77.83 The following Function with conditions 129.15/77.83 "addToFM_C combiner EmptyFM key elt = unitFM key elt; 129.15/77.83 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt|new_key < keymkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r|new_key > keymkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)|otherwiseBranch new_key (combiner elt new_elt) size fm_l fm_r; 129.15/77.83 " 129.15/77.83 is transformed to 129.15/77.83 "addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt; 129.15/77.83 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt; 129.15/77.83 " 129.15/77.83 "addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r; 129.15/77.83 " 129.15/77.83 "addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt); 129.15/77.83 addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise; 129.15/77.83 " 129.15/77.83 "addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r; 129.15/77.83 addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key); 129.15/77.83 " 129.15/77.83 "addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key); 129.75/78.01 " 129.75/78.01 "addToFM_C4 combiner EmptyFM key elt = unitFM key elt; 129.75/78.01 addToFM_C4 yuv yuw yux yuy = addToFM_C3 yuv yuw yux yuy; 129.75/78.01 " 129.75/78.01 The following Function with conditions 129.75/78.01 "mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt; 129.75/78.01 mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt; 129.75/78.01 mkVBalBranch key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz)|sIZE_RATIO * size_l < size_rmkBalBranch wuv wuw (mkVBalBranch key elt (Branch vzv vzw vzx vzy vzz) wuy) wuz|sIZE_RATIO * size_r < size_lmkBalBranch vzv vzw vzy (mkVBalBranch key elt vzz (Branch wuv wuw wux wuy wuz))|otherwisemkBranch 13 key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz) where { 129.75/78.01 size_l = sizeFM (Branch vzv vzw vzx vzy vzz); 129.75/78.01 ; 129.75/78.01 size_r = sizeFM (Branch wuv wuw wux wuy wuz); 129.75/78.01 } 129.75/78.01 ; 129.75/78.01 " 129.75/78.01 is transformed to 129.75/78.01 "mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r; 129.75/78.01 mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM; 129.75/78.01 mkVBalBranch key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz) = mkVBalBranch3 key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz); 129.75/78.01 " 129.75/78.01 "mkVBalBranch3 key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz) = mkVBalBranch2 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz (sIZE_RATIO * size_l < size_r) where { 129.75/78.01 mkVBalBranch0 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz True = mkBranch 13 key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz); 129.75/78.01 ; 129.75/78.01 mkVBalBranch1 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz True = mkBalBranch vzv vzw vzy (mkVBalBranch key elt vzz (Branch wuv wuw wux wuy wuz)); 129.75/78.01 mkVBalBranch1 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz False = mkVBalBranch0 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz otherwise; 129.75/78.01 ; 129.75/78.01 mkVBalBranch2 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz True = mkBalBranch wuv wuw (mkVBalBranch key elt (Branch vzv vzw vzx vzy vzz) wuy) wuz; 129.75/78.01 mkVBalBranch2 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz False = mkVBalBranch1 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz (sIZE_RATIO * size_r < size_l); 129.75/78.01 ; 129.75/78.01 size_l = sizeFM (Branch vzv vzw vzx vzy vzz); 129.75/78.01 ; 129.75/78.01 size_r = sizeFM (Branch wuv wuw wux wuy wuz); 129.75/78.01 } 129.75/78.01 ; 129.75/78.01 " 129.75/78.01 "mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt; 129.75/78.01 mkVBalBranch4 yvw yvx yvy yvz = mkVBalBranch3 yvw yvx yvy yvz; 129.75/78.01 " 129.75/78.01 "mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt; 129.75/78.01 mkVBalBranch5 ywv yww ywx ywy = mkVBalBranch4 ywv yww ywx ywy; 129.75/78.01 " 129.75/78.01 The following Function with conditions 129.75/78.01 "splitGT EmptyFM split_key = emptyFM; 129.75/78.01 splitGT (Branch key elt wvw fm_l fm_r) split_key|split_key > keysplitGT fm_r split_key|split_key < keymkVBalBranch key elt (splitGT fm_l split_key) fm_r|otherwisefm_r; 129.75/78.01 " 129.75/78.01 is transformed to 129.75/78.01 "splitGT EmptyFM split_key = splitGT4 EmptyFM split_key; 129.75/78.01 splitGT (Branch key elt wvw fm_l fm_r) split_key = splitGT3 (Branch key elt wvw fm_l fm_r) split_key; 129.75/78.01 " 129.75/78.01 "splitGT1 key elt wvw fm_l fm_r split_key True = mkVBalBranch key elt (splitGT fm_l split_key) fm_r; 129.75/78.01 splitGT1 key elt wvw fm_l fm_r split_key False = splitGT0 key elt wvw fm_l fm_r split_key otherwise; 129.75/78.01 " 129.75/78.01 "splitGT2 key elt wvw fm_l fm_r split_key True = splitGT fm_r split_key; 129.75/78.01 splitGT2 key elt wvw fm_l fm_r split_key False = splitGT1 key elt wvw fm_l fm_r split_key (split_key < key); 129.75/78.01 " 129.75/78.01 "splitGT0 key elt wvw fm_l fm_r split_key True = fm_r; 129.75/78.01 " 129.75/78.01 "splitGT3 (Branch key elt wvw fm_l fm_r) split_key = splitGT2 key elt wvw fm_l fm_r split_key (split_key > key); 129.75/78.01 " 129.75/78.01 "splitGT4 EmptyFM split_key = emptyFM; 129.75/78.01 splitGT4 yxv yxw = splitGT3 yxv yxw; 129.75/78.01 " 129.75/78.01 The following Function with conditions 129.75/78.01 "mkBalBranch1 fm_L fm_R (Branch wwu wwv www fm_ll fm_lr)|sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R; 129.75/78.01 " 129.75/78.01 is transformed to 129.75/78.01 "mkBalBranch1 fm_L fm_R (Branch wwu wwv www fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch wwu wwv www fm_ll fm_lr); 129.75/78.01 " 129.75/78.01 "mkBalBranch11 fm_L fm_R wwu wwv www fm_ll fm_lr True = single_R fm_L fm_R; 129.75/78.01 mkBalBranch11 fm_L fm_R wwu wwv www fm_ll fm_lr False = mkBalBranch10 fm_L fm_R wwu wwv www fm_ll fm_lr otherwise; 129.75/78.01 " 129.75/78.01 "mkBalBranch10 fm_L fm_R wwu wwv www fm_ll fm_lr True = double_R fm_L fm_R; 129.75/78.01 " 129.75/78.01 "mkBalBranch12 fm_L fm_R (Branch wwu wwv www fm_ll fm_lr) = mkBalBranch11 fm_L fm_R wwu wwv www fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); 129.75/78.01 " 129.75/78.01 The following Function with conditions 129.75/78.01 "mkBalBranch0 fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr)|sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R; 129.75/78.01 " 129.75/78.01 is transformed to 129.75/78.01 "mkBalBranch0 fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr); 129.75/78.01 " 129.75/78.01 "mkBalBranch00 fm_L fm_R wwz wxu wxv fm_rl fm_rr True = double_L fm_L fm_R; 129.75/78.01 " 129.75/78.01 "mkBalBranch01 fm_L fm_R wwz wxu wxv fm_rl fm_rr True = single_L fm_L fm_R; 129.75/78.01 mkBalBranch01 fm_L fm_R wwz wxu wxv fm_rl fm_rr False = mkBalBranch00 fm_L fm_R wwz wxu wxv fm_rl fm_rr otherwise; 129.75/78.01 " 129.75/78.01 "mkBalBranch02 fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr) = mkBalBranch01 fm_L fm_R wwz wxu wxv fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); 129.75/78.01 " 129.75/78.01 The following Function with conditions 129.75/78.01 "mkBalBranch key elt fm_L fm_R|size_l + size_r < 2mkBranch 1 key elt fm_L fm_R|size_r > sIZE_RATIO * size_lmkBalBranch0 fm_L fm_R fm_R|size_l > sIZE_RATIO * size_rmkBalBranch1 fm_L fm_R fm_L|otherwisemkBranch 2 key elt fm_L fm_R where { 129.75/78.01 double_L fm_l (Branch key_r elt_r wwx (Branch key_rl elt_rl wwy fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 129.75/78.01 ; 129.75/78.01 double_R (Branch key_l elt_l wvy fm_ll (Branch key_lr elt_lr wvz fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); 129.75/78.01 ; 129.75/78.01 mkBalBranch0 fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr)|sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R; 129.75/78.01 ; 129.75/78.01 mkBalBranch1 fm_L fm_R (Branch wwu wwv www fm_ll fm_lr)|sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R; 129.75/78.01 ; 129.75/78.01 single_L fm_l (Branch key_r elt_r wxw fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 129.75/78.01 ; 129.75/78.01 single_R (Branch key_l elt_l wvx fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 129.75/78.01 ; 129.75/78.01 size_l = sizeFM fm_L; 129.75/78.01 ; 129.75/78.01 size_r = sizeFM fm_R; 129.75/78.01 } 129.75/78.01 ; 129.75/78.01 " 129.75/78.01 is transformed to 129.75/78.01 "mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R; 129.75/78.01 " 129.75/78.01 "mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { 129.75/78.01 double_L fm_l (Branch key_r elt_r wwx (Branch key_rl elt_rl wwy fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 129.75/78.01 ; 129.75/78.01 double_R (Branch key_l elt_l wvy fm_ll (Branch key_lr elt_lr wvz fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); 129.75/78.01 ; 129.75/78.01 mkBalBranch0 fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr); 129.75/78.01 ; 129.75/78.01 mkBalBranch00 fm_L fm_R wwz wxu wxv fm_rl fm_rr True = double_L fm_L fm_R; 129.75/78.01 ; 129.75/78.01 mkBalBranch01 fm_L fm_R wwz wxu wxv fm_rl fm_rr True = single_L fm_L fm_R; 129.75/78.01 mkBalBranch01 fm_L fm_R wwz wxu wxv fm_rl fm_rr False = mkBalBranch00 fm_L fm_R wwz wxu wxv fm_rl fm_rr otherwise; 129.75/78.01 ; 129.75/78.01 mkBalBranch02 fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr) = mkBalBranch01 fm_L fm_R wwz wxu wxv fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); 129.75/78.01 ; 129.75/78.01 mkBalBranch1 fm_L fm_R (Branch wwu wwv www fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch wwu wwv www fm_ll fm_lr); 129.75/78.01 ; 129.75/78.01 mkBalBranch10 fm_L fm_R wwu wwv www fm_ll fm_lr True = double_R fm_L fm_R; 129.75/78.01 ; 129.75/78.01 mkBalBranch11 fm_L fm_R wwu wwv www fm_ll fm_lr True = single_R fm_L fm_R; 129.75/78.01 mkBalBranch11 fm_L fm_R wwu wwv www fm_ll fm_lr False = mkBalBranch10 fm_L fm_R wwu wwv www fm_ll fm_lr otherwise; 129.75/78.01 ; 129.75/78.01 mkBalBranch12 fm_L fm_R (Branch wwu wwv www fm_ll fm_lr) = mkBalBranch11 fm_L fm_R wwu wwv www fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); 129.75/78.01 ; 129.75/78.01 mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; 129.75/78.01 ; 129.75/78.01 mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L; 129.75/78.01 mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise; 129.75/78.01 ; 129.75/78.01 mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R; 129.75/78.01 mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r); 129.75/78.01 ; 129.75/78.01 mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; 129.75/78.01 mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l); 129.75/78.01 ; 129.75/78.01 single_L fm_l (Branch key_r elt_r wxw fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 129.75/78.01 ; 129.75/78.01 single_R (Branch key_l elt_l wvx fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 129.75/78.01 ; 129.75/78.01 size_l = sizeFM fm_L; 129.75/78.01 ; 129.75/78.01 size_r = sizeFM fm_R; 129.75/78.01 } 129.75/78.01 ; 129.75/78.01 " 129.75/78.01 The following Function with conditions 129.75/78.01 "intersectFM_C combiner fm1 EmptyFM = emptyFM; 129.75/78.01 intersectFM_C combiner EmptyFM fm2 = emptyFM; 129.75/78.01 intersectFM_C combiner fm1 (Branch split_key elt2 wyx left right)|Maybe.isJust maybe_elt1mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)|otherwiseglueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) where { 129.75/78.01 elt1 = elt10 vv1; 129.75/78.01 ; 129.75/78.01 elt10 (Just elt1) = elt1; 129.75/78.01 ; 129.75/78.01 gts = splitGT fm1 split_key; 129.75/78.01 ; 129.75/78.01 lts = splitLT fm1 split_key; 129.75/78.01 ; 129.75/78.01 maybe_elt1 = lookupFM fm1 split_key; 129.75/78.01 ; 129.75/78.01 vv1 = maybe_elt1; 129.75/78.01 } 129.75/78.01 ; 129.75/78.01 " 129.75/78.01 is transformed to 129.75/78.01 "intersectFM_C combiner fm1 EmptyFM = intersectFM_C4 combiner fm1 EmptyFM; 129.75/78.01 intersectFM_C combiner EmptyFM fm2 = intersectFM_C3 combiner EmptyFM fm2; 129.75/78.01 intersectFM_C combiner fm1 (Branch split_key elt2 wyx left right) = intersectFM_C2 combiner fm1 (Branch split_key elt2 wyx left right); 129.75/78.01 " 129.75/78.01 "intersectFM_C2 combiner fm1 (Branch split_key elt2 wyx left right) = intersectFM_C1 combiner fm1 split_key elt2 wyx left right (Maybe.isJust maybe_elt1) where { 129.75/78.01 elt1 = elt10 vv1; 129.75/78.01 ; 129.75/78.01 elt10 (Just elt1) = elt1; 129.75/78.01 ; 129.75/78.01 gts = splitGT fm1 split_key; 129.75/78.01 ; 129.75/78.01 intersectFM_C0 combiner fm1 split_key elt2 wyx left right True = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right); 129.75/78.01 ; 129.75/78.01 intersectFM_C1 combiner fm1 split_key elt2 wyx left right True = mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right); 129.75/78.01 intersectFM_C1 combiner fm1 split_key elt2 wyx left right False = intersectFM_C0 combiner fm1 split_key elt2 wyx left right otherwise; 129.75/78.01 ; 129.75/78.01 lts = splitLT fm1 split_key; 129.75/78.01 ; 129.75/78.01 maybe_elt1 = lookupFM fm1 split_key; 129.75/78.01 ; 129.75/78.01 vv1 = maybe_elt1; 129.75/78.01 } 129.75/78.01 ; 129.75/78.01 " 129.75/78.01 "intersectFM_C3 combiner EmptyFM fm2 = emptyFM; 129.75/78.01 intersectFM_C3 yyv yyw yyx = intersectFM_C2 yyv yyw yyx; 129.75/78.01 " 129.75/78.01 "intersectFM_C4 combiner fm1 EmptyFM = emptyFM; 129.75/78.01 intersectFM_C4 yyz yzu yzv = intersectFM_C3 yyz yzu yzv; 129.75/78.01 " 129.75/78.01 129.75/78.01 ---------------------------------------- 129.75/78.01 129.75/78.01 (10) 129.75/78.01 Obligation: 129.75/78.01 mainModule Main 129.75/78.01 module FiniteMap where { 129.75/78.01 import qualified Main; 129.75/78.01 import qualified Maybe; 129.75/78.01 import qualified Prelude; 129.75/78.01 data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; 129.75/78.01 129.75/78.01 instance (Eq a, Eq b) => Eq FiniteMap b a where { 129.75/78.01 (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; 129.75/78.01 } 129.75/78.01 addToFM :: Ord b => FiniteMap b a -> b -> a -> FiniteMap b a; 129.75/78.01 addToFM fm key elt = addToFM_C addToFM0 fm key elt; 129.75/78.01 129.75/78.01 addToFM0 old new = new; 129.75/78.01 129.75/78.01 addToFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> b -> a -> FiniteMap b a; 129.75/78.01 addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt; 129.75/78.01 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt; 129.75/78.01 129.75/78.01 addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r; 129.75/78.01 129.75/78.01 addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt); 129.75/78.01 addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise; 129.75/78.01 129.75/78.01 addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r; 129.75/78.01 addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key); 129.75/78.01 129.75/78.01 addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key); 129.75/78.01 129.75/78.01 addToFM_C4 combiner EmptyFM key elt = unitFM key elt; 129.75/78.01 addToFM_C4 yuv yuw yux yuy = addToFM_C3 yuv yuw yux yuy; 129.75/78.01 129.75/78.01 deleteMax :: Ord a => FiniteMap a b -> FiniteMap a b; 129.75/78.01 deleteMax (Branch key elt wvu fm_l EmptyFM) = fm_l; 129.75/78.01 deleteMax (Branch key elt wvv fm_l fm_r) = mkBalBranch key elt fm_l (deleteMax fm_r); 129.75/78.01 129.75/78.01 deleteMin :: Ord b => FiniteMap b a -> FiniteMap b a; 129.75/78.01 deleteMin (Branch key elt wyv EmptyFM fm_r) = fm_r; 129.75/78.01 deleteMin (Branch key elt wyw fm_l fm_r) = mkBalBranch key elt (deleteMin fm_l) fm_r; 129.75/78.01 129.75/78.01 emptyFM :: FiniteMap b a; 129.75/78.01 emptyFM = EmptyFM; 129.75/78.01 129.75/78.01 findMax :: FiniteMap a b -> (a,b); 129.75/78.01 findMax (Branch key elt vvw vvx EmptyFM) = (key,elt); 129.75/78.01 findMax (Branch key elt vvy vvz fm_r) = findMax fm_r; 129.75/78.01 129.75/78.01 findMin :: FiniteMap a b -> (a,b); 129.75/78.01 findMin (Branch key elt wyy EmptyFM wyz) = (key,elt); 129.75/78.01 findMin (Branch key elt wzu fm_l wzv) = findMin fm_l; 129.75/78.01 129.75/78.01 fmToList :: FiniteMap a b -> [(a,b)]; 129.75/78.01 fmToList fm = foldFM fmToList0 [] fm; 129.75/78.01 129.75/78.01 fmToList0 key elt rest = (key,elt) : rest; 129.75/78.01 129.75/78.01 foldFM :: (b -> a -> c -> c) -> c -> FiniteMap b a -> c; 129.75/78.01 foldFM k z EmptyFM = z; 129.75/78.01 foldFM k z (Branch key elt vyy fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; 129.75/78.01 129.75/78.01 glueBal :: Ord b => FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 129.75/78.01 glueBal EmptyFM fm2 = glueBal4 EmptyFM fm2; 129.75/78.01 glueBal fm1 EmptyFM = glueBal3 fm1 EmptyFM; 129.75/78.01 glueBal fm1 fm2 = glueBal2 fm1 fm2; 129.75/78.01 129.75/78.01 glueBal2 fm1 fm2 = glueBal1 fm1 fm2 (sizeFM fm2 > sizeFM fm1) where { 129.75/78.01 glueBal0 fm1 fm2 True = mkBalBranch mid_key1 mid_elt1 (deleteMax fm1) fm2; 129.75/78.01 glueBal1 fm1 fm2 True = mkBalBranch mid_key2 mid_elt2 fm1 (deleteMin fm2); 129.75/78.01 glueBal1 fm1 fm2 False = glueBal0 fm1 fm2 otherwise; 129.75/78.01 mid_elt1 = mid_elt10 vv2; 129.75/78.01 mid_elt10 (vwv,mid_elt1) = mid_elt1; 129.75/78.01 mid_elt2 = mid_elt20 vv3; 129.75/78.01 mid_elt20 (vwu,mid_elt2) = mid_elt2; 129.75/78.01 mid_key1 = mid_key10 vv2; 129.75/78.01 mid_key10 (mid_key1,vww) = mid_key1; 129.75/78.01 mid_key2 = mid_key20 vv3; 129.75/78.01 mid_key20 (mid_key2,vwx) = mid_key2; 129.75/78.01 vv2 = findMax fm1; 129.75/78.01 vv3 = findMin fm2; 129.75/78.01 }; 129.75/78.01 129.75/78.01 glueBal3 fm1 EmptyFM = fm1; 129.75/78.01 glueBal3 xxu xxv = glueBal2 xxu xxv; 129.75/78.01 129.75/78.01 glueBal4 EmptyFM fm2 = fm2; 129.75/78.01 glueBal4 xxx xxy = glueBal3 xxx xxy; 129.75/78.01 129.75/78.01 glueVBal :: Ord b => FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 129.75/78.01 glueVBal EmptyFM fm2 = glueVBal5 EmptyFM fm2; 129.75/78.01 glueVBal fm1 EmptyFM = glueVBal4 fm1 EmptyFM; 129.75/78.01 glueVBal (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx) = glueVBal3 (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx); 129.75/78.01 129.75/78.01 glueVBal3 (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx) = glueVBal2 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx (sIZE_RATIO * size_l < size_r) where { 129.75/78.01 glueVBal0 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx True = glueBal (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx); 129.75/78.01 glueVBal1 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx True = mkBalBranch vwz vxu vxw (glueVBal vxx (Branch vxz vyu vyv vyw vyx)); 129.75/78.01 glueVBal1 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx False = glueVBal0 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx otherwise; 129.75/78.01 glueVBal2 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx True = mkBalBranch vxz vyu (glueVBal (Branch vwz vxu vxv vxw vxx) vyw) vyx; 129.75/78.01 glueVBal2 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx False = glueVBal1 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx (sIZE_RATIO * size_r < size_l); 129.75/78.01 size_l = sizeFM (Branch vwz vxu vxv vxw vxx); 129.75/78.01 size_r = sizeFM (Branch vxz vyu vyv vyw vyx); 129.75/78.01 }; 129.75/78.01 129.75/78.01 glueVBal4 fm1 EmptyFM = fm1; 129.75/78.01 glueVBal4 xyw xyx = glueVBal3 xyw xyx; 129.75/78.01 129.75/78.01 glueVBal5 EmptyFM fm2 = fm2; 129.75/78.01 glueVBal5 xyz xzu = glueVBal4 xyz xzu; 129.75/78.01 129.75/78.01 intersectFM :: Ord a => FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 129.75/78.01 intersectFM fm1 fm2 = intersectFM_C intersectFM0 fm1 fm2; 129.75/78.01 129.75/78.01 intersectFM0 left right = right; 129.75/78.01 129.75/78.01 intersectFM_C :: Ord b => (d -> c -> a) -> FiniteMap b d -> FiniteMap b c -> FiniteMap b a; 129.75/78.01 intersectFM_C combiner fm1 EmptyFM = intersectFM_C4 combiner fm1 EmptyFM; 129.75/78.01 intersectFM_C combiner EmptyFM fm2 = intersectFM_C3 combiner EmptyFM fm2; 129.75/78.01 intersectFM_C combiner fm1 (Branch split_key elt2 wyx left right) = intersectFM_C2 combiner fm1 (Branch split_key elt2 wyx left right); 129.75/78.01 129.75/78.01 intersectFM_C2 combiner fm1 (Branch split_key elt2 wyx left right) = intersectFM_C1 combiner fm1 split_key elt2 wyx left right (Maybe.isJust maybe_elt1) where { 129.75/78.01 elt1 = elt10 vv1; 129.75/78.01 elt10 (Just elt1) = elt1; 129.75/78.01 gts = splitGT fm1 split_key; 129.75/78.01 intersectFM_C0 combiner fm1 split_key elt2 wyx left right True = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right); 129.75/78.01 intersectFM_C1 combiner fm1 split_key elt2 wyx left right True = mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right); 129.75/78.01 intersectFM_C1 combiner fm1 split_key elt2 wyx left right False = intersectFM_C0 combiner fm1 split_key elt2 wyx left right otherwise; 129.75/78.01 lts = splitLT fm1 split_key; 129.75/78.01 maybe_elt1 = lookupFM fm1 split_key; 129.75/78.01 vv1 = maybe_elt1; 129.75/78.01 }; 129.75/78.01 129.75/78.01 intersectFM_C3 combiner EmptyFM fm2 = emptyFM; 129.75/78.01 intersectFM_C3 yyv yyw yyx = intersectFM_C2 yyv yyw yyx; 129.75/78.01 129.75/78.01 intersectFM_C4 combiner fm1 EmptyFM = emptyFM; 129.75/78.01 intersectFM_C4 yyz yzu yzv = intersectFM_C3 yyz yzu yzv; 129.75/78.01 129.75/78.01 lookupFM :: Ord b => FiniteMap b a -> b -> Maybe a; 129.75/78.01 lookupFM EmptyFM key = lookupFM4 EmptyFM key; 129.75/78.01 lookupFM (Branch key elt vyz fm_l fm_r) key_to_find = lookupFM3 (Branch key elt vyz fm_l fm_r) key_to_find; 129.75/78.01 129.75/78.01 lookupFM0 key elt vyz fm_l fm_r key_to_find True = Just elt; 129.75/78.02 129.75/78.02 lookupFM1 key elt vyz fm_l fm_r key_to_find True = lookupFM fm_r key_to_find; 129.75/78.02 lookupFM1 key elt vyz fm_l fm_r key_to_find False = lookupFM0 key elt vyz fm_l fm_r key_to_find otherwise; 129.75/78.02 129.75/78.02 lookupFM2 key elt vyz fm_l fm_r key_to_find True = lookupFM fm_l key_to_find; 129.75/78.02 lookupFM2 key elt vyz fm_l fm_r key_to_find False = lookupFM1 key elt vyz fm_l fm_r key_to_find (key_to_find > key); 129.75/78.02 129.75/78.02 lookupFM3 (Branch key elt vyz fm_l fm_r) key_to_find = lookupFM2 key elt vyz fm_l fm_r key_to_find (key_to_find < key); 129.75/78.02 129.75/78.02 lookupFM4 EmptyFM key = Nothing; 129.75/78.02 lookupFM4 xzx xzy = lookupFM3 xzx xzy; 129.75/78.02 129.75/78.02 mkBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 129.75/78.02 mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R; 129.75/78.02 129.75/78.02 mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { 129.75/78.02 double_L fm_l (Branch key_r elt_r wwx (Branch key_rl elt_rl wwy fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 129.75/78.02 double_R (Branch key_l elt_l wvy fm_ll (Branch key_lr elt_lr wvz fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); 129.75/78.02 mkBalBranch0 fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr); 129.75/78.02 mkBalBranch00 fm_L fm_R wwz wxu wxv fm_rl fm_rr True = double_L fm_L fm_R; 129.75/78.02 mkBalBranch01 fm_L fm_R wwz wxu wxv fm_rl fm_rr True = single_L fm_L fm_R; 129.75/78.02 mkBalBranch01 fm_L fm_R wwz wxu wxv fm_rl fm_rr False = mkBalBranch00 fm_L fm_R wwz wxu wxv fm_rl fm_rr otherwise; 129.75/78.02 mkBalBranch02 fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr) = mkBalBranch01 fm_L fm_R wwz wxu wxv fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); 129.75/78.02 mkBalBranch1 fm_L fm_R (Branch wwu wwv www fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch wwu wwv www fm_ll fm_lr); 129.75/78.02 mkBalBranch10 fm_L fm_R wwu wwv www fm_ll fm_lr True = double_R fm_L fm_R; 129.75/78.02 mkBalBranch11 fm_L fm_R wwu wwv www fm_ll fm_lr True = single_R fm_L fm_R; 129.75/78.02 mkBalBranch11 fm_L fm_R wwu wwv www fm_ll fm_lr False = mkBalBranch10 fm_L fm_R wwu wwv www fm_ll fm_lr otherwise; 129.75/78.02 mkBalBranch12 fm_L fm_R (Branch wwu wwv www fm_ll fm_lr) = mkBalBranch11 fm_L fm_R wwu wwv www fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); 129.75/78.02 mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; 129.75/78.02 mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L; 129.75/78.02 mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise; 129.75/78.02 mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R; 129.75/78.02 mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r); 129.75/78.02 mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; 129.75/78.02 mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l); 129.75/78.02 single_L fm_l (Branch key_r elt_r wxw fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 129.75/78.02 single_R (Branch key_l elt_l wvx fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 129.75/78.02 size_l = sizeFM fm_L; 129.75/78.02 size_r = sizeFM fm_R; 129.75/78.02 }; 129.75/78.02 129.75/78.02 mkBranch :: Ord b => Int -> b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 129.75/78.02 mkBranch which key elt fm_l fm_r = let { 129.75/78.02 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 129.75/78.02 } in result where { 129.75/78.02 balance_ok = True; 129.75/78.02 left_ok = left_ok0 fm_l key fm_l; 129.75/78.02 left_ok0 fm_l key EmptyFM = True; 129.75/78.02 left_ok0 fm_l key (Branch left_key vuu vuv vuw vux) = let { 129.75/78.02 biggest_left_key = fst (findMax fm_l); 129.75/78.02 } in biggest_left_key < key; 129.75/78.02 left_size = sizeFM fm_l; 129.75/78.02 right_ok = right_ok0 fm_r key fm_r; 129.75/78.02 right_ok0 fm_r key EmptyFM = True; 129.75/78.02 right_ok0 fm_r key (Branch right_key vuy vuz vvu vvv) = let { 129.75/78.02 smallest_right_key = fst (findMin fm_r); 129.75/78.02 } in key < smallest_right_key; 129.75/78.02 right_size = sizeFM fm_r; 129.75/78.02 unbox :: Int -> Int; 129.75/78.02 unbox x = x; 129.75/78.02 }; 129.75/78.02 129.75/78.02 mkVBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 129.75/78.02 mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r; 129.75/78.02 mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM; 129.75/78.02 mkVBalBranch key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz) = mkVBalBranch3 key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz); 129.75/78.02 129.75/78.02 mkVBalBranch3 key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz) = mkVBalBranch2 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz (sIZE_RATIO * size_l < size_r) where { 129.75/78.02 mkVBalBranch0 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz True = mkBranch 13 key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz); 129.75/78.02 mkVBalBranch1 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz True = mkBalBranch vzv vzw vzy (mkVBalBranch key elt vzz (Branch wuv wuw wux wuy wuz)); 129.75/78.02 mkVBalBranch1 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz False = mkVBalBranch0 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz otherwise; 129.75/78.02 mkVBalBranch2 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz True = mkBalBranch wuv wuw (mkVBalBranch key elt (Branch vzv vzw vzx vzy vzz) wuy) wuz; 129.75/78.02 mkVBalBranch2 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz False = mkVBalBranch1 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz (sIZE_RATIO * size_r < size_l); 129.75/78.02 size_l = sizeFM (Branch vzv vzw vzx vzy vzz); 129.75/78.02 size_r = sizeFM (Branch wuv wuw wux wuy wuz); 129.75/78.02 }; 129.75/78.02 129.75/78.02 mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt; 129.75/78.02 mkVBalBranch4 yvw yvx yvy yvz = mkVBalBranch3 yvw yvx yvy yvz; 129.75/78.02 129.75/78.02 mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt; 129.75/78.02 mkVBalBranch5 ywv yww ywx ywy = mkVBalBranch4 ywv yww ywx ywy; 129.75/78.02 129.75/78.02 sIZE_RATIO :: Int; 129.75/78.02 sIZE_RATIO = 5; 129.75/78.02 129.75/78.02 sizeFM :: FiniteMap a b -> Int; 129.75/78.02 sizeFM EmptyFM = 0; 129.75/78.02 sizeFM (Branch wxx wxy size wxz wyu) = size; 129.75/78.02 129.75/78.02 splitGT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; 129.75/78.02 splitGT EmptyFM split_key = splitGT4 EmptyFM split_key; 129.75/78.02 splitGT (Branch key elt wvw fm_l fm_r) split_key = splitGT3 (Branch key elt wvw fm_l fm_r) split_key; 129.75/78.02 129.75/78.02 splitGT0 key elt wvw fm_l fm_r split_key True = fm_r; 129.75/78.02 129.75/78.02 splitGT1 key elt wvw fm_l fm_r split_key True = mkVBalBranch key elt (splitGT fm_l split_key) fm_r; 129.75/78.02 splitGT1 key elt wvw fm_l fm_r split_key False = splitGT0 key elt wvw fm_l fm_r split_key otherwise; 129.75/78.02 129.75/78.02 splitGT2 key elt wvw fm_l fm_r split_key True = splitGT fm_r split_key; 129.75/78.02 splitGT2 key elt wvw fm_l fm_r split_key False = splitGT1 key elt wvw fm_l fm_r split_key (split_key < key); 129.75/78.02 129.75/78.02 splitGT3 (Branch key elt wvw fm_l fm_r) split_key = splitGT2 key elt wvw fm_l fm_r split_key (split_key > key); 129.75/78.02 129.75/78.02 splitGT4 EmptyFM split_key = emptyFM; 129.75/78.02 splitGT4 yxv yxw = splitGT3 yxv yxw; 129.75/78.02 129.75/78.02 splitLT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; 129.75/78.02 splitLT EmptyFM split_key = splitLT4 EmptyFM split_key; 129.75/78.02 splitLT (Branch key elt zz fm_l fm_r) split_key = splitLT3 (Branch key elt zz fm_l fm_r) split_key; 129.75/78.02 129.75/78.02 splitLT0 key elt zz fm_l fm_r split_key True = fm_l; 129.75/78.02 129.75/78.02 splitLT1 key elt zz fm_l fm_r split_key True = mkVBalBranch key elt fm_l (splitLT fm_r split_key); 129.75/78.02 splitLT1 key elt zz fm_l fm_r split_key False = splitLT0 key elt zz fm_l fm_r split_key otherwise; 129.75/78.02 129.75/78.02 splitLT2 key elt zz fm_l fm_r split_key True = splitLT fm_l split_key; 129.75/78.02 splitLT2 key elt zz fm_l fm_r split_key False = splitLT1 key elt zz fm_l fm_r split_key (split_key > key); 129.75/78.02 129.75/78.02 splitLT3 (Branch key elt zz fm_l fm_r) split_key = splitLT2 key elt zz fm_l fm_r split_key (split_key < key); 129.75/78.02 129.75/78.02 splitLT4 EmptyFM split_key = emptyFM; 129.75/78.02 splitLT4 xwx xwy = splitLT3 xwx xwy; 129.75/78.02 129.75/78.02 unitFM :: a -> b -> FiniteMap a b; 129.75/78.02 unitFM key elt = Branch key elt 1 emptyFM emptyFM; 129.75/78.02 129.75/78.02 } 129.75/78.02 module Maybe where { 129.75/78.02 import qualified FiniteMap; 129.75/78.02 import qualified Main; 129.75/78.02 import qualified Prelude; 129.75/78.02 isJust :: Maybe a -> Bool; 129.75/78.02 isJust Nothing = False; 129.75/78.02 isJust wzw = True; 129.75/78.02 129.75/78.02 } 129.75/78.02 module Main where { 129.75/78.02 import qualified FiniteMap; 129.75/78.02 import qualified Maybe; 129.75/78.02 import qualified Prelude; 129.75/78.02 } 129.75/78.02 129.75/78.02 ---------------------------------------- 129.75/78.02 129.75/78.02 (11) LetRed (EQUIVALENT) 129.75/78.02 Let/Where Reductions: 129.75/78.02 The bindings of the following Let/Where expression 129.75/78.02 "gcd' (abs x) (abs y) where { 129.75/78.02 gcd' x wzx = gcd'2 x wzx; 129.75/78.02 gcd' x y = gcd'0 x y; 129.75/78.02 ; 129.75/78.02 gcd'0 x y = gcd' y (x `rem` y); 129.75/78.02 ; 129.75/78.02 gcd'1 True x wzx = x; 129.75/78.02 gcd'1 wzy wzz xuu = gcd'0 wzz xuu; 129.75/78.02 ; 129.75/78.02 gcd'2 x wzx = gcd'1 (wzx == 0) x wzx; 129.75/78.02 gcd'2 xuv xuw = gcd'0 xuv xuw; 129.75/78.02 } 129.75/78.02 " 129.75/78.02 are unpacked to the following functions on top level 129.75/78.02 "gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` y); 129.75/78.02 " 129.75/78.02 "gcd0Gcd'2 x wzx = gcd0Gcd'1 (wzx == 0) x wzx; 129.75/78.02 gcd0Gcd'2 xuv xuw = gcd0Gcd'0 xuv xuw; 129.75/78.02 " 129.75/78.02 "gcd0Gcd'1 True x wzx = x; 129.75/78.02 gcd0Gcd'1 wzy wzz xuu = gcd0Gcd'0 wzz xuu; 129.75/78.02 " 129.75/78.02 "gcd0Gcd' x wzx = gcd0Gcd'2 x wzx; 129.75/78.02 gcd0Gcd' x y = gcd0Gcd'0 x y; 129.75/78.02 " 129.75/78.02 The bindings of the following Let/Where expression 129.75/78.02 "reduce1 x y (y == 0) where { 129.75/78.02 d = gcd x y; 129.75/78.02 ; 129.75/78.02 reduce0 x y True = x `quot` d :% (y `quot` d); 129.75/78.02 ; 129.75/78.02 reduce1 x y True = error []; 129.75/78.02 reduce1 x y False = reduce0 x y otherwise; 129.75/78.02 } 129.75/78.02 " 129.75/78.02 are unpacked to the following functions on top level 129.75/78.02 "reduce2D yzw yzx = gcd yzw yzx; 129.75/78.02 " 129.75/78.02 "reduce2Reduce0 yzw yzx x y True = x `quot` reduce2D yzw yzx :% (y `quot` reduce2D yzw yzx); 129.75/78.02 " 129.75/78.02 "reduce2Reduce1 yzw yzx x y True = error []; 129.75/78.02 reduce2Reduce1 yzw yzx x y False = reduce2Reduce0 yzw yzx x y otherwise; 129.75/78.02 " 129.75/78.02 The bindings of the following Let/Where expression 129.75/78.02 "glueBal1 fm1 fm2 (sizeFM fm2 > sizeFM fm1) where { 129.75/78.02 glueBal0 fm1 fm2 True = mkBalBranch mid_key1 mid_elt1 (deleteMax fm1) fm2; 129.75/78.02 ; 129.75/78.02 glueBal1 fm1 fm2 True = mkBalBranch mid_key2 mid_elt2 fm1 (deleteMin fm2); 129.75/78.02 glueBal1 fm1 fm2 False = glueBal0 fm1 fm2 otherwise; 129.75/78.02 ; 129.75/78.02 mid_elt1 = mid_elt10 vv2; 129.75/78.02 ; 129.75/78.02 mid_elt10 (vwv,mid_elt1) = mid_elt1; 129.75/78.02 ; 129.75/78.02 mid_elt2 = mid_elt20 vv3; 129.75/78.02 ; 129.75/78.02 mid_elt20 (vwu,mid_elt2) = mid_elt2; 129.75/78.02 ; 129.75/78.02 mid_key1 = mid_key10 vv2; 129.75/78.02 ; 129.75/78.02 mid_key10 (mid_key1,vww) = mid_key1; 129.75/78.02 ; 129.75/78.02 mid_key2 = mid_key20 vv3; 129.75/78.02 ; 129.75/78.02 mid_key20 (mid_key2,vwx) = mid_key2; 129.75/78.02 ; 129.75/78.02 vv2 = findMax fm1; 129.75/78.02 ; 129.75/78.02 vv3 = findMin fm2; 129.75/78.02 } 129.75/78.02 " 129.75/78.02 are unpacked to the following functions on top level 129.75/78.02 "glueBal2Vv3 yzy yzz = findMin yzy; 129.75/78.02 " 129.75/78.02 "glueBal2Mid_key2 yzy yzz = glueBal2Mid_key20 yzy yzz (glueBal2Vv3 yzy yzz); 129.75/78.02 " 129.75/78.02 "glueBal2Mid_elt10 yzy yzz (vwv,mid_elt1) = mid_elt1; 129.75/78.02 " 129.75/78.02 "glueBal2Mid_key10 yzy yzz (mid_key1,vww) = mid_key1; 129.75/78.02 " 129.75/78.02 "glueBal2Vv2 yzy yzz = findMax yzz; 129.75/78.02 " 129.75/78.02 "glueBal2Mid_elt2 yzy yzz = glueBal2Mid_elt20 yzy yzz (glueBal2Vv3 yzy yzz); 129.75/78.02 " 129.75/78.02 "glueBal2Mid_elt1 yzy yzz = glueBal2Mid_elt10 yzy yzz (glueBal2Vv2 yzy yzz); 129.75/78.02 " 129.75/78.02 "glueBal2Mid_elt20 yzy yzz (vwu,mid_elt2) = mid_elt2; 129.75/78.02 " 129.75/78.02 "glueBal2GlueBal0 yzy yzz fm1 fm2 True = mkBalBranch (glueBal2Mid_key1 yzy yzz) (glueBal2Mid_elt1 yzy yzz) (deleteMax fm1) fm2; 129.75/78.02 " 129.75/78.02 "glueBal2GlueBal1 yzy yzz fm1 fm2 True = mkBalBranch (glueBal2Mid_key2 yzy yzz) (glueBal2Mid_elt2 yzy yzz) fm1 (deleteMin fm2); 129.75/78.02 glueBal2GlueBal1 yzy yzz fm1 fm2 False = glueBal2GlueBal0 yzy yzz fm1 fm2 otherwise; 129.75/78.02 " 129.75/78.02 "glueBal2Mid_key20 yzy yzz (mid_key2,vwx) = mid_key2; 129.75/78.02 " 129.75/78.02 "glueBal2Mid_key1 yzy yzz = glueBal2Mid_key10 yzy yzz (glueBal2Vv2 yzy yzz); 129.75/78.02 " 129.75/78.02 The bindings of the following Let/Where expression 129.75/78.02 "mkVBalBranch2 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz (sIZE_RATIO * size_l < size_r) where { 129.75/78.02 mkVBalBranch0 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz True = mkBranch 13 key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz); 129.75/78.02 ; 129.75/78.02 mkVBalBranch1 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz True = mkBalBranch vzv vzw vzy (mkVBalBranch key elt vzz (Branch wuv wuw wux wuy wuz)); 129.75/78.02 mkVBalBranch1 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz False = mkVBalBranch0 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz otherwise; 129.75/78.02 ; 129.75/78.02 mkVBalBranch2 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz True = mkBalBranch wuv wuw (mkVBalBranch key elt (Branch vzv vzw vzx vzy vzz) wuy) wuz; 129.75/78.02 mkVBalBranch2 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz False = mkVBalBranch1 key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz (sIZE_RATIO * size_r < size_l); 129.75/78.02 ; 129.75/78.02 size_l = sizeFM (Branch vzv vzw vzx vzy vzz); 129.75/78.02 ; 129.75/78.02 size_r = sizeFM (Branch wuv wuw wux wuy wuz); 129.75/78.02 } 129.75/78.02 " 129.75/78.02 are unpacked to the following functions on top level 129.75/78.02 "mkVBalBranch3MkVBalBranch1 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz True = mkBalBranch vzv vzw vzy (mkVBalBranch key elt vzz (Branch wuv wuw wux wuy wuz)); 129.75/78.02 mkVBalBranch3MkVBalBranch1 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz False = mkVBalBranch3MkVBalBranch0 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz otherwise; 129.75/78.02 " 129.75/78.02 "mkVBalBranch3MkVBalBranch2 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz True = mkBalBranch wuv wuw (mkVBalBranch key elt (Branch vzv vzw vzx vzy vzz) wuy) wuz; 129.75/78.02 mkVBalBranch3MkVBalBranch2 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz False = mkVBalBranch3MkVBalBranch1 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz (sIZE_RATIO * mkVBalBranch3Size_r zuu zuv zuw zux zuy zuz zvu zvv zvw zvx < mkVBalBranch3Size_l zuu zuv zuw zux zuy zuz zvu zvv zvw zvx); 129.75/78.02 " 129.75/78.02 "mkVBalBranch3MkVBalBranch0 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz True = mkBranch 13 key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz); 129.75/78.02 " 129.75/78.02 "mkVBalBranch3Size_l zuu zuv zuw zux zuy zuz zvu zvv zvw zvx = sizeFM (Branch zuu zuv zuw zux zuy); 129.75/78.02 " 129.75/78.02 "mkVBalBranch3Size_r zuu zuv zuw zux zuy zuz zvu zvv zvw zvx = sizeFM (Branch zuz zvu zvv zvw zvx); 129.75/78.02 " 129.75/78.02 The bindings of the following Let/Where expression 129.75/78.02 "mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { 129.75/78.02 double_L fm_l (Branch key_r elt_r wwx (Branch key_rl elt_rl wwy fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 129.75/78.02 ; 129.75/78.02 double_R (Branch key_l elt_l wvy fm_ll (Branch key_lr elt_lr wvz fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); 129.75/78.02 ; 129.75/78.02 mkBalBranch0 fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr); 129.75/78.02 ; 129.75/78.02 mkBalBranch00 fm_L fm_R wwz wxu wxv fm_rl fm_rr True = double_L fm_L fm_R; 129.75/78.02 ; 129.75/78.02 mkBalBranch01 fm_L fm_R wwz wxu wxv fm_rl fm_rr True = single_L fm_L fm_R; 129.75/78.02 mkBalBranch01 fm_L fm_R wwz wxu wxv fm_rl fm_rr False = mkBalBranch00 fm_L fm_R wwz wxu wxv fm_rl fm_rr otherwise; 129.75/78.02 ; 129.75/78.02 mkBalBranch02 fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr) = mkBalBranch01 fm_L fm_R wwz wxu wxv fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); 129.75/78.02 ; 129.75/78.02 mkBalBranch1 fm_L fm_R (Branch wwu wwv www fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch wwu wwv www fm_ll fm_lr); 129.75/78.02 ; 129.75/78.02 mkBalBranch10 fm_L fm_R wwu wwv www fm_ll fm_lr True = double_R fm_L fm_R; 129.75/78.02 ; 129.75/78.02 mkBalBranch11 fm_L fm_R wwu wwv www fm_ll fm_lr True = single_R fm_L fm_R; 129.75/78.02 mkBalBranch11 fm_L fm_R wwu wwv www fm_ll fm_lr False = mkBalBranch10 fm_L fm_R wwu wwv www fm_ll fm_lr otherwise; 129.75/78.02 ; 129.75/78.02 mkBalBranch12 fm_L fm_R (Branch wwu wwv www fm_ll fm_lr) = mkBalBranch11 fm_L fm_R wwu wwv www fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); 129.75/78.02 ; 129.75/78.02 mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; 129.75/78.02 ; 129.75/78.02 mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L; 129.75/78.02 mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise; 129.75/78.02 ; 129.75/78.02 mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R; 129.75/78.02 mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r); 129.75/78.02 ; 129.75/78.02 mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; 129.75/78.02 mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l); 129.75/78.02 ; 129.75/78.02 single_L fm_l (Branch key_r elt_r wxw fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 129.75/78.02 ; 129.75/78.02 single_R (Branch key_l elt_l wvx fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 130.15/78.11 ; 130.15/78.11 size_l = sizeFM fm_L; 130.15/78.11 ; 130.15/78.11 size_r = sizeFM fm_R; 130.15/78.11 } 130.15/78.11 " 130.15/78.11 are unpacked to the following functions on top level 130.15/78.11 "mkBalBranch6MkBalBranch4 zvy zvz zwu zwv key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 zvy zvz zwu zwv fm_L fm_R fm_R; 130.15/78.11 mkBalBranch6MkBalBranch4 zvy zvz zwu zwv key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 zvy zvz zwu zwv key elt fm_L fm_R (mkBalBranch6Size_l zvy zvz zwu zwv > sIZE_RATIO * mkBalBranch6Size_r zvy zvz zwu zwv); 130.15/78.11 " 130.15/78.11 "mkBalBranch6Size_r zvy zvz zwu zwv = sizeFM zvy; 130.15/78.11 " 130.15/78.11 "mkBalBranch6MkBalBranch01 zvy zvz zwu zwv fm_L fm_R wwz wxu wxv fm_rl fm_rr True = mkBalBranch6Single_L zvy zvz zwu zwv fm_L fm_R; 130.15/78.11 mkBalBranch6MkBalBranch01 zvy zvz zwu zwv fm_L fm_R wwz wxu wxv fm_rl fm_rr False = mkBalBranch6MkBalBranch00 zvy zvz zwu zwv fm_L fm_R wwz wxu wxv fm_rl fm_rr otherwise; 130.15/78.11 " 130.15/78.11 "mkBalBranch6MkBalBranch12 zvy zvz zwu zwv fm_L fm_R (Branch wwu wwv www fm_ll fm_lr) = mkBalBranch6MkBalBranch11 zvy zvz zwu zwv fm_L fm_R wwu wwv www fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); 130.15/78.11 " 130.15/78.11 "mkBalBranch6Single_L zvy zvz zwu zwv fm_l (Branch key_r elt_r wxw fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 zvz zwu fm_l fm_rl) fm_rr; 130.15/78.11 " 130.15/78.11 "mkBalBranch6MkBalBranch3 zvy zvz zwu zwv key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 zvy zvz zwu zwv fm_L fm_R fm_L; 130.15/78.11 mkBalBranch6MkBalBranch3 zvy zvz zwu zwv key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 zvy zvz zwu zwv key elt fm_L fm_R otherwise; 130.15/78.11 " 130.15/78.11 "mkBalBranch6MkBalBranch2 zvy zvz zwu zwv key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; 130.15/78.11 " 130.15/78.11 "mkBalBranch6MkBalBranch00 zvy zvz zwu zwv fm_L fm_R wwz wxu wxv fm_rl fm_rr True = mkBalBranch6Double_L zvy zvz zwu zwv fm_L fm_R; 130.15/78.11 " 130.15/78.11 "mkBalBranch6MkBalBranch02 zvy zvz zwu zwv fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr) = mkBalBranch6MkBalBranch01 zvy zvz zwu zwv fm_L fm_R wwz wxu wxv fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); 130.15/78.11 " 130.15/78.11 "mkBalBranch6MkBalBranch5 zvy zvz zwu zwv key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; 130.15/78.11 mkBalBranch6MkBalBranch5 zvy zvz zwu zwv key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 zvy zvz zwu zwv key elt fm_L fm_R (mkBalBranch6Size_r zvy zvz zwu zwv > sIZE_RATIO * mkBalBranch6Size_l zvy zvz zwu zwv); 130.15/78.11 " 130.15/78.11 "mkBalBranch6MkBalBranch11 zvy zvz zwu zwv fm_L fm_R wwu wwv www fm_ll fm_lr True = mkBalBranch6Single_R zvy zvz zwu zwv fm_L fm_R; 130.15/78.11 mkBalBranch6MkBalBranch11 zvy zvz zwu zwv fm_L fm_R wwu wwv www fm_ll fm_lr False = mkBalBranch6MkBalBranch10 zvy zvz zwu zwv fm_L fm_R wwu wwv www fm_ll fm_lr otherwise; 130.15/78.11 " 130.15/78.11 "mkBalBranch6MkBalBranch10 zvy zvz zwu zwv fm_L fm_R wwu wwv www fm_ll fm_lr True = mkBalBranch6Double_R zvy zvz zwu zwv fm_L fm_R; 130.15/78.11 " 130.15/78.11 "mkBalBranch6MkBalBranch0 zvy zvz zwu zwv fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr) = mkBalBranch6MkBalBranch02 zvy zvz zwu zwv fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr); 130.15/78.11 " 130.15/78.11 "mkBalBranch6MkBalBranch1 zvy zvz zwu zwv fm_L fm_R (Branch wwu wwv www fm_ll fm_lr) = mkBalBranch6MkBalBranch12 zvy zvz zwu zwv fm_L fm_R (Branch wwu wwv www fm_ll fm_lr); 130.15/78.11 " 130.15/78.11 "mkBalBranch6Size_l zvy zvz zwu zwv = sizeFM zwv; 130.15/78.11 " 130.15/78.11 "mkBalBranch6Double_R zvy zvz zwu zwv (Branch key_l elt_l wvy fm_ll (Branch key_lr elt_lr wvz fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 zvz zwu fm_lrr fm_r); 130.15/78.11 " 130.15/78.11 "mkBalBranch6Double_L zvy zvz zwu zwv fm_l (Branch key_r elt_r wwx (Branch key_rl elt_rl wwy fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 zvz zwu fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 130.15/78.11 " 130.15/78.11 "mkBalBranch6Single_R zvy zvz zwu zwv (Branch key_l elt_l wvx fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 zvz zwu fm_lr fm_r); 130.15/78.11 " 130.15/78.11 The bindings of the following Let/Where expression 130.15/78.11 "intersectFM_C1 combiner fm1 split_key elt2 wyx left right (Maybe.isJust maybe_elt1) where { 130.15/78.11 elt1 = elt10 vv1; 130.15/78.11 ; 130.15/78.11 elt10 (Just elt1) = elt1; 130.15/78.11 ; 130.15/78.11 gts = splitGT fm1 split_key; 130.15/78.11 ; 130.15/78.11 intersectFM_C0 combiner fm1 split_key elt2 wyx left right True = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right); 130.15/78.11 ; 130.15/78.11 intersectFM_C1 combiner fm1 split_key elt2 wyx left right True = mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right); 130.15/78.11 intersectFM_C1 combiner fm1 split_key elt2 wyx left right False = intersectFM_C0 combiner fm1 split_key elt2 wyx left right otherwise; 130.15/78.11 ; 130.15/78.11 lts = splitLT fm1 split_key; 130.15/78.11 ; 130.15/78.11 maybe_elt1 = lookupFM fm1 split_key; 130.15/78.11 ; 130.15/78.11 vv1 = maybe_elt1; 130.15/78.11 } 130.15/78.11 " 130.15/78.11 are unpacked to the following functions on top level 130.15/78.11 "intersectFM_C2Elt10 zww zwx (Just elt1) = elt1; 130.15/78.11 " 130.15/78.11 "intersectFM_C2Elt1 zww zwx = intersectFM_C2Elt10 zww zwx (intersectFM_C2Vv1 zww zwx); 130.15/78.11 " 130.15/78.11 "intersectFM_C2Maybe_elt1 zww zwx = lookupFM zww zwx; 130.15/78.11 " 130.15/78.11 "intersectFM_C2Lts zww zwx = splitLT zww zwx; 130.15/78.11 " 130.15/78.11 "intersectFM_C2Vv1 zww zwx = intersectFM_C2Maybe_elt1 zww zwx; 130.15/78.11 " 130.15/78.11 "intersectFM_C2IntersectFM_C1 zww zwx combiner fm1 split_key elt2 wyx left right True = mkVBalBranch split_key (combiner (intersectFM_C2Elt1 zww zwx) elt2) (intersectFM_C combiner (intersectFM_C2Lts zww zwx) left) (intersectFM_C combiner (intersectFM_C2Gts zww zwx) right); 130.15/78.11 intersectFM_C2IntersectFM_C1 zww zwx combiner fm1 split_key elt2 wyx left right False = intersectFM_C2IntersectFM_C0 zww zwx combiner fm1 split_key elt2 wyx left right otherwise; 130.15/78.11 " 130.15/78.11 "intersectFM_C2IntersectFM_C0 zww zwx combiner fm1 split_key elt2 wyx left right True = glueVBal (intersectFM_C combiner (intersectFM_C2Lts zww zwx) left) (intersectFM_C combiner (intersectFM_C2Gts zww zwx) right); 130.15/78.11 " 130.15/78.11 "intersectFM_C2Gts zww zwx = splitGT zww zwx; 130.15/78.11 " 130.15/78.11 The bindings of the following Let/Where expression 130.15/78.11 "let { 130.15/78.11 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 130.15/78.11 } in result where { 130.15/78.11 balance_ok = True; 130.15/78.11 ; 130.15/78.11 left_ok = left_ok0 fm_l key fm_l; 130.15/78.11 ; 130.15/78.11 left_ok0 fm_l key EmptyFM = True; 130.15/78.11 left_ok0 fm_l key (Branch left_key vuu vuv vuw vux) = let { 130.15/78.11 biggest_left_key = fst (findMax fm_l); 130.15/78.11 } in biggest_left_key < key; 130.15/78.11 ; 130.15/78.11 left_size = sizeFM fm_l; 130.15/78.11 ; 130.15/78.11 right_ok = right_ok0 fm_r key fm_r; 130.15/78.11 ; 130.15/78.11 right_ok0 fm_r key EmptyFM = True; 130.15/78.11 right_ok0 fm_r key (Branch right_key vuy vuz vvu vvv) = let { 130.15/78.11 smallest_right_key = fst (findMin fm_r); 130.15/78.11 } in key < smallest_right_key; 130.15/78.11 ; 130.15/78.11 right_size = sizeFM fm_r; 130.15/78.11 ; 130.15/78.11 unbox x = x; 130.15/78.11 } 130.15/78.11 " 130.15/78.11 are unpacked to the following functions on top level 130.15/78.11 "mkBranchLeft_size zwy zwz zxu = sizeFM zwy; 130.15/78.11 " 130.15/78.11 "mkBranchRight_ok zwy zwz zxu = mkBranchRight_ok0 zwy zwz zxu zwz zxu zwz; 130.15/78.11 " 130.15/78.11 "mkBranchLeft_ok0 zwy zwz zxu fm_l key EmptyFM = True; 130.15/78.11 mkBranchLeft_ok0 zwy zwz zxu fm_l key (Branch left_key vuu vuv vuw vux) = mkBranchLeft_ok0Biggest_left_key fm_l < key; 130.15/78.11 " 130.15/78.11 "mkBranchLeft_ok zwy zwz zxu = mkBranchLeft_ok0 zwy zwz zxu zwy zxu zwy; 130.15/78.11 " 130.15/78.11 "mkBranchBalance_ok zwy zwz zxu = True; 130.15/78.11 " 130.15/78.11 "mkBranchUnbox zwy zwz zxu x = x; 130.15/78.11 " 130.15/78.11 "mkBranchRight_size zwy zwz zxu = sizeFM zwz; 130.15/78.11 " 130.15/78.11 "mkBranchRight_ok0 zwy zwz zxu fm_r key EmptyFM = True; 130.15/78.11 mkBranchRight_ok0 zwy zwz zxu fm_r key (Branch right_key vuy vuz vvu vvv) = key < mkBranchRight_ok0Smallest_right_key fm_r; 130.15/78.11 " 130.15/78.11 The bindings of the following Let/Where expression 130.15/78.11 "let { 130.15/78.11 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 130.15/78.11 } in result" 130.15/78.11 are unpacked to the following functions on top level 130.15/78.11 "mkBranchResult zxv zxw zxx zxy = Branch zxv zxw (mkBranchUnbox zxx zxy zxv (1 + mkBranchLeft_size zxx zxy zxv + mkBranchRight_size zxx zxy zxv)) zxx zxy; 130.15/78.11 " 130.15/78.11 The bindings of the following Let/Where expression 130.15/78.11 "glueVBal2 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx (sIZE_RATIO * size_l < size_r) where { 130.15/78.11 glueVBal0 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx True = glueBal (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx); 130.15/78.11 ; 130.15/78.11 glueVBal1 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx True = mkBalBranch vwz vxu vxw (glueVBal vxx (Branch vxz vyu vyv vyw vyx)); 130.15/78.11 glueVBal1 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx False = glueVBal0 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx otherwise; 130.15/78.11 ; 130.15/78.11 glueVBal2 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx True = mkBalBranch vxz vyu (glueVBal (Branch vwz vxu vxv vxw vxx) vyw) vyx; 130.15/78.11 glueVBal2 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx False = glueVBal1 vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx (sIZE_RATIO * size_r < size_l); 130.15/78.11 ; 130.15/78.11 size_l = sizeFM (Branch vwz vxu vxv vxw vxx); 130.15/78.11 ; 130.15/78.11 size_r = sizeFM (Branch vxz vyu vyv vyw vyx); 130.15/78.11 } 130.15/78.11 " 130.15/78.11 are unpacked to the following functions on top level 130.15/78.11 "glueVBal3GlueVBal0 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx True = glueBal (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx); 130.15/78.11 " 130.15/78.11 "glueVBal3GlueVBal2 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx True = mkBalBranch vxz vyu (glueVBal (Branch vwz vxu vxv vxw vxx) vyw) vyx; 130.15/78.11 glueVBal3GlueVBal2 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx False = glueVBal3GlueVBal1 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx (sIZE_RATIO * glueVBal3Size_r zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw < glueVBal3Size_l zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw); 130.15/78.11 " 130.15/78.11 "glueVBal3Size_r zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw = sizeFM (Branch zxz zyu zyv zyw zyx); 130.15/78.11 " 130.15/78.11 "glueVBal3GlueVBal1 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx True = mkBalBranch vwz vxu vxw (glueVBal vxx (Branch vxz vyu vyv vyw vyx)); 130.15/78.11 glueVBal3GlueVBal1 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx False = glueVBal3GlueVBal0 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx otherwise; 130.15/78.11 " 130.15/78.11 "glueVBal3Size_l zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw = sizeFM (Branch zyy zyz zzu zzv zzw); 130.15/78.11 " 130.15/78.11 The bindings of the following Let/Where expression 130.15/78.11 "let { 130.15/78.11 biggest_left_key = fst (findMax fm_l); 130.15/78.11 } in biggest_left_key < key" 130.15/78.11 are unpacked to the following functions on top level 130.15/78.11 "mkBranchLeft_ok0Biggest_left_key zzx = fst (findMax zzx); 130.15/78.11 " 130.15/78.11 The bindings of the following Let/Where expression 130.15/78.11 "let { 130.15/78.11 smallest_right_key = fst (findMin fm_r); 130.15/78.11 } in key < smallest_right_key" 130.15/78.11 are unpacked to the following functions on top level 130.15/78.11 "mkBranchRight_ok0Smallest_right_key zzy = fst (findMin zzy); 130.15/78.11 " 130.15/78.11 130.15/78.11 ---------------------------------------- 130.15/78.11 130.15/78.11 (12) 130.15/78.11 Obligation: 130.15/78.11 mainModule Main 130.15/78.11 module FiniteMap where { 130.15/78.11 import qualified Main; 130.15/78.11 import qualified Maybe; 130.15/78.11 import qualified Prelude; 130.15/78.11 data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; 130.15/78.11 130.15/78.11 instance (Eq a, Eq b) => Eq FiniteMap b a where { 130.15/78.11 (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; 130.15/78.11 } 130.15/78.11 addToFM :: Ord b => FiniteMap b a -> b -> a -> FiniteMap b a; 130.15/78.11 addToFM fm key elt = addToFM_C addToFM0 fm key elt; 130.15/78.11 130.15/78.11 addToFM0 old new = new; 130.15/78.11 130.15/78.11 addToFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> b -> a -> FiniteMap b a; 130.15/78.11 addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt; 130.15/78.11 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt; 130.15/78.11 130.15/78.11 addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r; 130.15/78.11 130.15/78.11 addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt); 130.15/78.11 addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise; 130.15/78.11 130.15/78.11 addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r; 130.15/78.11 addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key); 130.15/78.11 130.15/78.11 addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key); 130.15/78.11 130.15/78.11 addToFM_C4 combiner EmptyFM key elt = unitFM key elt; 130.15/78.11 addToFM_C4 yuv yuw yux yuy = addToFM_C3 yuv yuw yux yuy; 130.15/78.11 130.15/78.11 deleteMax :: Ord a => FiniteMap a b -> FiniteMap a b; 130.15/78.11 deleteMax (Branch key elt wvu fm_l EmptyFM) = fm_l; 130.15/78.11 deleteMax (Branch key elt wvv fm_l fm_r) = mkBalBranch key elt fm_l (deleteMax fm_r); 130.15/78.11 130.15/78.11 deleteMin :: Ord a => FiniteMap a b -> FiniteMap a b; 130.15/78.11 deleteMin (Branch key elt wyv EmptyFM fm_r) = fm_r; 130.15/78.11 deleteMin (Branch key elt wyw fm_l fm_r) = mkBalBranch key elt (deleteMin fm_l) fm_r; 130.15/78.11 130.15/78.11 emptyFM :: FiniteMap b a; 130.15/78.11 emptyFM = EmptyFM; 130.15/78.11 130.15/78.11 findMax :: FiniteMap a b -> (a,b); 130.15/78.11 findMax (Branch key elt vvw vvx EmptyFM) = (key,elt); 130.15/78.11 findMax (Branch key elt vvy vvz fm_r) = findMax fm_r; 130.15/78.11 130.15/78.11 findMin :: FiniteMap b a -> (b,a); 130.15/78.11 findMin (Branch key elt wyy EmptyFM wyz) = (key,elt); 130.15/78.11 findMin (Branch key elt wzu fm_l wzv) = findMin fm_l; 130.15/78.11 130.15/78.11 fmToList :: FiniteMap b a -> [(b,a)]; 130.15/78.11 fmToList fm = foldFM fmToList0 [] fm; 130.15/78.11 130.15/78.11 fmToList0 key elt rest = (key,elt) : rest; 130.15/78.11 130.15/78.11 foldFM :: (c -> b -> a -> a) -> a -> FiniteMap c b -> a; 130.15/78.11 foldFM k z EmptyFM = z; 130.15/78.11 foldFM k z (Branch key elt vyy fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; 130.15/78.11 130.15/78.11 glueBal :: Ord a => FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 130.15/78.11 glueBal EmptyFM fm2 = glueBal4 EmptyFM fm2; 130.15/78.11 glueBal fm1 EmptyFM = glueBal3 fm1 EmptyFM; 130.15/78.11 glueBal fm1 fm2 = glueBal2 fm1 fm2; 130.15/78.11 130.15/78.11 glueBal2 fm1 fm2 = glueBal2GlueBal1 fm2 fm1 fm1 fm2 (sizeFM fm2 > sizeFM fm1); 130.15/78.11 130.15/78.11 glueBal2GlueBal0 yzy yzz fm1 fm2 True = mkBalBranch (glueBal2Mid_key1 yzy yzz) (glueBal2Mid_elt1 yzy yzz) (deleteMax fm1) fm2; 130.15/78.11 130.15/78.11 glueBal2GlueBal1 yzy yzz fm1 fm2 True = mkBalBranch (glueBal2Mid_key2 yzy yzz) (glueBal2Mid_elt2 yzy yzz) fm1 (deleteMin fm2); 130.15/78.11 glueBal2GlueBal1 yzy yzz fm1 fm2 False = glueBal2GlueBal0 yzy yzz fm1 fm2 otherwise; 130.15/78.11 130.15/78.11 glueBal2Mid_elt1 yzy yzz = glueBal2Mid_elt10 yzy yzz (glueBal2Vv2 yzy yzz); 130.15/78.11 130.15/78.11 glueBal2Mid_elt10 yzy yzz (vwv,mid_elt1) = mid_elt1; 130.15/78.11 130.15/78.11 glueBal2Mid_elt2 yzy yzz = glueBal2Mid_elt20 yzy yzz (glueBal2Vv3 yzy yzz); 130.15/78.11 130.15/78.11 glueBal2Mid_elt20 yzy yzz (vwu,mid_elt2) = mid_elt2; 130.15/78.11 130.15/78.11 glueBal2Mid_key1 yzy yzz = glueBal2Mid_key10 yzy yzz (glueBal2Vv2 yzy yzz); 130.15/78.11 130.15/78.11 glueBal2Mid_key10 yzy yzz (mid_key1,vww) = mid_key1; 130.15/78.11 130.15/78.11 glueBal2Mid_key2 yzy yzz = glueBal2Mid_key20 yzy yzz (glueBal2Vv3 yzy yzz); 130.15/78.11 130.15/78.11 glueBal2Mid_key20 yzy yzz (mid_key2,vwx) = mid_key2; 130.15/78.11 130.15/78.11 glueBal2Vv2 yzy yzz = findMax yzz; 130.15/78.11 130.15/78.11 glueBal2Vv3 yzy yzz = findMin yzy; 130.15/78.11 130.15/78.11 glueBal3 fm1 EmptyFM = fm1; 130.15/78.11 glueBal3 xxu xxv = glueBal2 xxu xxv; 130.15/78.11 130.15/78.11 glueBal4 EmptyFM fm2 = fm2; 130.15/78.11 glueBal4 xxx xxy = glueBal3 xxx xxy; 130.15/78.11 130.15/78.11 glueVBal :: Ord b => FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 130.15/78.11 glueVBal EmptyFM fm2 = glueVBal5 EmptyFM fm2; 130.15/78.11 glueVBal fm1 EmptyFM = glueVBal4 fm1 EmptyFM; 130.15/78.11 glueVBal (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx) = glueVBal3 (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx); 130.15/78.11 130.15/78.11 glueVBal3 (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx) = glueVBal3GlueVBal2 vxz vyu vyv vyw vyx vwz vxu vxv vxw vxx vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx (sIZE_RATIO * glueVBal3Size_l vxz vyu vyv vyw vyx vwz vxu vxv vxw vxx < glueVBal3Size_r vxz vyu vyv vyw vyx vwz vxu vxv vxw vxx); 130.15/78.11 130.15/78.11 glueVBal3GlueVBal0 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx True = glueBal (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx); 130.15/78.11 130.15/78.11 glueVBal3GlueVBal1 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx True = mkBalBranch vwz vxu vxw (glueVBal vxx (Branch vxz vyu vyv vyw vyx)); 130.15/78.11 glueVBal3GlueVBal1 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx False = glueVBal3GlueVBal0 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx otherwise; 130.15/78.11 130.15/78.11 glueVBal3GlueVBal2 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx True = mkBalBranch vxz vyu (glueVBal (Branch vwz vxu vxv vxw vxx) vyw) vyx; 130.15/78.11 glueVBal3GlueVBal2 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx False = glueVBal3GlueVBal1 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx (sIZE_RATIO * glueVBal3Size_r zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw < glueVBal3Size_l zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw); 130.15/78.11 130.15/78.11 glueVBal3Size_l zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw = sizeFM (Branch zyy zyz zzu zzv zzw); 130.15/78.11 130.15/78.11 glueVBal3Size_r zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw = sizeFM (Branch zxz zyu zyv zyw zyx); 130.15/78.11 130.15/78.11 glueVBal4 fm1 EmptyFM = fm1; 130.15/78.11 glueVBal4 xyw xyx = glueVBal3 xyw xyx; 130.15/78.11 130.15/78.11 glueVBal5 EmptyFM fm2 = fm2; 130.15/78.11 glueVBal5 xyz xzu = glueVBal4 xyz xzu; 130.15/78.11 130.15/78.11 intersectFM :: Ord b => FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 130.15/78.11 intersectFM fm1 fm2 = intersectFM_C intersectFM0 fm1 fm2; 130.15/78.11 130.15/78.11 intersectFM0 left right = right; 130.15/78.11 130.15/78.11 intersectFM_C :: Ord d => (a -> c -> b) -> FiniteMap d a -> FiniteMap d c -> FiniteMap d b; 130.15/78.11 intersectFM_C combiner fm1 EmptyFM = intersectFM_C4 combiner fm1 EmptyFM; 130.15/78.11 intersectFM_C combiner EmptyFM fm2 = intersectFM_C3 combiner EmptyFM fm2; 130.15/78.11 intersectFM_C combiner fm1 (Branch split_key elt2 wyx left right) = intersectFM_C2 combiner fm1 (Branch split_key elt2 wyx left right); 130.15/78.11 130.15/78.11 intersectFM_C2 combiner fm1 (Branch split_key elt2 wyx left right) = intersectFM_C2IntersectFM_C1 fm1 split_key combiner fm1 split_key elt2 wyx left right (Maybe.isJust (intersectFM_C2Maybe_elt1 fm1 split_key)); 130.15/78.11 130.15/78.11 intersectFM_C2Elt1 zww zwx = intersectFM_C2Elt10 zww zwx (intersectFM_C2Vv1 zww zwx); 130.15/78.11 130.15/78.11 intersectFM_C2Elt10 zww zwx (Just elt1) = elt1; 130.15/78.11 130.15/78.11 intersectFM_C2Gts zww zwx = splitGT zww zwx; 130.15/78.11 130.15/78.11 intersectFM_C2IntersectFM_C0 zww zwx combiner fm1 split_key elt2 wyx left right True = glueVBal (intersectFM_C combiner (intersectFM_C2Lts zww zwx) left) (intersectFM_C combiner (intersectFM_C2Gts zww zwx) right); 130.15/78.11 130.15/78.11 intersectFM_C2IntersectFM_C1 zww zwx combiner fm1 split_key elt2 wyx left right True = mkVBalBranch split_key (combiner (intersectFM_C2Elt1 zww zwx) elt2) (intersectFM_C combiner (intersectFM_C2Lts zww zwx) left) (intersectFM_C combiner (intersectFM_C2Gts zww zwx) right); 130.15/78.11 intersectFM_C2IntersectFM_C1 zww zwx combiner fm1 split_key elt2 wyx left right False = intersectFM_C2IntersectFM_C0 zww zwx combiner fm1 split_key elt2 wyx left right otherwise; 130.15/78.11 130.15/78.11 intersectFM_C2Lts zww zwx = splitLT zww zwx; 130.15/78.11 130.15/78.11 intersectFM_C2Maybe_elt1 zww zwx = lookupFM zww zwx; 130.15/78.11 130.15/78.11 intersectFM_C2Vv1 zww zwx = intersectFM_C2Maybe_elt1 zww zwx; 130.15/78.11 130.15/78.11 intersectFM_C3 combiner EmptyFM fm2 = emptyFM; 130.15/78.11 intersectFM_C3 yyv yyw yyx = intersectFM_C2 yyv yyw yyx; 130.15/78.11 130.15/78.11 intersectFM_C4 combiner fm1 EmptyFM = emptyFM; 130.15/78.11 intersectFM_C4 yyz yzu yzv = intersectFM_C3 yyz yzu yzv; 130.15/78.11 130.15/78.11 lookupFM :: Ord a => FiniteMap a b -> a -> Maybe b; 130.15/78.11 lookupFM EmptyFM key = lookupFM4 EmptyFM key; 130.15/78.11 lookupFM (Branch key elt vyz fm_l fm_r) key_to_find = lookupFM3 (Branch key elt vyz fm_l fm_r) key_to_find; 130.15/78.11 130.15/78.11 lookupFM0 key elt vyz fm_l fm_r key_to_find True = Just elt; 130.15/78.11 130.15/78.11 lookupFM1 key elt vyz fm_l fm_r key_to_find True = lookupFM fm_r key_to_find; 130.15/78.11 lookupFM1 key elt vyz fm_l fm_r key_to_find False = lookupFM0 key elt vyz fm_l fm_r key_to_find otherwise; 130.15/78.11 130.15/78.11 lookupFM2 key elt vyz fm_l fm_r key_to_find True = lookupFM fm_l key_to_find; 130.15/78.11 lookupFM2 key elt vyz fm_l fm_r key_to_find False = lookupFM1 key elt vyz fm_l fm_r key_to_find (key_to_find > key); 130.15/78.11 130.15/78.11 lookupFM3 (Branch key elt vyz fm_l fm_r) key_to_find = lookupFM2 key elt vyz fm_l fm_r key_to_find (key_to_find < key); 130.15/78.11 130.15/78.11 lookupFM4 EmptyFM key = Nothing; 130.15/78.11 lookupFM4 xzx xzy = lookupFM3 xzx xzy; 130.15/78.11 130.15/78.11 mkBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 130.15/78.11 mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R; 130.15/78.11 130.15/78.11 mkBalBranch6 key elt fm_L fm_R = mkBalBranch6MkBalBranch5 fm_R key elt fm_L key elt fm_L fm_R (mkBalBranch6Size_l fm_R key elt fm_L + mkBalBranch6Size_r fm_R key elt fm_L < 2); 130.15/78.11 130.15/78.11 mkBalBranch6Double_L zvy zvz zwu zwv fm_l (Branch key_r elt_r wwx (Branch key_rl elt_rl wwy fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 zvz zwu fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 130.15/78.11 130.15/78.11 mkBalBranch6Double_R zvy zvz zwu zwv (Branch key_l elt_l wvy fm_ll (Branch key_lr elt_lr wvz fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 zvz zwu fm_lrr fm_r); 130.15/78.11 130.15/78.11 mkBalBranch6MkBalBranch0 zvy zvz zwu zwv fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr) = mkBalBranch6MkBalBranch02 zvy zvz zwu zwv fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr); 130.15/78.11 130.15/78.11 mkBalBranch6MkBalBranch00 zvy zvz zwu zwv fm_L fm_R wwz wxu wxv fm_rl fm_rr True = mkBalBranch6Double_L zvy zvz zwu zwv fm_L fm_R; 130.15/78.11 130.15/78.11 mkBalBranch6MkBalBranch01 zvy zvz zwu zwv fm_L fm_R wwz wxu wxv fm_rl fm_rr True = mkBalBranch6Single_L zvy zvz zwu zwv fm_L fm_R; 130.15/78.11 mkBalBranch6MkBalBranch01 zvy zvz zwu zwv fm_L fm_R wwz wxu wxv fm_rl fm_rr False = mkBalBranch6MkBalBranch00 zvy zvz zwu zwv fm_L fm_R wwz wxu wxv fm_rl fm_rr otherwise; 130.15/78.11 130.15/78.11 mkBalBranch6MkBalBranch02 zvy zvz zwu zwv fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr) = mkBalBranch6MkBalBranch01 zvy zvz zwu zwv fm_L fm_R wwz wxu wxv fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); 130.15/78.11 130.15/78.11 mkBalBranch6MkBalBranch1 zvy zvz zwu zwv fm_L fm_R (Branch wwu wwv www fm_ll fm_lr) = mkBalBranch6MkBalBranch12 zvy zvz zwu zwv fm_L fm_R (Branch wwu wwv www fm_ll fm_lr); 130.15/78.11 130.15/78.11 mkBalBranch6MkBalBranch10 zvy zvz zwu zwv fm_L fm_R wwu wwv www fm_ll fm_lr True = mkBalBranch6Double_R zvy zvz zwu zwv fm_L fm_R; 130.15/78.11 130.15/78.11 mkBalBranch6MkBalBranch11 zvy zvz zwu zwv fm_L fm_R wwu wwv www fm_ll fm_lr True = mkBalBranch6Single_R zvy zvz zwu zwv fm_L fm_R; 130.15/78.11 mkBalBranch6MkBalBranch11 zvy zvz zwu zwv fm_L fm_R wwu wwv www fm_ll fm_lr False = mkBalBranch6MkBalBranch10 zvy zvz zwu zwv fm_L fm_R wwu wwv www fm_ll fm_lr otherwise; 130.15/78.11 130.15/78.11 mkBalBranch6MkBalBranch12 zvy zvz zwu zwv fm_L fm_R (Branch wwu wwv www fm_ll fm_lr) = mkBalBranch6MkBalBranch11 zvy zvz zwu zwv fm_L fm_R wwu wwv www fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); 130.15/78.11 130.15/78.11 mkBalBranch6MkBalBranch2 zvy zvz zwu zwv key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; 130.15/78.11 130.15/78.11 mkBalBranch6MkBalBranch3 zvy zvz zwu zwv key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 zvy zvz zwu zwv fm_L fm_R fm_L; 130.15/78.11 mkBalBranch6MkBalBranch3 zvy zvz zwu zwv key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 zvy zvz zwu zwv key elt fm_L fm_R otherwise; 130.15/78.11 130.15/78.11 mkBalBranch6MkBalBranch4 zvy zvz zwu zwv key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 zvy zvz zwu zwv fm_L fm_R fm_R; 130.15/78.11 mkBalBranch6MkBalBranch4 zvy zvz zwu zwv key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 zvy zvz zwu zwv key elt fm_L fm_R (mkBalBranch6Size_l zvy zvz zwu zwv > sIZE_RATIO * mkBalBranch6Size_r zvy zvz zwu zwv); 130.15/78.11 130.15/78.11 mkBalBranch6MkBalBranch5 zvy zvz zwu zwv key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; 130.15/78.11 mkBalBranch6MkBalBranch5 zvy zvz zwu zwv key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 zvy zvz zwu zwv key elt fm_L fm_R (mkBalBranch6Size_r zvy zvz zwu zwv > sIZE_RATIO * mkBalBranch6Size_l zvy zvz zwu zwv); 130.15/78.11 130.15/78.11 mkBalBranch6Single_L zvy zvz zwu zwv fm_l (Branch key_r elt_r wxw fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 zvz zwu fm_l fm_rl) fm_rr; 130.15/78.11 130.15/78.11 mkBalBranch6Single_R zvy zvz zwu zwv (Branch key_l elt_l wvx fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 zvz zwu fm_lr fm_r); 130.15/78.11 130.15/78.11 mkBalBranch6Size_l zvy zvz zwu zwv = sizeFM zwv; 130.15/78.11 130.15/78.11 mkBalBranch6Size_r zvy zvz zwu zwv = sizeFM zvy; 130.15/78.11 130.15/78.11 mkBranch :: Ord b => Int -> b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 130.15/78.11 mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_l fm_r; 130.15/78.11 130.15/78.11 mkBranchBalance_ok zwy zwz zxu = True; 130.15/78.11 130.15/78.11 mkBranchLeft_ok zwy zwz zxu = mkBranchLeft_ok0 zwy zwz zxu zwy zxu zwy; 130.15/78.11 130.15/78.11 mkBranchLeft_ok0 zwy zwz zxu fm_l key EmptyFM = True; 130.15/78.11 mkBranchLeft_ok0 zwy zwz zxu fm_l key (Branch left_key vuu vuv vuw vux) = mkBranchLeft_ok0Biggest_left_key fm_l < key; 130.15/78.11 130.15/78.11 mkBranchLeft_ok0Biggest_left_key zzx = fst (findMax zzx); 130.15/78.11 130.15/78.11 mkBranchLeft_size zwy zwz zxu = sizeFM zwy; 130.15/78.11 130.15/78.11 mkBranchResult zxv zxw zxx zxy = Branch zxv zxw (mkBranchUnbox zxx zxy zxv (1 + mkBranchLeft_size zxx zxy zxv + mkBranchRight_size zxx zxy zxv)) zxx zxy; 130.15/78.11 130.15/78.11 mkBranchRight_ok zwy zwz zxu = mkBranchRight_ok0 zwy zwz zxu zwz zxu zwz; 130.15/78.11 130.15/78.11 mkBranchRight_ok0 zwy zwz zxu fm_r key EmptyFM = True; 130.15/78.11 mkBranchRight_ok0 zwy zwz zxu fm_r key (Branch right_key vuy vuz vvu vvv) = key < mkBranchRight_ok0Smallest_right_key fm_r; 130.15/78.11 130.15/78.11 mkBranchRight_ok0Smallest_right_key zzy = fst (findMin zzy); 130.15/78.11 130.15/78.11 mkBranchRight_size zwy zwz zxu = sizeFM zwz; 130.15/78.11 130.15/78.11 mkBranchUnbox :: Ord a => -> (FiniteMap a b) ( -> (FiniteMap a b) ( -> a (Int -> Int))); 130.15/78.11 mkBranchUnbox zwy zwz zxu x = x; 130.15/78.11 130.15/78.11 mkVBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 130.15/78.11 mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r; 130.15/78.11 mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM; 130.15/78.11 mkVBalBranch key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz) = mkVBalBranch3 key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz); 130.15/78.11 130.15/78.11 mkVBalBranch3 key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz) = mkVBalBranch3MkVBalBranch2 vzv vzw vzx vzy vzz wuv wuw wux wuy wuz key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz (sIZE_RATIO * mkVBalBranch3Size_l vzv vzw vzx vzy vzz wuv wuw wux wuy wuz < mkVBalBranch3Size_r vzv vzw vzx vzy vzz wuv wuw wux wuy wuz); 130.15/78.11 130.15/78.11 mkVBalBranch3MkVBalBranch0 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz True = mkBranch 13 key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz); 130.15/78.11 130.15/78.11 mkVBalBranch3MkVBalBranch1 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz True = mkBalBranch vzv vzw vzy (mkVBalBranch key elt vzz (Branch wuv wuw wux wuy wuz)); 130.15/78.11 mkVBalBranch3MkVBalBranch1 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz False = mkVBalBranch3MkVBalBranch0 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz otherwise; 130.15/78.11 130.15/78.11 mkVBalBranch3MkVBalBranch2 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz True = mkBalBranch wuv wuw (mkVBalBranch key elt (Branch vzv vzw vzx vzy vzz) wuy) wuz; 130.15/78.11 mkVBalBranch3MkVBalBranch2 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz False = mkVBalBranch3MkVBalBranch1 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz (sIZE_RATIO * mkVBalBranch3Size_r zuu zuv zuw zux zuy zuz zvu zvv zvw zvx < mkVBalBranch3Size_l zuu zuv zuw zux zuy zuz zvu zvv zvw zvx); 130.15/78.11 130.15/78.11 mkVBalBranch3Size_l zuu zuv zuw zux zuy zuz zvu zvv zvw zvx = sizeFM (Branch zuu zuv zuw zux zuy); 130.15/78.11 130.15/78.11 mkVBalBranch3Size_r zuu zuv zuw zux zuy zuz zvu zvv zvw zvx = sizeFM (Branch zuz zvu zvv zvw zvx); 130.15/78.11 130.15/78.11 mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt; 130.15/78.11 mkVBalBranch4 yvw yvx yvy yvz = mkVBalBranch3 yvw yvx yvy yvz; 130.15/78.11 130.15/78.11 mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt; 130.15/78.11 mkVBalBranch5 ywv yww ywx ywy = mkVBalBranch4 ywv yww ywx ywy; 130.15/78.11 130.15/78.11 sIZE_RATIO :: Int; 130.15/78.11 sIZE_RATIO = 5; 130.15/78.11 130.15/78.11 sizeFM :: FiniteMap a b -> Int; 130.15/78.11 sizeFM EmptyFM = 0; 130.15/78.11 sizeFM (Branch wxx wxy size wxz wyu) = size; 130.15/78.11 130.15/78.11 splitGT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; 130.15/78.11 splitGT EmptyFM split_key = splitGT4 EmptyFM split_key; 130.15/78.11 splitGT (Branch key elt wvw fm_l fm_r) split_key = splitGT3 (Branch key elt wvw fm_l fm_r) split_key; 130.15/78.11 130.15/78.11 splitGT0 key elt wvw fm_l fm_r split_key True = fm_r; 130.15/78.11 130.15/78.11 splitGT1 key elt wvw fm_l fm_r split_key True = mkVBalBranch key elt (splitGT fm_l split_key) fm_r; 130.15/78.11 splitGT1 key elt wvw fm_l fm_r split_key False = splitGT0 key elt wvw fm_l fm_r split_key otherwise; 130.15/78.11 130.15/78.11 splitGT2 key elt wvw fm_l fm_r split_key True = splitGT fm_r split_key; 130.15/78.11 splitGT2 key elt wvw fm_l fm_r split_key False = splitGT1 key elt wvw fm_l fm_r split_key (split_key < key); 130.15/78.11 130.15/78.11 splitGT3 (Branch key elt wvw fm_l fm_r) split_key = splitGT2 key elt wvw fm_l fm_r split_key (split_key > key); 130.15/78.11 130.15/78.11 splitGT4 EmptyFM split_key = emptyFM; 130.15/78.11 splitGT4 yxv yxw = splitGT3 yxv yxw; 130.15/78.11 130.15/78.11 splitLT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; 130.15/78.11 splitLT EmptyFM split_key = splitLT4 EmptyFM split_key; 130.15/78.11 splitLT (Branch key elt zz fm_l fm_r) split_key = splitLT3 (Branch key elt zz fm_l fm_r) split_key; 130.15/78.11 130.15/78.11 splitLT0 key elt zz fm_l fm_r split_key True = fm_l; 130.15/78.11 130.15/78.11 splitLT1 key elt zz fm_l fm_r split_key True = mkVBalBranch key elt fm_l (splitLT fm_r split_key); 130.15/78.11 splitLT1 key elt zz fm_l fm_r split_key False = splitLT0 key elt zz fm_l fm_r split_key otherwise; 130.15/78.11 130.15/78.11 splitLT2 key elt zz fm_l fm_r split_key True = splitLT fm_l split_key; 130.15/78.11 splitLT2 key elt zz fm_l fm_r split_key False = splitLT1 key elt zz fm_l fm_r split_key (split_key > key); 130.15/78.11 130.15/78.11 splitLT3 (Branch key elt zz fm_l fm_r) split_key = splitLT2 key elt zz fm_l fm_r split_key (split_key < key); 130.15/78.11 130.15/78.11 splitLT4 EmptyFM split_key = emptyFM; 130.15/78.11 splitLT4 xwx xwy = splitLT3 xwx xwy; 130.15/78.11 130.15/78.11 unitFM :: a -> b -> FiniteMap a b; 130.15/78.11 unitFM key elt = Branch key elt 1 emptyFM emptyFM; 130.15/78.11 130.15/78.11 } 130.15/78.11 module Maybe where { 130.15/78.11 import qualified FiniteMap; 130.15/78.11 import qualified Main; 130.15/78.11 import qualified Prelude; 130.15/78.11 isJust :: Maybe a -> Bool; 130.15/78.11 isJust Nothing = False; 130.15/78.11 isJust wzw = True; 130.15/78.11 130.15/78.11 } 130.15/78.11 module Main where { 130.15/78.11 import qualified FiniteMap; 130.15/78.11 import qualified Maybe; 130.15/78.11 import qualified Prelude; 130.15/78.11 } 130.15/78.11 130.15/78.11 ---------------------------------------- 130.15/78.11 130.15/78.11 (13) NumRed (SOUND) 130.15/78.11 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 130.15/78.11 ---------------------------------------- 130.15/78.11 130.15/78.11 (14) 130.15/78.11 Obligation: 130.15/78.11 mainModule Main 130.15/78.11 module FiniteMap where { 130.15/78.11 import qualified Main; 130.15/78.11 import qualified Maybe; 130.15/78.11 import qualified Prelude; 130.15/78.11 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 130.15/78.11 130.15/78.11 instance (Eq a, Eq b) => Eq FiniteMap b a where { 130.15/78.11 (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; 130.15/78.11 } 130.15/78.11 addToFM :: Ord b => FiniteMap b a -> b -> a -> FiniteMap b a; 130.15/78.11 addToFM fm key elt = addToFM_C addToFM0 fm key elt; 130.15/78.11 130.15/78.11 addToFM0 old new = new; 130.15/78.11 130.15/78.11 addToFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> a -> b -> FiniteMap a b; 130.15/78.11 addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt; 130.15/78.11 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt; 130.15/78.11 130.15/78.11 addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r; 130.15/78.11 130.15/78.11 addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt); 130.15/78.11 addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise; 130.15/78.11 130.15/78.11 addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r; 130.15/78.11 addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key); 130.15/78.11 130.15/78.11 addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key); 130.15/78.11 130.15/78.11 addToFM_C4 combiner EmptyFM key elt = unitFM key elt; 130.15/78.11 addToFM_C4 yuv yuw yux yuy = addToFM_C3 yuv yuw yux yuy; 130.15/78.11 130.15/78.11 deleteMax :: Ord a => FiniteMap a b -> FiniteMap a b; 130.15/78.11 deleteMax (Branch key elt wvu fm_l EmptyFM) = fm_l; 130.15/78.11 deleteMax (Branch key elt wvv fm_l fm_r) = mkBalBranch key elt fm_l (deleteMax fm_r); 130.15/78.11 130.15/78.11 deleteMin :: Ord a => FiniteMap a b -> FiniteMap a b; 130.15/78.11 deleteMin (Branch key elt wyv EmptyFM fm_r) = fm_r; 130.15/78.11 deleteMin (Branch key elt wyw fm_l fm_r) = mkBalBranch key elt (deleteMin fm_l) fm_r; 130.15/78.11 130.15/78.11 emptyFM :: FiniteMap b a; 130.15/78.11 emptyFM = EmptyFM; 130.15/78.11 130.15/78.11 findMax :: FiniteMap a b -> (a,b); 130.15/78.11 findMax (Branch key elt vvw vvx EmptyFM) = (key,elt); 130.15/78.11 findMax (Branch key elt vvy vvz fm_r) = findMax fm_r; 130.15/78.11 130.15/78.11 findMin :: FiniteMap a b -> (a,b); 130.15/78.11 findMin (Branch key elt wyy EmptyFM wyz) = (key,elt); 130.15/78.11 findMin (Branch key elt wzu fm_l wzv) = findMin fm_l; 130.15/78.11 130.15/78.11 fmToList :: FiniteMap b a -> [(b,a)]; 130.15/78.11 fmToList fm = foldFM fmToList0 [] fm; 130.15/78.11 130.15/78.11 fmToList0 key elt rest = (key,elt) : rest; 130.15/78.11 130.15/78.11 foldFM :: (a -> b -> c -> c) -> c -> FiniteMap a b -> c; 130.15/78.11 foldFM k z EmptyFM = z; 130.15/78.11 foldFM k z (Branch key elt vyy fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; 130.15/78.11 130.15/78.11 glueBal :: Ord b => FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 130.15/78.11 glueBal EmptyFM fm2 = glueBal4 EmptyFM fm2; 130.15/78.11 glueBal fm1 EmptyFM = glueBal3 fm1 EmptyFM; 130.15/78.11 glueBal fm1 fm2 = glueBal2 fm1 fm2; 130.15/78.11 130.15/78.11 glueBal2 fm1 fm2 = glueBal2GlueBal1 fm2 fm1 fm1 fm2 (sizeFM fm2 > sizeFM fm1); 130.15/78.11 130.15/78.11 glueBal2GlueBal0 yzy yzz fm1 fm2 True = mkBalBranch (glueBal2Mid_key1 yzy yzz) (glueBal2Mid_elt1 yzy yzz) (deleteMax fm1) fm2; 130.15/78.11 130.15/78.11 glueBal2GlueBal1 yzy yzz fm1 fm2 True = mkBalBranch (glueBal2Mid_key2 yzy yzz) (glueBal2Mid_elt2 yzy yzz) fm1 (deleteMin fm2); 130.15/78.11 glueBal2GlueBal1 yzy yzz fm1 fm2 False = glueBal2GlueBal0 yzy yzz fm1 fm2 otherwise; 130.15/78.11 130.15/78.11 glueBal2Mid_elt1 yzy yzz = glueBal2Mid_elt10 yzy yzz (glueBal2Vv2 yzy yzz); 130.15/78.11 130.15/78.11 glueBal2Mid_elt10 yzy yzz (vwv,mid_elt1) = mid_elt1; 130.15/78.11 130.15/78.11 glueBal2Mid_elt2 yzy yzz = glueBal2Mid_elt20 yzy yzz (glueBal2Vv3 yzy yzz); 130.15/78.11 130.15/78.11 glueBal2Mid_elt20 yzy yzz (vwu,mid_elt2) = mid_elt2; 130.15/78.11 130.15/78.11 glueBal2Mid_key1 yzy yzz = glueBal2Mid_key10 yzy yzz (glueBal2Vv2 yzy yzz); 130.15/78.11 130.15/78.11 glueBal2Mid_key10 yzy yzz (mid_key1,vww) = mid_key1; 130.15/78.11 130.15/78.11 glueBal2Mid_key2 yzy yzz = glueBal2Mid_key20 yzy yzz (glueBal2Vv3 yzy yzz); 130.15/78.11 130.15/78.11 glueBal2Mid_key20 yzy yzz (mid_key2,vwx) = mid_key2; 130.15/78.11 130.15/78.11 glueBal2Vv2 yzy yzz = findMax yzz; 130.15/78.11 130.15/78.11 glueBal2Vv3 yzy yzz = findMin yzy; 130.15/78.11 130.15/78.11 glueBal3 fm1 EmptyFM = fm1; 130.15/78.11 glueBal3 xxu xxv = glueBal2 xxu xxv; 130.15/78.11 130.15/78.11 glueBal4 EmptyFM fm2 = fm2; 130.15/78.11 glueBal4 xxx xxy = glueBal3 xxx xxy; 130.15/78.11 130.15/78.11 glueVBal :: Ord a => FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 130.15/78.11 glueVBal EmptyFM fm2 = glueVBal5 EmptyFM fm2; 130.15/78.11 glueVBal fm1 EmptyFM = glueVBal4 fm1 EmptyFM; 130.15/78.11 glueVBal (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx) = glueVBal3 (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx); 130.15/78.11 130.15/78.11 glueVBal3 (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx) = glueVBal3GlueVBal2 vxz vyu vyv vyw vyx vwz vxu vxv vxw vxx vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx (sIZE_RATIO * glueVBal3Size_l vxz vyu vyv vyw vyx vwz vxu vxv vxw vxx < glueVBal3Size_r vxz vyu vyv vyw vyx vwz vxu vxv vxw vxx); 130.15/78.11 130.15/78.11 glueVBal3GlueVBal0 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx True = glueBal (Branch vwz vxu vxv vxw vxx) (Branch vxz vyu vyv vyw vyx); 130.15/78.11 130.15/78.11 glueVBal3GlueVBal1 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx True = mkBalBranch vwz vxu vxw (glueVBal vxx (Branch vxz vyu vyv vyw vyx)); 130.15/78.11 glueVBal3GlueVBal1 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx False = glueVBal3GlueVBal0 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx otherwise; 130.15/78.11 130.15/78.11 glueVBal3GlueVBal2 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx True = mkBalBranch vxz vyu (glueVBal (Branch vwz vxu vxv vxw vxx) vyw) vyx; 130.15/78.11 glueVBal3GlueVBal2 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx False = glueVBal3GlueVBal1 zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw vwz vxu vxv vxw vxx vxz vyu vyv vyw vyx (sIZE_RATIO * glueVBal3Size_r zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw < glueVBal3Size_l zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw); 130.15/78.11 130.15/78.11 glueVBal3Size_l zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw = sizeFM (Branch zyy zyz zzu zzv zzw); 130.15/78.11 130.15/78.11 glueVBal3Size_r zxz zyu zyv zyw zyx zyy zyz zzu zzv zzw = sizeFM (Branch zxz zyu zyv zyw zyx); 130.15/78.11 130.15/78.11 glueVBal4 fm1 EmptyFM = fm1; 130.15/78.11 glueVBal4 xyw xyx = glueVBal3 xyw xyx; 130.15/78.11 130.15/78.11 glueVBal5 EmptyFM fm2 = fm2; 130.15/78.11 glueVBal5 xyz xzu = glueVBal4 xyz xzu; 130.15/78.11 130.15/78.11 intersectFM :: Ord b => FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 130.15/78.11 intersectFM fm1 fm2 = intersectFM_C intersectFM0 fm1 fm2; 130.15/78.11 130.15/78.11 intersectFM0 left right = right; 130.15/78.11 130.15/78.11 intersectFM_C :: Ord a => (b -> d -> c) -> FiniteMap a b -> FiniteMap a d -> FiniteMap a c; 130.15/78.11 intersectFM_C combiner fm1 EmptyFM = intersectFM_C4 combiner fm1 EmptyFM; 130.15/78.11 intersectFM_C combiner EmptyFM fm2 = intersectFM_C3 combiner EmptyFM fm2; 130.15/78.11 intersectFM_C combiner fm1 (Branch split_key elt2 wyx left right) = intersectFM_C2 combiner fm1 (Branch split_key elt2 wyx left right); 130.15/78.11 130.15/78.11 intersectFM_C2 combiner fm1 (Branch split_key elt2 wyx left right) = intersectFM_C2IntersectFM_C1 fm1 split_key combiner fm1 split_key elt2 wyx left right (Maybe.isJust (intersectFM_C2Maybe_elt1 fm1 split_key)); 130.15/78.11 130.15/78.11 intersectFM_C2Elt1 zww zwx = intersectFM_C2Elt10 zww zwx (intersectFM_C2Vv1 zww zwx); 130.15/78.11 130.15/78.11 intersectFM_C2Elt10 zww zwx (Just elt1) = elt1; 130.15/78.11 130.15/78.11 intersectFM_C2Gts zww zwx = splitGT zww zwx; 130.15/78.11 130.15/78.11 intersectFM_C2IntersectFM_C0 zww zwx combiner fm1 split_key elt2 wyx left right True = glueVBal (intersectFM_C combiner (intersectFM_C2Lts zww zwx) left) (intersectFM_C combiner (intersectFM_C2Gts zww zwx) right); 130.15/78.11 130.15/78.11 intersectFM_C2IntersectFM_C1 zww zwx combiner fm1 split_key elt2 wyx left right True = mkVBalBranch split_key (combiner (intersectFM_C2Elt1 zww zwx) elt2) (intersectFM_C combiner (intersectFM_C2Lts zww zwx) left) (intersectFM_C combiner (intersectFM_C2Gts zww zwx) right); 130.15/78.11 intersectFM_C2IntersectFM_C1 zww zwx combiner fm1 split_key elt2 wyx left right False = intersectFM_C2IntersectFM_C0 zww zwx combiner fm1 split_key elt2 wyx left right otherwise; 130.15/78.11 130.15/78.11 intersectFM_C2Lts zww zwx = splitLT zww zwx; 130.15/78.11 130.15/78.11 intersectFM_C2Maybe_elt1 zww zwx = lookupFM zww zwx; 130.15/78.11 130.15/78.11 intersectFM_C2Vv1 zww zwx = intersectFM_C2Maybe_elt1 zww zwx; 130.15/78.11 130.15/78.11 intersectFM_C3 combiner EmptyFM fm2 = emptyFM; 130.15/78.11 intersectFM_C3 yyv yyw yyx = intersectFM_C2 yyv yyw yyx; 130.15/78.11 130.15/78.11 intersectFM_C4 combiner fm1 EmptyFM = emptyFM; 130.15/78.11 intersectFM_C4 yyz yzu yzv = intersectFM_C3 yyz yzu yzv; 130.15/78.11 130.15/78.11 lookupFM :: Ord a => FiniteMap a b -> a -> Maybe b; 130.15/78.11 lookupFM EmptyFM key = lookupFM4 EmptyFM key; 130.15/78.11 lookupFM (Branch key elt vyz fm_l fm_r) key_to_find = lookupFM3 (Branch key elt vyz fm_l fm_r) key_to_find; 130.15/78.11 130.15/78.11 lookupFM0 key elt vyz fm_l fm_r key_to_find True = Just elt; 130.15/78.11 130.15/78.11 lookupFM1 key elt vyz fm_l fm_r key_to_find True = lookupFM fm_r key_to_find; 130.15/78.11 lookupFM1 key elt vyz fm_l fm_r key_to_find False = lookupFM0 key elt vyz fm_l fm_r key_to_find otherwise; 130.15/78.11 130.15/78.11 lookupFM2 key elt vyz fm_l fm_r key_to_find True = lookupFM fm_l key_to_find; 130.15/78.11 lookupFM2 key elt vyz fm_l fm_r key_to_find False = lookupFM1 key elt vyz fm_l fm_r key_to_find (key_to_find > key); 130.15/78.11 130.15/78.11 lookupFM3 (Branch key elt vyz fm_l fm_r) key_to_find = lookupFM2 key elt vyz fm_l fm_r key_to_find (key_to_find < key); 130.15/78.11 130.15/78.11 lookupFM4 EmptyFM key = Nothing; 130.15/78.11 lookupFM4 xzx xzy = lookupFM3 xzx xzy; 130.15/78.11 130.15/78.11 mkBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 130.15/78.11 mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R; 130.15/78.11 130.15/78.11 mkBalBranch6 key elt fm_L fm_R = mkBalBranch6MkBalBranch5 fm_R key elt fm_L key elt fm_L fm_R (mkBalBranch6Size_l fm_R key elt fm_L + mkBalBranch6Size_r fm_R key elt fm_L < Pos (Succ (Succ Zero))); 130.15/78.11 130.15/78.11 mkBalBranch6Double_L zvy zvz zwu zwv fm_l (Branch key_r elt_r wwx (Branch key_rl elt_rl wwy fm_rll fm_rlr) fm_rr) = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) key_rl elt_rl (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) zvz zwu fm_l fm_rll) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) key_r elt_r fm_rlr fm_rr); 130.15/78.11 130.15/78.11 mkBalBranch6Double_R zvy zvz zwu zwv (Branch key_l elt_l wvy fm_ll (Branch key_lr elt_lr wvz fm_lrl fm_lrr)) fm_r = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) key_lr elt_lr (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))) key_l elt_l fm_ll fm_lrl) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) zvz zwu fm_lrr fm_r); 130.15/78.11 130.15/78.11 mkBalBranch6MkBalBranch0 zvy zvz zwu zwv fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr) = mkBalBranch6MkBalBranch02 zvy zvz zwu zwv fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr); 130.15/78.11 130.15/78.11 mkBalBranch6MkBalBranch00 zvy zvz zwu zwv fm_L fm_R wwz wxu wxv fm_rl fm_rr True = mkBalBranch6Double_L zvy zvz zwu zwv fm_L fm_R; 130.15/78.11 130.15/78.11 mkBalBranch6MkBalBranch01 zvy zvz zwu zwv fm_L fm_R wwz wxu wxv fm_rl fm_rr True = mkBalBranch6Single_L zvy zvz zwu zwv fm_L fm_R; 130.15/78.11 mkBalBranch6MkBalBranch01 zvy zvz zwu zwv fm_L fm_R wwz wxu wxv fm_rl fm_rr False = mkBalBranch6MkBalBranch00 zvy zvz zwu zwv fm_L fm_R wwz wxu wxv fm_rl fm_rr otherwise; 130.15/78.11 130.15/78.11 mkBalBranch6MkBalBranch02 zvy zvz zwu zwv fm_L fm_R (Branch wwz wxu wxv fm_rl fm_rr) = mkBalBranch6MkBalBranch01 zvy zvz zwu zwv fm_L fm_R wwz wxu wxv fm_rl fm_rr (sizeFM fm_rl < Pos (Succ (Succ Zero)) * sizeFM fm_rr); 130.15/78.11 130.15/78.11 mkBalBranch6MkBalBranch1 zvy zvz zwu zwv fm_L fm_R (Branch wwu wwv www fm_ll fm_lr) = mkBalBranch6MkBalBranch12 zvy zvz zwu zwv fm_L fm_R (Branch wwu wwv www fm_ll fm_lr); 130.15/78.12 130.15/78.12 mkBalBranch6MkBalBranch10 zvy zvz zwu zwv fm_L fm_R wwu wwv www fm_ll fm_lr True = mkBalBranch6Double_R zvy zvz zwu zwv fm_L fm_R; 130.15/78.12 130.15/78.12 mkBalBranch6MkBalBranch11 zvy zvz zwu zwv fm_L fm_R wwu wwv www fm_ll fm_lr True = mkBalBranch6Single_R zvy zvz zwu zwv fm_L fm_R; 130.15/78.12 mkBalBranch6MkBalBranch11 zvy zvz zwu zwv fm_L fm_R wwu wwv www fm_ll fm_lr False = mkBalBranch6MkBalBranch10 zvy zvz zwu zwv fm_L fm_R wwu wwv www fm_ll fm_lr otherwise; 130.15/78.12 130.15/78.12 mkBalBranch6MkBalBranch12 zvy zvz zwu zwv fm_L fm_R (Branch wwu wwv www fm_ll fm_lr) = mkBalBranch6MkBalBranch11 zvy zvz zwu zwv fm_L fm_R wwu wwv www fm_ll fm_lr (sizeFM fm_lr < Pos (Succ (Succ Zero)) * sizeFM fm_ll); 130.15/78.12 130.15/78.12 mkBalBranch6MkBalBranch2 zvy zvz zwu zwv key elt fm_L fm_R True = mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R; 130.15/78.12 130.15/78.12 mkBalBranch6MkBalBranch3 zvy zvz zwu zwv key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 zvy zvz zwu zwv fm_L fm_R fm_L; 130.15/78.12 mkBalBranch6MkBalBranch3 zvy zvz zwu zwv key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 zvy zvz zwu zwv key elt fm_L fm_R otherwise; 130.15/78.12 130.15/78.12 mkBalBranch6MkBalBranch4 zvy zvz zwu zwv key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 zvy zvz zwu zwv fm_L fm_R fm_R; 130.15/78.12 mkBalBranch6MkBalBranch4 zvy zvz zwu zwv key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 zvy zvz zwu zwv key elt fm_L fm_R (mkBalBranch6Size_l zvy zvz zwu zwv > sIZE_RATIO * mkBalBranch6Size_r zvy zvz zwu zwv); 130.15/78.12 130.15/78.12 mkBalBranch6MkBalBranch5 zvy zvz zwu zwv key elt fm_L fm_R True = mkBranch (Pos (Succ Zero)) key elt fm_L fm_R; 130.15/78.12 mkBalBranch6MkBalBranch5 zvy zvz zwu zwv key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 zvy zvz zwu zwv key elt fm_L fm_R (mkBalBranch6Size_r zvy zvz zwu zwv > sIZE_RATIO * mkBalBranch6Size_l zvy zvz zwu zwv); 130.15/78.12 130.15/78.12 mkBalBranch6Single_L zvy zvz zwu zwv fm_l (Branch key_r elt_r wxw fm_rl fm_rr) = mkBranch (Pos (Succ (Succ (Succ Zero)))) key_r elt_r (mkBranch (Pos (Succ (Succ (Succ (Succ Zero))))) zvz zwu fm_l fm_rl) fm_rr; 130.15/78.12 130.15/78.12 mkBalBranch6Single_R zvy zvz zwu zwv (Branch key_l elt_l wvx fm_ll fm_lr) fm_r = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))) key_l elt_l fm_ll (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))) zvz zwu fm_lr fm_r); 130.15/78.12 130.15/78.12 mkBalBranch6Size_l zvy zvz zwu zwv = sizeFM zwv; 130.15/78.12 130.15/78.12 mkBalBranch6Size_r zvy zvz zwu zwv = sizeFM zvy; 130.15/78.12 130.15/78.12 mkBranch :: Ord a => Int -> a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 130.15/78.12 mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_l fm_r; 130.15/78.12 130.15/78.12 mkBranchBalance_ok zwy zwz zxu = True; 130.15/78.12 130.15/78.12 mkBranchLeft_ok zwy zwz zxu = mkBranchLeft_ok0 zwy zwz zxu zwy zxu zwy; 130.15/78.12 130.15/78.12 mkBranchLeft_ok0 zwy zwz zxu fm_l key EmptyFM = True; 130.15/78.12 mkBranchLeft_ok0 zwy zwz zxu fm_l key (Branch left_key vuu vuv vuw vux) = mkBranchLeft_ok0Biggest_left_key fm_l < key; 130.15/78.12 130.15/78.12 mkBranchLeft_ok0Biggest_left_key zzx = fst (findMax zzx); 130.15/78.12 130.15/78.12 mkBranchLeft_size zwy zwz zxu = sizeFM zwy; 130.15/78.12 130.15/78.12 mkBranchResult zxv zxw zxx zxy = Branch zxv zxw (mkBranchUnbox zxx zxy zxv (Pos (Succ Zero) + mkBranchLeft_size zxx zxy zxv + mkBranchRight_size zxx zxy zxv)) zxx zxy; 130.15/78.12 130.15/78.12 mkBranchRight_ok zwy zwz zxu = mkBranchRight_ok0 zwy zwz zxu zwz zxu zwz; 130.15/78.12 130.15/78.12 mkBranchRight_ok0 zwy zwz zxu fm_r key EmptyFM = True; 130.15/78.12 mkBranchRight_ok0 zwy zwz zxu fm_r key (Branch right_key vuy vuz vvu vvv) = key < mkBranchRight_ok0Smallest_right_key fm_r; 130.15/78.12 130.15/78.12 mkBranchRight_ok0Smallest_right_key zzy = fst (findMin zzy); 130.15/78.12 130.15/78.12 mkBranchRight_size zwy zwz zxu = sizeFM zwz; 130.15/78.12 130.15/78.12 mkBranchUnbox :: Ord a => -> (FiniteMap a b) ( -> (FiniteMap a b) ( -> a (Int -> Int))); 130.15/78.12 mkBranchUnbox zwy zwz zxu x = x; 130.15/78.12 130.15/78.12 mkVBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 130.15/78.12 mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r; 130.15/78.12 mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM; 130.15/78.12 mkVBalBranch key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz) = mkVBalBranch3 key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz); 130.15/78.12 130.15/78.12 mkVBalBranch3 key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz) = mkVBalBranch3MkVBalBranch2 vzv vzw vzx vzy vzz wuv wuw wux wuy wuz key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz (sIZE_RATIO * mkVBalBranch3Size_l vzv vzw vzx vzy vzz wuv wuw wux wuy wuz < mkVBalBranch3Size_r vzv vzw vzx vzy vzz wuv wuw wux wuy wuz); 130.15/78.12 130.15/78.12 mkVBalBranch3MkVBalBranch0 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz True = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) key elt (Branch vzv vzw vzx vzy vzz) (Branch wuv wuw wux wuy wuz); 130.15/78.12 130.15/78.12 mkVBalBranch3MkVBalBranch1 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz True = mkBalBranch vzv vzw vzy (mkVBalBranch key elt vzz (Branch wuv wuw wux wuy wuz)); 130.15/78.12 mkVBalBranch3MkVBalBranch1 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz False = mkVBalBranch3MkVBalBranch0 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz otherwise; 130.15/78.12 130.15/78.12 mkVBalBranch3MkVBalBranch2 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz True = mkBalBranch wuv wuw (mkVBalBranch key elt (Branch vzv vzw vzx vzy vzz) wuy) wuz; 130.15/78.12 mkVBalBranch3MkVBalBranch2 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz False = mkVBalBranch3MkVBalBranch1 zuu zuv zuw zux zuy zuz zvu zvv zvw zvx key elt vzv vzw vzx vzy vzz wuv wuw wux wuy wuz (sIZE_RATIO * mkVBalBranch3Size_r zuu zuv zuw zux zuy zuz zvu zvv zvw zvx < mkVBalBranch3Size_l zuu zuv zuw zux zuy zuz zvu zvv zvw zvx); 130.15/78.12 130.15/78.12 mkVBalBranch3Size_l zuu zuv zuw zux zuy zuz zvu zvv zvw zvx = sizeFM (Branch zuu zuv zuw zux zuy); 130.15/78.12 130.15/78.12 mkVBalBranch3Size_r zuu zuv zuw zux zuy zuz zvu zvv zvw zvx = sizeFM (Branch zuz zvu zvv zvw zvx); 130.15/78.12 130.15/78.12 mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt; 130.15/78.12 mkVBalBranch4 yvw yvx yvy yvz = mkVBalBranch3 yvw yvx yvy yvz; 130.15/78.12 130.15/78.12 mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt; 130.15/78.12 mkVBalBranch5 ywv yww ywx ywy = mkVBalBranch4 ywv yww ywx ywy; 130.15/78.12 130.15/78.12 sIZE_RATIO :: Int; 130.15/78.12 sIZE_RATIO = Pos (Succ (Succ (Succ (Succ (Succ Zero))))); 130.15/78.12 130.15/78.12 sizeFM :: FiniteMap b a -> Int; 130.15/78.12 sizeFM EmptyFM = Pos Zero; 130.15/78.12 sizeFM (Branch wxx wxy size wxz wyu) = size; 130.15/78.12 130.15/78.12 splitGT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; 130.15/78.12 splitGT EmptyFM split_key = splitGT4 EmptyFM split_key; 130.15/78.12 splitGT (Branch key elt wvw fm_l fm_r) split_key = splitGT3 (Branch key elt wvw fm_l fm_r) split_key; 130.15/78.12 130.15/78.12 splitGT0 key elt wvw fm_l fm_r split_key True = fm_r; 130.15/78.12 130.15/78.12 splitGT1 key elt wvw fm_l fm_r split_key True = mkVBalBranch key elt (splitGT fm_l split_key) fm_r; 130.15/78.12 splitGT1 key elt wvw fm_l fm_r split_key False = splitGT0 key elt wvw fm_l fm_r split_key otherwise; 130.15/78.12 130.15/78.12 splitGT2 key elt wvw fm_l fm_r split_key True = splitGT fm_r split_key; 130.15/78.12 splitGT2 key elt wvw fm_l fm_r split_key False = splitGT1 key elt wvw fm_l fm_r split_key (split_key < key); 130.15/78.12 130.15/78.12 splitGT3 (Branch key elt wvw fm_l fm_r) split_key = splitGT2 key elt wvw fm_l fm_r split_key (split_key > key); 130.15/78.12 130.15/78.12 splitGT4 EmptyFM split_key = emptyFM; 130.15/78.12 splitGT4 yxv yxw = splitGT3 yxv yxw; 130.15/78.12 130.15/78.12 splitLT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; 130.15/78.12 splitLT EmptyFM split_key = splitLT4 EmptyFM split_key; 130.15/78.12 splitLT (Branch key elt zz fm_l fm_r) split_key = splitLT3 (Branch key elt zz fm_l fm_r) split_key; 130.15/78.12 130.15/78.12 splitLT0 key elt zz fm_l fm_r split_key True = fm_l; 130.15/78.12 130.15/78.12 splitLT1 key elt zz fm_l fm_r split_key True = mkVBalBranch key elt fm_l (splitLT fm_r split_key); 130.15/78.12 splitLT1 key elt zz fm_l fm_r split_key False = splitLT0 key elt zz fm_l fm_r split_key otherwise; 130.15/78.12 130.15/78.12 splitLT2 key elt zz fm_l fm_r split_key True = splitLT fm_l split_key; 130.15/78.12 splitLT2 key elt zz fm_l fm_r split_key False = splitLT1 key elt zz fm_l fm_r split_key (split_key > key); 130.15/78.12 130.15/78.12 splitLT3 (Branch key elt zz fm_l fm_r) split_key = splitLT2 key elt zz fm_l fm_r split_key (split_key < key); 130.15/78.12 130.15/78.12 splitLT4 EmptyFM split_key = emptyFM; 130.15/78.12 splitLT4 xwx xwy = splitLT3 xwx xwy; 130.15/78.12 130.15/78.12 unitFM :: a -> b -> FiniteMap a b; 130.15/78.12 unitFM key elt = Branch key elt (Pos (Succ Zero)) emptyFM emptyFM; 130.15/78.12 130.15/78.12 } 130.15/78.12 module Maybe where { 130.15/78.12 import qualified FiniteMap; 130.15/78.12 import qualified Main; 130.15/78.12 import qualified Prelude; 130.15/78.12 isJust :: Maybe a -> Bool; 130.15/78.12 isJust Nothing = False; 130.15/78.12 isJust wzw = True; 130.15/78.12 130.15/78.12 } 130.15/78.12 module Main where { 130.15/78.12 import qualified FiniteMap; 130.15/78.12 import qualified Maybe; 130.15/78.12 import qualified Prelude; 130.15/78.12 } 130.15/78.12 130.15/78.12 ---------------------------------------- 130.15/78.12 130.15/78.12 (15) Narrow (SOUND) 130.15/78.12 Haskell To QDPs 130.15/78.12 130.15/78.12 digraph dp_graph { 130.15/78.12 node [outthreshold=100, inthreshold=100];1[label="FiniteMap.intersectFM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 130.15/78.12 3[label="FiniteMap.intersectFM zzz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 130.15/78.12 4[label="FiniteMap.intersectFM zzz3 zzz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 130.15/78.12 5[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 zzz3 zzz4",fontsize=16,color="burlywood",shape="triangle"];64816[label="zzz4/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];5 -> 64816[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64816 -> 6[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64817[label="zzz4/FiniteMap.Branch zzz40 zzz41 zzz42 zzz43 zzz44",fontsize=10,color="white",style="solid",shape="box"];5 -> 64817[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64817 -> 7[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 6[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 zzz3 FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 130.15/78.12 7[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 zzz3 (FiniteMap.Branch zzz40 zzz41 zzz42 zzz43 zzz44)",fontsize=16,color="burlywood",shape="box"];64818[label="zzz3/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];7 -> 64818[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64818 -> 9[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64819[label="zzz3/FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34",fontsize=10,color="white",style="solid",shape="box"];7 -> 64819[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64819 -> 10[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 8[label="FiniteMap.intersectFM_C4 FiniteMap.intersectFM0 zzz3 FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3]; 130.15/78.12 9[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 FiniteMap.EmptyFM (FiniteMap.Branch zzz40 zzz41 zzz42 zzz43 zzz44)",fontsize=16,color="black",shape="box"];9 -> 12[label="",style="solid", color="black", weight=3]; 130.15/78.12 10[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) (FiniteMap.Branch zzz40 zzz41 zzz42 zzz43 zzz44)",fontsize=16,color="black",shape="box"];10 -> 13[label="",style="solid", color="black", weight=3]; 130.15/78.12 11[label="FiniteMap.emptyFM",fontsize=16,color="black",shape="triangle"];11 -> 14[label="",style="solid", color="black", weight=3]; 130.15/78.12 12[label="FiniteMap.intersectFM_C3 FiniteMap.intersectFM0 FiniteMap.EmptyFM (FiniteMap.Branch zzz40 zzz41 zzz42 zzz43 zzz44)",fontsize=16,color="black",shape="box"];12 -> 15[label="",style="solid", color="black", weight=3]; 130.15/78.12 13[label="FiniteMap.intersectFM_C2 FiniteMap.intersectFM0 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) (FiniteMap.Branch zzz40 zzz41 zzz42 zzz43 zzz44)",fontsize=16,color="black",shape="box"];13 -> 16[label="",style="solid", color="black", weight=3]; 130.15/78.12 14[label="FiniteMap.EmptyFM",fontsize=16,color="green",shape="box"];15 -> 11[label="",style="dashed", color="red", weight=0]; 130.15/78.12 15[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];16[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) zzz40 FiniteMap.intersectFM0 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) zzz40 zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.intersectFM_C2Maybe_elt1 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) zzz40))",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3]; 130.15/78.12 17[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) zzz40 FiniteMap.intersectFM0 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) zzz40 zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) zzz40))",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3]; 130.15/78.12 18[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) zzz40 FiniteMap.intersectFM0 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) zzz40 zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) zzz40))",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3]; 130.15/78.12 19[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) zzz40 FiniteMap.intersectFM0 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) zzz40 zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 zzz30 zzz31 zzz32 zzz33 zzz34 zzz40 (zzz40 < zzz30)))",fontsize=16,color="black",shape="box"];19 -> 20[label="",style="solid", color="black", weight=3]; 130.15/78.12 20[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) zzz40 FiniteMap.intersectFM0 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) zzz40 zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 zzz30 zzz31 zzz32 zzz33 zzz34 zzz40 (compare zzz40 zzz30 == LT)))",fontsize=16,color="black",shape="box"];20 -> 21[label="",style="solid", color="black", weight=3]; 130.15/78.12 21[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) zzz40 FiniteMap.intersectFM0 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) zzz40 zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 zzz30 zzz31 zzz32 zzz33 zzz34 zzz40 (primCmpInt zzz40 zzz30 == LT)))",fontsize=16,color="burlywood",shape="box"];64820[label="zzz40/Pos zzz400",fontsize=10,color="white",style="solid",shape="box"];21 -> 64820[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64820 -> 22[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64821[label="zzz40/Neg zzz400",fontsize=10,color="white",style="solid",shape="box"];21 -> 64821[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64821 -> 23[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 22[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) (Pos zzz400) FiniteMap.intersectFM0 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) (Pos zzz400) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 zzz30 zzz31 zzz32 zzz33 zzz34 (Pos zzz400) (primCmpInt (Pos zzz400) zzz30 == LT)))",fontsize=16,color="burlywood",shape="box"];64822[label="zzz400/Succ zzz4000",fontsize=10,color="white",style="solid",shape="box"];22 -> 64822[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64822 -> 24[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64823[label="zzz400/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 64823[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64823 -> 25[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 23[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) (Neg zzz400) FiniteMap.intersectFM0 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) (Neg zzz400) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 zzz30 zzz31 zzz32 zzz33 zzz34 (Neg zzz400) (primCmpInt (Neg zzz400) zzz30 == LT)))",fontsize=16,color="burlywood",shape="box"];64824[label="zzz400/Succ zzz4000",fontsize=10,color="white",style="solid",shape="box"];23 -> 64824[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64824 -> 26[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64825[label="zzz400/Zero",fontsize=10,color="white",style="solid",shape="box"];23 -> 64825[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64825 -> 27[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 24[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 zzz30 zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) (primCmpInt (Pos (Succ zzz4000)) zzz30 == LT)))",fontsize=16,color="burlywood",shape="box"];64826[label="zzz30/Pos zzz300",fontsize=10,color="white",style="solid",shape="box"];24 -> 64826[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64826 -> 28[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64827[label="zzz30/Neg zzz300",fontsize=10,color="white",style="solid",shape="box"];24 -> 64827[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64827 -> 29[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 25[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 zzz30 zzz31 zzz32 zzz33 zzz34 (Pos Zero) (primCmpInt (Pos Zero) zzz30 == LT)))",fontsize=16,color="burlywood",shape="box"];64828[label="zzz30/Pos zzz300",fontsize=10,color="white",style="solid",shape="box"];25 -> 64828[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64828 -> 30[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64829[label="zzz30/Neg zzz300",fontsize=10,color="white",style="solid",shape="box"];25 -> 64829[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64829 -> 31[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 26[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 zzz30 zzz31 zzz32 zzz33 zzz34 (Neg (Succ zzz4000)) (primCmpInt (Neg (Succ zzz4000)) zzz30 == LT)))",fontsize=16,color="burlywood",shape="box"];64830[label="zzz30/Pos zzz300",fontsize=10,color="white",style="solid",shape="box"];26 -> 64830[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64830 -> 32[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64831[label="zzz30/Neg zzz300",fontsize=10,color="white",style="solid",shape="box"];26 -> 64831[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64831 -> 33[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 27[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch zzz30 zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 zzz30 zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpInt (Neg Zero) zzz30 == LT)))",fontsize=16,color="burlywood",shape="box"];64832[label="zzz30/Pos zzz300",fontsize=10,color="white",style="solid",shape="box"];27 -> 64832[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64832 -> 34[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64833[label="zzz30/Neg zzz300",fontsize=10,color="white",style="solid",shape="box"];27 -> 64833[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64833 -> 35[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 28[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz300) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) (primCmpInt (Pos (Succ zzz4000)) (Pos zzz300) == LT)))",fontsize=16,color="black",shape="box"];28 -> 36[label="",style="solid", color="black", weight=3]; 130.15/78.12 29[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz300) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) (primCmpInt (Pos (Succ zzz4000)) (Neg zzz300) == LT)))",fontsize=16,color="black",shape="box"];29 -> 37[label="",style="solid", color="black", weight=3]; 130.15/78.12 30[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz300) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Pos zzz300) == LT)))",fontsize=16,color="burlywood",shape="box"];64834[label="zzz300/Succ zzz3000",fontsize=10,color="white",style="solid",shape="box"];30 -> 64834[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64834 -> 38[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64835[label="zzz300/Zero",fontsize=10,color="white",style="solid",shape="box"];30 -> 64835[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64835 -> 39[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 31[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz300) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Neg zzz300) == LT)))",fontsize=16,color="burlywood",shape="box"];64836[label="zzz300/Succ zzz3000",fontsize=10,color="white",style="solid",shape="box"];31 -> 64836[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64836 -> 40[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64837[label="zzz300/Zero",fontsize=10,color="white",style="solid",shape="box"];31 -> 64837[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64837 -> 41[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 32[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz300) zzz31 zzz32 zzz33 zzz34 (Neg (Succ zzz4000)) (primCmpInt (Neg (Succ zzz4000)) (Pos zzz300) == LT)))",fontsize=16,color="black",shape="box"];32 -> 42[label="",style="solid", color="black", weight=3]; 130.15/78.12 33[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz300) zzz31 zzz32 zzz33 zzz34 (Neg (Succ zzz4000)) (primCmpInt (Neg (Succ zzz4000)) (Neg zzz300) == LT)))",fontsize=16,color="black",shape="box"];33 -> 43[label="",style="solid", color="black", weight=3]; 130.15/78.12 34[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz300) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpInt (Neg Zero) (Pos zzz300) == LT)))",fontsize=16,color="burlywood",shape="box"];64838[label="zzz300/Succ zzz3000",fontsize=10,color="white",style="solid",shape="box"];34 -> 64838[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64838 -> 44[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64839[label="zzz300/Zero",fontsize=10,color="white",style="solid",shape="box"];34 -> 64839[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64839 -> 45[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 35[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz300) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpInt (Neg Zero) (Neg zzz300) == LT)))",fontsize=16,color="burlywood",shape="box"];64840[label="zzz300/Succ zzz3000",fontsize=10,color="white",style="solid",shape="box"];35 -> 64840[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64840 -> 46[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64841[label="zzz300/Zero",fontsize=10,color="white",style="solid",shape="box"];35 -> 64841[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64841 -> 47[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 36[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz300) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) (primCmpNat (Succ zzz4000) zzz300 == LT)))",fontsize=16,color="burlywood",shape="box"];64842[label="zzz300/Succ zzz3000",fontsize=10,color="white",style="solid",shape="box"];36 -> 64842[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64842 -> 48[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64843[label="zzz300/Zero",fontsize=10,color="white",style="solid",shape="box"];36 -> 64843[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64843 -> 49[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 37[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz300) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) (GT == LT)))",fontsize=16,color="black",shape="box"];37 -> 50[label="",style="solid", color="black", weight=3]; 130.15/78.12 38[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Pos (Succ zzz3000)) == LT)))",fontsize=16,color="black",shape="box"];38 -> 51[label="",style="solid", color="black", weight=3]; 130.15/78.12 39[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];39 -> 52[label="",style="solid", color="black", weight=3]; 130.15/78.12 40[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ zzz3000)) == LT)))",fontsize=16,color="black",shape="box"];40 -> 53[label="",style="solid", color="black", weight=3]; 130.15/78.12 41[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == LT)))",fontsize=16,color="black",shape="box"];41 -> 54[label="",style="solid", color="black", weight=3]; 130.15/78.12 42[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz300) zzz31 zzz32 zzz33 zzz34 (Neg (Succ zzz4000)) (LT == LT)))",fontsize=16,color="black",shape="box"];42 -> 55[label="",style="solid", color="black", weight=3]; 130.15/78.12 43[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz300) zzz31 zzz32 zzz33 zzz34 (Neg (Succ zzz4000)) (primCmpNat zzz300 (Succ zzz4000) == LT)))",fontsize=16,color="burlywood",shape="box"];64844[label="zzz300/Succ zzz3000",fontsize=10,color="white",style="solid",shape="box"];43 -> 64844[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64844 -> 56[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64845[label="zzz300/Zero",fontsize=10,color="white",style="solid",shape="box"];43 -> 64845[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64845 -> 57[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 44[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpInt (Neg Zero) (Pos (Succ zzz3000)) == LT)))",fontsize=16,color="black",shape="box"];44 -> 58[label="",style="solid", color="black", weight=3]; 130.15/78.12 45[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];45 -> 59[label="",style="solid", color="black", weight=3]; 130.15/78.12 46[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ zzz3000)) == LT)))",fontsize=16,color="black",shape="box"];46 -> 60[label="",style="solid", color="black", weight=3]; 130.15/78.12 47[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == LT)))",fontsize=16,color="black",shape="box"];47 -> 61[label="",style="solid", color="black", weight=3]; 130.15/78.12 48[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) (primCmpNat (Succ zzz4000) (Succ zzz3000) == LT)))",fontsize=16,color="black",shape="box"];48 -> 62[label="",style="solid", color="black", weight=3]; 130.15/78.12 49[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) (primCmpNat (Succ zzz4000) Zero == LT)))",fontsize=16,color="black",shape="box"];49 -> 63[label="",style="solid", color="black", weight=3]; 130.15/78.12 50[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz300) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) False))",fontsize=16,color="black",shape="box"];50 -> 64[label="",style="solid", color="black", weight=3]; 130.15/78.12 51[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (primCmpNat Zero (Succ zzz3000) == LT)))",fontsize=16,color="black",shape="box"];51 -> 65[label="",style="solid", color="black", weight=3]; 130.15/78.12 52[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos 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Zero) (EQ == LT)))",fontsize=16,color="black",shape="box"];54 -> 68[label="",style="solid", color="black", weight=3]; 130.15/78.12 55[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz300) zzz31 zzz32 zzz33 zzz34 (Neg (Succ zzz4000)) True))",fontsize=16,color="black",shape="box"];55 -> 69[label="",style="solid", color="black", weight=3]; 130.15/78.12 56[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Neg (Succ zzz4000)) (primCmpNat (Succ zzz3000) (Succ zzz4000) == LT)))",fontsize=16,color="black",shape="box"];56 -> 70[label="",style="solid", color="black", weight=3]; 130.15/78.12 57[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg (Succ zzz4000)) (primCmpNat Zero (Succ zzz4000) == LT)))",fontsize=16,color="black",shape="box"];57 -> 71[label="",style="solid", color="black", weight=3]; 130.15/78.12 58[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (LT == LT)))",fontsize=16,color="black",shape="box"];58 -> 72[label="",style="solid", color="black", weight=3]; 130.15/78.12 59[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (EQ == LT)))",fontsize=16,color="black",shape="box"];59 -> 73[label="",style="solid", color="black", weight=3]; 130.15/78.12 60[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpNat (Succ zzz3000) Zero == LT)))",fontsize=16,color="black",shape="box"];60 -> 74[label="",style="solid", color="black", weight=3]; 130.15/78.12 61[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (EQ == LT)))",fontsize=16,color="black",shape="box"];61 -> 75[label="",style="solid", color="black", weight=3]; 130.15/78.12 62 -> 22809[label="",style="dashed", color="red", weight=0]; 130.15/78.12 62[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) (primCmpNat zzz4000 zzz3000 == LT)))",fontsize=16,color="magenta"];62 -> 22810[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 62 -> 22811[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 62 -> 22812[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 62 -> 22813[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 62 -> 22814[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 62 -> 22815[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 62 -> 22816[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 62 -> 22817[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 62 -> 22818[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 62 -> 22819[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 62 -> 22820[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 62 -> 22821[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 62 -> 22822[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 62 -> 22823[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 62 -> 22824[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 62 -> 22825[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 62 -> 22826[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 63[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) (GT == LT)))",fontsize=16,color="black",shape="box"];63 -> 78[label="",style="solid", color="black", weight=3]; 130.15/78.12 64[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz300) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) (Pos (Succ zzz4000) > Neg zzz300)))",fontsize=16,color="black",shape="box"];64 -> 79[label="",style="solid", color="black", weight=3]; 130.15/78.12 65[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (LT == LT)))",fontsize=16,color="black",shape="box"];65 -> 80[label="",style="solid", color="black", weight=3]; 130.15/78.12 66[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust 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False))",fontsize=16,color="black",shape="box"];68 -> 83[label="",style="solid", color="black", weight=3]; 130.15/78.12 69[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM zzz33 (Neg (Succ zzz4000))))",fontsize=16,color="burlywood",shape="box"];64846[label="zzz33/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];69 -> 64846[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64846 -> 84[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64847[label="zzz33/FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334",fontsize=10,color="white",style="solid",shape="box"];69 -> 64847[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64847 -> 85[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 70 -> 23616[label="",style="dashed", color="red", weight=0]; 130.15/78.12 70[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Neg (Succ zzz4000)) (primCmpNat zzz3000 zzz4000 == LT)))",fontsize=16,color="magenta"];70 -> 23617[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 70 -> 23618[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 70 -> 23619[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 70 -> 23620[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 70 -> 23621[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 70 -> 23622[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 70 -> 23623[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 70 -> 23624[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 70 -> 23625[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 70 -> 23626[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 70 -> 23627[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 70 -> 23628[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 70 -> 23629[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 70 -> 23630[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 70 -> 23631[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 70 -> 23632[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 70 -> 23633[label="",style="dashed", color="magenta", weight=3]; 130.15/78.12 71[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg (Succ zzz4000)) (LT == LT)))",fontsize=16,color="black",shape="box"];71 -> 88[label="",style="solid", color="black", weight=3]; 130.15/78.12 72[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Neg Zero) True))",fontsize=16,color="black",shape="box"];72 -> 89[label="",style="solid", color="black", weight=3]; 130.15/78.12 73[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) False))",fontsize=16,color="black",shape="box"];73 -> 90[label="",style="solid", color="black", weight=3]; 130.15/78.12 74[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (GT == LT)))",fontsize=16,color="black",shape="box"];74 -> 91[label="",style="solid", color="black", weight=3]; 130.15/78.12 75[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) False))",fontsize=16,color="black",shape="box"];75 -> 92[label="",style="solid", color="black", weight=3]; 130.15/78.12 22810[label="zzz31",fontsize=16,color="green",shape="box"];22811[label="zzz43",fontsize=16,color="green",shape="box"];22812[label="zzz3000",fontsize=16,color="green",shape="box"];22813[label="zzz4000",fontsize=16,color="green",shape="box"];22814[label="zzz34",fontsize=16,color="green",shape="box"];22815[label="zzz41",fontsize=16,color="green",shape="box"];22816[label="zzz42",fontsize=16,color="green",shape="box"];22817[label="zzz31",fontsize=16,color="green",shape="box"];22818[label="zzz3000",fontsize=16,color="green",shape="box"];22819[label="zzz3000",fontsize=16,color="green",shape="box"];22820[label="zzz44",fontsize=16,color="green",shape="box"];22821[label="zzz32",fontsize=16,color="green",shape="box"];22822[label="zzz32",fontsize=16,color="green",shape="box"];22823[label="zzz34",fontsize=16,color="green",shape="box"];22824[label="zzz33",fontsize=16,color="green",shape="box"];22825[label="zzz4000",fontsize=16,color="green",shape="box"];22826[label="zzz33",fontsize=16,color="green",shape="box"];22809[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz2088)) zzz2089 zzz2090 zzz2091 zzz2092 (Pos (Succ zzz2083)) (primCmpNat zzz2093 zzz2094 == LT)))",fontsize=16,color="burlywood",shape="triangle"];64848[label="zzz2093/Succ zzz20930",fontsize=10,color="white",style="solid",shape="box"];22809 -> 64848[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64848 -> 23031[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64849[label="zzz2093/Zero",fontsize=10,color="white",style="solid",shape="box"];22809 -> 64849[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64849 -> 23032[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 78[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) False))",fontsize=16,color="black",shape="box"];78 -> 97[label="",style="solid", color="black", weight=3]; 130.15/78.12 79[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz300) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) (compare (Pos (Succ zzz4000)) (Neg zzz300) == GT)))",fontsize=16,color="black",shape="box"];79 -> 98[label="",style="solid", color="black", weight=3]; 130.15/78.12 80[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Pos Zero) True))",fontsize=16,color="black",shape="box"];80 -> 99[label="",style="solid", color="black", weight=3]; 130.15/78.12 81[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (Pos Zero > Pos Zero)))",fontsize=16,color="black",shape="box"];81 -> 100[label="",style="solid", color="black", weight=3]; 130.15/78.12 82[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (Pos Zero > Neg (Succ zzz3000))))",fontsize=16,color="black",shape="box"];82 -> 101[label="",style="solid", color="black", weight=3]; 130.15/78.12 83[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (Pos Zero > Neg Zero)))",fontsize=16,color="black",shape="box"];83 -> 102[label="",style="solid", color="black", weight=3]; 130.15/78.12 84[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM FiniteMap.EmptyFM (Neg (Succ zzz4000))))",fontsize=16,color="black",shape="box"];84 -> 103[label="",style="solid", color="black", weight=3]; 130.15/78.12 85[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) (Neg (Succ zzz4000))))",fontsize=16,color="black",shape="box"];85 -> 104[label="",style="solid", color="black", weight=3]; 130.15/78.12 23617[label="zzz33",fontsize=16,color="green",shape="box"];23618[label="zzz44",fontsize=16,color="green",shape="box"];23619[label="zzz32",fontsize=16,color="green",shape="box"];23620[label="zzz34",fontsize=16,color="green",shape="box"];23621[label="zzz31",fontsize=16,color="green",shape="box"];23622[label="zzz43",fontsize=16,color="green",shape="box"];23623[label="zzz32",fontsize=16,color="green",shape="box"];23624[label="zzz4000",fontsize=16,color="green",shape="box"];23625[label="zzz3000",fontsize=16,color="green",shape="box"];23626[label="zzz42",fontsize=16,color="green",shape="box"];23627[label="zzz34",fontsize=16,color="green",shape="box"];23628[label="zzz33",fontsize=16,color="green",shape="box"];23629[label="zzz3000",fontsize=16,color="green",shape="box"];23630[label="zzz4000",fontsize=16,color="green",shape="box"];23631[label="zzz31",fontsize=16,color="green",shape="box"];23632[label="zzz3000",fontsize=16,color="green",shape="box"];23633[label="zzz41",fontsize=16,color="green",shape="box"];23616[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz2153)) zzz2154 zzz2155 zzz2156 zzz2157 (Neg (Succ zzz2148)) (primCmpNat zzz2158 zzz2159 == LT)))",fontsize=16,color="burlywood",shape="triangle"];64850[label="zzz2158/Succ zzz21580",fontsize=10,color="white",style="solid",shape="box"];23616 -> 64850[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64850 -> 23838[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64851[label="zzz2158/Zero",fontsize=10,color="white",style="solid",shape="box"];23616 -> 64851[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64851 -> 23839[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 88[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg (Succ zzz4000)) True))",fontsize=16,color="black",shape="box"];88 -> 109[label="",style="solid", color="black", weight=3]; 130.15/78.12 89[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM zzz33 (Neg Zero)))",fontsize=16,color="burlywood",shape="box"];64852[label="zzz33/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];89 -> 64852[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64852 -> 110[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64853[label="zzz33/FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334",fontsize=10,color="white",style="solid",shape="box"];89 -> 64853[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64853 -> 111[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 90[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (Neg Zero > Pos Zero)))",fontsize=16,color="black",shape="box"];90 -> 112[label="",style="solid", color="black", weight=3]; 130.15/78.12 91[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Neg Zero) False))",fontsize=16,color="black",shape="box"];91 -> 113[label="",style="solid", color="black", weight=3]; 130.15/78.12 92[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (Neg Zero > Neg Zero)))",fontsize=16,color="black",shape="box"];92 -> 114[label="",style="solid", color="black", weight=3]; 130.15/78.12 23031[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz2088)) zzz2089 zzz2090 zzz2091 zzz2092 (Pos (Succ zzz2083)) (primCmpNat (Succ zzz20930) zzz2094 == LT)))",fontsize=16,color="burlywood",shape="box"];64854[label="zzz2094/Succ zzz20940",fontsize=10,color="white",style="solid",shape="box"];23031 -> 64854[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64854 -> 23091[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64855[label="zzz2094/Zero",fontsize=10,color="white",style="solid",shape="box"];23031 -> 64855[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64855 -> 23092[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 23032[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz2088)) zzz2089 zzz2090 zzz2091 zzz2092 (Pos (Succ zzz2083)) (primCmpNat Zero zzz2094 == LT)))",fontsize=16,color="burlywood",shape="box"];64856[label="zzz2094/Succ zzz20940",fontsize=10,color="white",style="solid",shape="box"];23032 -> 64856[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64856 -> 23093[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64857[label="zzz2094/Zero",fontsize=10,color="white",style="solid",shape="box"];23032 -> 64857[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64857 -> 23094[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 97[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) (Pos (Succ zzz4000) > Pos Zero)))",fontsize=16,color="black",shape="box"];97 -> 119[label="",style="solid", color="black", weight=3]; 130.15/78.12 98[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz300) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) (primCmpInt (Pos (Succ zzz4000)) (Neg zzz300) == GT)))",fontsize=16,color="black",shape="box"];98 -> 120[label="",style="solid", color="black", weight=3]; 130.15/78.12 99[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM zzz33 (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];64858[label="zzz33/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];99 -> 64858[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64858 -> 121[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64859[label="zzz33/FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334",fontsize=10,color="white",style="solid",shape="box"];99 -> 64859[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64859 -> 122[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 100[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (compare (Pos Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];100 -> 123[label="",style="solid", color="black", weight=3]; 130.15/78.12 101[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (compare (Pos Zero) (Neg (Succ zzz3000)) == GT)))",fontsize=16,color="black",shape="box"];101 -> 124[label="",style="solid", color="black", weight=3]; 130.15/78.12 102[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (compare (Pos Zero) (Neg Zero) == GT)))",fontsize=16,color="black",shape="box"];102 -> 125[label="",style="solid", color="black", weight=3]; 130.15/78.12 103[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Neg (Succ zzz4000))))",fontsize=16,color="black",shape="box"];103 -> 126[label="",style="solid", color="black", weight=3]; 130.15/78.12 104[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) (Neg (Succ zzz4000))))",fontsize=16,color="black",shape="box"];104 -> 127[label="",style="solid", color="black", weight=3]; 130.15/78.12 23838[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz2153)) zzz2154 zzz2155 zzz2156 zzz2157 (Neg (Succ zzz2148)) (primCmpNat (Succ zzz21580) zzz2159 == LT)))",fontsize=16,color="burlywood",shape="box"];64860[label="zzz2159/Succ zzz21590",fontsize=10,color="white",style="solid",shape="box"];23838 -> 64860[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64860 -> 23899[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64861[label="zzz2159/Zero",fontsize=10,color="white",style="solid",shape="box"];23838 -> 64861[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64861 -> 23900[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 23839[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz2153)) zzz2154 zzz2155 zzz2156 zzz2157 (Neg (Succ zzz2148)) (primCmpNat Zero zzz2159 == LT)))",fontsize=16,color="burlywood",shape="box"];64862[label="zzz2159/Succ zzz21590",fontsize=10,color="white",style="solid",shape="box"];23839 -> 64862[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64862 -> 23901[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64863[label="zzz2159/Zero",fontsize=10,color="white",style="solid",shape="box"];23839 -> 64863[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64863 -> 23902[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 109[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM zzz33 (Neg (Succ zzz4000))))",fontsize=16,color="burlywood",shape="box"];64864[label="zzz33/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];109 -> 64864[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64864 -> 132[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 64865[label="zzz33/FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334",fontsize=10,color="white",style="solid",shape="box"];109 -> 64865[label="",style="solid", color="burlywood", weight=9]; 130.15/78.12 64865 -> 133[label="",style="solid", color="burlywood", weight=3]; 130.15/78.12 110[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM FiniteMap.EmptyFM (Neg Zero)))",fontsize=16,color="black",shape="box"];110 -> 134[label="",style="solid", color="black", weight=3]; 130.15/78.12 111[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) (Neg Zero)))",fontsize=16,color="black",shape="box"];111 -> 135[label="",style="solid", color="black", weight=3]; 130.15/78.12 112[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (compare (Neg Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];112 -> 136[label="",style="solid", color="black", weight=3]; 130.15/78.12 113[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (Neg Zero > Neg (Succ zzz3000))))",fontsize=16,color="black",shape="box"];113 -> 137[label="",style="solid", color="black", weight=3]; 130.15/78.12 114[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (compare (Neg Zero) (Neg Zero) == GT)))",fontsize=16,color="black",shape="box"];114 -> 138[label="",style="solid", color="black", weight=3]; 130.15/78.12 23091[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz2088)) zzz2089 zzz2090 zzz2091 zzz2092 (Pos (Succ zzz2083)) (primCmpNat (Succ zzz20930) (Succ zzz20940) == LT)))",fontsize=16,color="black",shape="box"];23091 -> 23271[label="",style="solid", color="black", weight=3]; 130.15/78.12 23092[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz2088)) zzz2089 zzz2090 zzz2091 zzz2092 (Pos (Succ zzz2083)) (primCmpNat (Succ zzz20930) Zero == LT)))",fontsize=16,color="black",shape="box"];23092 -> 23272[label="",style="solid", color="black", weight=3]; 130.15/78.12 23093[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz2088)) zzz2089 zzz2090 zzz2091 zzz2092 (Pos (Succ zzz2083)) (primCmpNat Zero (Succ zzz20940) == LT)))",fontsize=16,color="black",shape="box"];23093 -> 23273[label="",style="solid", color="black", weight=3]; 130.15/78.12 23094[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz2088)) zzz2089 zzz2090 zzz2091 zzz2092 (Pos (Succ zzz2083)) (primCmpNat Zero Zero == LT)))",fontsize=16,color="black",shape="box"];23094 -> 23274[label="",style="solid", color="black", weight=3]; 130.15/78.12 119[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) (compare (Pos (Succ zzz4000)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];119 -> 144[label="",style="solid", color="black", weight=3]; 130.15/78.12 120[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz300) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) (GT == GT)))",fontsize=16,color="black",shape="box"];120 -> 145[label="",style="solid", color="black", weight=3]; 130.15/78.12 121[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM FiniteMap.EmptyFM (Pos Zero)))",fontsize=16,color="black",shape="box"];121 -> 146[label="",style="solid", color="black", weight=3]; 130.15/78.12 122[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) (Pos Zero)))",fontsize=16,color="black",shape="box"];122 -> 147[label="",style="solid", color="black", weight=3]; 130.15/78.12 123[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];123 -> 148[label="",style="solid", color="black", weight=3]; 130.15/78.12 124[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ zzz3000)) == GT)))",fontsize=16,color="black",shape="box"];124 -> 149[label="",style="solid", color="black", weight=3]; 130.15/78.12 125[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == GT)))",fontsize=16,color="black",shape="box"];125 -> 150[label="",style="solid", color="black", weight=3]; 130.15/78.12 126[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust Nothing)",fontsize=16,color="black",shape="box"];126 -> 151[label="",style="solid", color="black", weight=3]; 130.15/78.12 127 -> 10027[label="",style="dashed", color="red", weight=0]; 130.15/78.12 127[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 zzz330 zzz331 zzz332 zzz333 zzz334 (Neg (Succ zzz4000)) (Neg (Succ zzz4000) < zzz330)))",fontsize=16,color="magenta"];127 -> 10028[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 127 -> 10029[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 127 -> 10030[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 127 -> 10031[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 127 -> 10032[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 127 -> 10033[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 127 -> 10034[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 127 -> 10035[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 127 -> 10036[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 127 -> 10037[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 127 -> 10038[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 127 -> 10039[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 127 -> 10040[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 127 -> 10041[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 127 -> 10042[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23899[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz2153)) zzz2154 zzz2155 zzz2156 zzz2157 (Neg (Succ zzz2148)) (primCmpNat (Succ zzz21580) (Succ zzz21590) == LT)))",fontsize=16,color="black",shape="box"];23899 -> 23947[label="",style="solid", color="black", weight=3]; 130.25/78.12 23900[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz2153)) zzz2154 zzz2155 zzz2156 zzz2157 (Neg (Succ zzz2148)) (primCmpNat (Succ zzz21580) Zero == LT)))",fontsize=16,color="black",shape="box"];23900 -> 23948[label="",style="solid", color="black", weight=3]; 130.25/78.12 23901[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz2153)) zzz2154 zzz2155 zzz2156 zzz2157 (Neg (Succ zzz2148)) (primCmpNat Zero (Succ zzz21590) == LT)))",fontsize=16,color="black",shape="box"];23901 -> 23949[label="",style="solid", color="black", weight=3]; 130.25/78.12 23902[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz2153)) zzz2154 zzz2155 zzz2156 zzz2157 (Neg (Succ zzz2148)) (primCmpNat Zero Zero == LT)))",fontsize=16,color="black",shape="box"];23902 -> 23950[label="",style="solid", color="black", weight=3]; 130.25/78.12 132[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM FiniteMap.EmptyFM (Neg (Succ zzz4000))))",fontsize=16,color="black",shape="box"];132 -> 158[label="",style="solid", color="black", weight=3]; 130.25/78.12 133[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) (Neg (Succ zzz4000))))",fontsize=16,color="black",shape="box"];133 -> 159[label="",style="solid", color="black", weight=3]; 130.25/78.12 134 -> 10691[label="",style="dashed", color="red", weight=0]; 130.25/78.12 134[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Neg Zero)))",fontsize=16,color="magenta"];134 -> 10692[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 134 -> 10693[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 134 -> 10694[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 134 -> 10695[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 134 -> 10696[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 134 -> 10697[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 134 -> 10698[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 134 -> 10699[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 134 -> 10700[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 135[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) (Neg Zero)))",fontsize=16,color="black",shape="box"];135 -> 161[label="",style="solid", color="black", weight=3]; 130.25/78.12 136[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];136 -> 162[label="",style="solid", color="black", weight=3]; 130.25/78.12 137[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (compare (Neg Zero) (Neg (Succ zzz3000)) == GT)))",fontsize=16,color="black",shape="box"];137 -> 163[label="",style="solid", color="black", weight=3]; 130.25/78.12 138[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == GT)))",fontsize=16,color="black",shape="box"];138 -> 164[label="",style="solid", color="black", weight=3]; 130.25/78.12 23271 -> 22809[label="",style="dashed", color="red", weight=0]; 130.25/78.12 23271[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz2088)) zzz2089 zzz2090 zzz2091 zzz2092 (Pos (Succ zzz2083)) (primCmpNat zzz20930 zzz20940 == LT)))",fontsize=16,color="magenta"];23271 -> 23375[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23271 -> 23376[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23272[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz2088)) zzz2089 zzz2090 zzz2091 zzz2092 (Pos (Succ zzz2083)) (GT == LT)))",fontsize=16,color="black",shape="box"];23272 -> 23377[label="",style="solid", color="black", weight=3]; 130.25/78.12 23273[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz2088)) zzz2089 zzz2090 zzz2091 zzz2092 (Pos (Succ zzz2083)) (LT == LT)))",fontsize=16,color="black",shape="box"];23273 -> 23378[label="",style="solid", color="black", weight=3]; 130.25/78.12 23274[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz2088)) zzz2089 zzz2090 zzz2091 zzz2092 (Pos (Succ zzz2083)) (EQ == LT)))",fontsize=16,color="black",shape="box"];23274 -> 23379[label="",style="solid", color="black", weight=3]; 130.25/78.12 144[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) (primCmpInt (Pos (Succ zzz4000)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];144 -> 172[label="",style="solid", color="black", weight=3]; 130.25/78.12 145[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz300) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) True))",fontsize=16,color="black",shape="box"];145 -> 173[label="",style="solid", color="black", weight=3]; 130.25/78.12 146[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Pos Zero)))",fontsize=16,color="black",shape="box"];146 -> 174[label="",style="solid", color="black", weight=3]; 130.25/78.12 147 -> 8891[label="",style="dashed", color="red", weight=0]; 130.25/78.12 147[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) (Pos Zero)))",fontsize=16,color="magenta"];147 -> 8892[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 147 -> 8893[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 147 -> 8894[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 147 -> 8895[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 147 -> 8896[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 147 -> 8897[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 147 -> 8898[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 147 -> 8899[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 147 -> 8900[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 147 -> 8901[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 147 -> 8902[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 147 -> 8903[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 147 -> 8904[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 147 -> 8905[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 148[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (EQ == GT)))",fontsize=16,color="black",shape="box"];148 -> 176[label="",style="solid", color="black", weight=3]; 130.25/78.12 149[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (GT == GT)))",fontsize=16,color="black",shape="box"];149 -> 177[label="",style="solid", color="black", weight=3]; 130.25/78.12 150[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (EQ == GT)))",fontsize=16,color="black",shape="box"];150 -> 178[label="",style="solid", color="black", weight=3]; 130.25/78.12 151[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 False",fontsize=16,color="black",shape="box"];151 -> 179[label="",style="solid", color="black", weight=3]; 130.25/78.12 10028[label="zzz32",fontsize=16,color="green",shape="box"];10029[label="zzz42",fontsize=16,color="green",shape="box"];10030[label="FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334",fontsize=16,color="green",shape="box"];10031[label="zzz41",fontsize=16,color="green",shape="box"];10032[label="zzz334",fontsize=16,color="green",shape="box"];10033[label="zzz34",fontsize=16,color="green",shape="box"];10034[label="zzz43",fontsize=16,color="green",shape="box"];10035[label="zzz333",fontsize=16,color="green",shape="box"];10036[label="zzz331",fontsize=16,color="green",shape="box"];10037[label="zzz44",fontsize=16,color="green",shape="box"];10038[label="zzz300",fontsize=16,color="green",shape="box"];10039[label="zzz332",fontsize=16,color="green",shape="box"];10040[label="zzz31",fontsize=16,color="green",shape="box"];10041[label="zzz4000",fontsize=16,color="green",shape="box"];10042[label="zzz330",fontsize=16,color="green",shape="box"];10027[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM2 zzz752 zzz753 zzz754 zzz755 zzz756 (Neg (Succ zzz747)) (Neg (Succ zzz747) < zzz752)))",fontsize=16,color="black",shape="triangle"];10027 -> 10268[label="",style="solid", color="black", weight=3]; 130.25/78.12 23947 -> 23616[label="",style="dashed", color="red", weight=0]; 130.25/78.12 23947[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz2153)) zzz2154 zzz2155 zzz2156 zzz2157 (Neg (Succ zzz2148)) (primCmpNat zzz21580 zzz21590 == LT)))",fontsize=16,color="magenta"];23947 -> 24159[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23947 -> 24160[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23948[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz2153)) zzz2154 zzz2155 zzz2156 zzz2157 (Neg (Succ zzz2148)) (GT == LT)))",fontsize=16,color="black",shape="box"];23948 -> 24161[label="",style="solid", color="black", weight=3]; 130.25/78.12 23949[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz2153)) zzz2154 zzz2155 zzz2156 zzz2157 (Neg (Succ zzz2148)) (LT == LT)))",fontsize=16,color="black",shape="box"];23949 -> 24162[label="",style="solid", color="black", weight=3]; 130.25/78.12 23950[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz2153)) zzz2154 zzz2155 zzz2156 zzz2157 (Neg (Succ zzz2148)) (EQ == LT)))",fontsize=16,color="black",shape="box"];23950 -> 24163[label="",style="solid", color="black", weight=3]; 130.25/78.12 158[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Neg (Succ zzz4000))))",fontsize=16,color="black",shape="box"];158 -> 188[label="",style="solid", color="black", weight=3]; 130.25/78.12 159 -> 11469[label="",style="dashed", color="red", weight=0]; 130.25/78.12 159[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) (Neg (Succ zzz4000))))",fontsize=16,color="magenta"];159 -> 11470[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 159 -> 11471[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 159 -> 11472[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 159 -> 11473[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 159 -> 11474[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 159 -> 11475[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 159 -> 11476[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 159 -> 11477[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 159 -> 11478[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 159 -> 11479[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 159 -> 11480[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 159 -> 11481[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 159 -> 11482[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 159 -> 11483[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10692[label="zzz31",fontsize=16,color="green",shape="box"];10693[label="zzz41",fontsize=16,color="green",shape="box"];10694[label="zzz3000",fontsize=16,color="green",shape="box"];10695[label="zzz32",fontsize=16,color="green",shape="box"];10696[label="zzz44",fontsize=16,color="green",shape="box"];10697[label="zzz34",fontsize=16,color="green",shape="box"];10698[label="zzz42",fontsize=16,color="green",shape="box"];10699[label="FiniteMap.EmptyFM",fontsize=16,color="green",shape="box"];10700[label="zzz43",fontsize=16,color="green",shape="box"];10691[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero) zzz835 zzz836 zzz837 zzz838 (Maybe.isJust (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Neg Zero)))",fontsize=16,color="black",shape="triangle"];10691 -> 10746[label="",style="solid", color="black", weight=3]; 130.25/78.12 161 -> 11718[label="",style="dashed", color="red", weight=0]; 130.25/78.12 161[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 zzz330 zzz331 zzz332 zzz333 zzz334 (Neg Zero) (Neg Zero < zzz330)))",fontsize=16,color="magenta"];161 -> 11719[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 161 -> 11720[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 161 -> 11721[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 161 -> 11722[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 161 -> 11723[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 161 -> 11724[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 161 -> 11725[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 161 -> 11726[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 161 -> 11727[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 161 -> 11728[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 161 -> 11729[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 161 -> 11730[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 161 -> 11731[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 161 -> 11732[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 162[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (EQ == GT)))",fontsize=16,color="black",shape="box"];162 -> 192[label="",style="solid", color="black", weight=3]; 130.25/78.12 163[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ zzz3000)) == GT)))",fontsize=16,color="black",shape="box"];163 -> 193[label="",style="solid", color="black", weight=3]; 130.25/78.12 164[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (EQ == GT)))",fontsize=16,color="black",shape="box"];164 -> 194[label="",style="solid", color="black", weight=3]; 130.25/78.12 23375[label="zzz20940",fontsize=16,color="green",shape="box"];23376[label="zzz20930",fontsize=16,color="green",shape="box"];23377[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz2088)) zzz2089 zzz2090 zzz2091 zzz2092 (Pos (Succ zzz2083)) False))",fontsize=16,color="black",shape="triangle"];23377 -> 23585[label="",style="solid", color="black", weight=3]; 130.25/78.12 23378[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz2088)) zzz2089 zzz2090 zzz2091 zzz2092 (Pos (Succ zzz2083)) True))",fontsize=16,color="black",shape="box"];23378 -> 23586[label="",style="solid", color="black", weight=3]; 130.25/78.12 23379 -> 23377[label="",style="dashed", color="red", weight=0]; 130.25/78.12 23379[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz2088)) zzz2089 zzz2090 zzz2091 zzz2092 (Pos (Succ zzz2083)) False))",fontsize=16,color="magenta"];172[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) (primCmpNat (Succ zzz4000) Zero == GT)))",fontsize=16,color="black",shape="box"];172 -> 203[label="",style="solid", color="black", weight=3]; 130.25/78.12 173[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM zzz34 (Pos (Succ zzz4000))))",fontsize=16,color="burlywood",shape="box"];64866[label="zzz34/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];173 -> 64866[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64866 -> 204[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64867[label="zzz34/FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344",fontsize=10,color="white",style="solid",shape="box"];173 -> 64867[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64867 -> 205[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 174[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust Nothing)",fontsize=16,color="black",shape="box"];174 -> 206[label="",style="solid", color="black", weight=3]; 130.25/78.12 8892[label="zzz44",fontsize=16,color="green",shape="box"];8893[label="zzz32",fontsize=16,color="green",shape="box"];8894[label="zzz43",fontsize=16,color="green",shape="box"];8895[label="zzz3000",fontsize=16,color="green",shape="box"];8896[label="FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334",fontsize=16,color="green",shape="box"];8897[label="zzz333",fontsize=16,color="green",shape="box"];8898[label="zzz31",fontsize=16,color="green",shape="box"];8899[label="zzz34",fontsize=16,color="green",shape="box"];8900[label="zzz332",fontsize=16,color="green",shape="box"];8901[label="zzz331",fontsize=16,color="green",shape="box"];8902[label="zzz42",fontsize=16,color="green",shape="box"];8903[label="zzz334",fontsize=16,color="green",shape="box"];8904[label="zzz41",fontsize=16,color="green",shape="box"];8905[label="zzz330",fontsize=16,color="green",shape="box"];8891[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz627 zzz628 zzz629 zzz630 zzz631) (Pos Zero)))",fontsize=16,color="black",shape="triangle"];8891 -> 8976[label="",style="solid", color="black", weight=3]; 130.25/78.12 176[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) False))",fontsize=16,color="black",shape="box"];176 -> 208[label="",style="solid", color="black", weight=3]; 130.25/78.12 177[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Pos Zero) True))",fontsize=16,color="black",shape="box"];177 -> 209[label="",style="solid", color="black", weight=3]; 130.25/78.12 178[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) False))",fontsize=16,color="black",shape="box"];178 -> 210[label="",style="solid", color="black", weight=3]; 130.25/78.12 179[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 otherwise",fontsize=16,color="black",shape="box"];179 -> 211[label="",style="solid", color="black", weight=3]; 130.25/78.12 10268[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM2 zzz752 zzz753 zzz754 zzz755 zzz756 (Neg (Succ zzz747)) (compare (Neg (Succ zzz747)) zzz752 == LT)))",fontsize=16,color="black",shape="box"];10268 -> 10334[label="",style="solid", color="black", weight=3]; 130.25/78.12 24159[label="zzz21580",fontsize=16,color="green",shape="box"];24160[label="zzz21590",fontsize=16,color="green",shape="box"];24161[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz2153)) zzz2154 zzz2155 zzz2156 zzz2157 (Neg (Succ zzz2148)) False))",fontsize=16,color="black",shape="triangle"];24161 -> 24192[label="",style="solid", color="black", weight=3]; 130.25/78.12 24162[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz2153)) zzz2154 zzz2155 zzz2156 zzz2157 (Neg (Succ zzz2148)) True))",fontsize=16,color="black",shape="box"];24162 -> 24193[label="",style="solid", color="black", weight=3]; 130.25/78.12 24163 -> 24161[label="",style="dashed", color="red", weight=0]; 130.25/78.12 24163[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz2153)) zzz2154 zzz2155 zzz2156 zzz2157 (Neg (Succ zzz2148)) False))",fontsize=16,color="magenta"];188[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust Nothing)",fontsize=16,color="black",shape="box"];188 -> 222[label="",style="solid", color="black", weight=3]; 130.25/78.12 11470[label="zzz31",fontsize=16,color="green",shape="box"];11471[label="zzz333",fontsize=16,color="green",shape="box"];11472[label="zzz331",fontsize=16,color="green",shape="box"];11473[label="zzz42",fontsize=16,color="green",shape="box"];11474[label="zzz34",fontsize=16,color="green",shape="box"];11475[label="zzz32",fontsize=16,color="green",shape="box"];11476[label="zzz44",fontsize=16,color="green",shape="box"];11477[label="zzz43",fontsize=16,color="green",shape="box"];11478[label="FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334",fontsize=16,color="green",shape="box"];11479[label="zzz41",fontsize=16,color="green",shape="box"];11480[label="zzz332",fontsize=16,color="green",shape="box"];11481[label="zzz4000",fontsize=16,color="green",shape="box"];11482[label="zzz330",fontsize=16,color="green",shape="box"];11483[label="zzz334",fontsize=16,color="green",shape="box"];11469[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz893 zzz894 zzz895 zzz896 zzz897) (Neg (Succ zzz888))))",fontsize=16,color="black",shape="triangle"];11469 -> 11666[label="",style="solid", color="black", weight=3]; 130.25/78.12 10746[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero) zzz835 zzz836 zzz837 zzz838 (Maybe.isJust Nothing)",fontsize=16,color="black",shape="box"];10746 -> 10954[label="",style="solid", color="black", weight=3]; 130.25/78.12 11719[label="zzz331",fontsize=16,color="green",shape="box"];11720[label="zzz333",fontsize=16,color="green",shape="box"];11721[label="zzz34",fontsize=16,color="green",shape="box"];11722[label="zzz332",fontsize=16,color="green",shape="box"];11723[label="zzz3000",fontsize=16,color="green",shape="box"];11724[label="zzz44",fontsize=16,color="green",shape="box"];11725[label="zzz41",fontsize=16,color="green",shape="box"];11726[label="zzz31",fontsize=16,color="green",shape="box"];11727[label="zzz32",fontsize=16,color="green",shape="box"];11728[label="FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334",fontsize=16,color="green",shape="box"];11729[label="zzz330",fontsize=16,color="green",shape="box"];11730[label="zzz334",fontsize=16,color="green",shape="box"];11731[label="zzz42",fontsize=16,color="green",shape="box"];11732[label="zzz43",fontsize=16,color="green",shape="box"];11718[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM2 zzz908 zzz909 zzz910 zzz911 zzz912 (Neg Zero) (Neg Zero < zzz908)))",fontsize=16,color="black",shape="triangle"];11718 -> 11803[label="",style="solid", color="black", weight=3]; 130.25/78.12 192[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) False))",fontsize=16,color="black",shape="box"];192 -> 226[label="",style="solid", color="black", weight=3]; 130.25/78.12 193[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpNat (Succ zzz3000) Zero == GT)))",fontsize=16,color="black",shape="box"];193 -> 227[label="",style="solid", color="black", weight=3]; 130.25/78.12 194[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) False))",fontsize=16,color="black",shape="box"];194 -> 228[label="",style="solid", color="black", weight=3]; 130.25/78.12 23585[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz2088)) zzz2089 zzz2090 zzz2091 zzz2092 (Pos (Succ zzz2083)) (Pos (Succ zzz2083) > Pos (Succ zzz2088))))",fontsize=16,color="black",shape="box"];23585 -> 23840[label="",style="solid", color="black", weight=3]; 130.25/78.12 23586[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM zzz2091 (Pos (Succ zzz2083))))",fontsize=16,color="burlywood",shape="triangle"];64868[label="zzz2091/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];23586 -> 64868[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64868 -> 23841[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64869[label="zzz2091/FiniteMap.Branch zzz20910 zzz20911 zzz20912 zzz20913 zzz20914",fontsize=10,color="white",style="solid",shape="box"];23586 -> 64869[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64869 -> 23842[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 203[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) (GT == GT)))",fontsize=16,color="black",shape="box"];203 -> 238[label="",style="solid", color="black", weight=3]; 130.25/78.12 204[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM FiniteMap.EmptyFM (Pos (Succ zzz4000))))",fontsize=16,color="black",shape="box"];204 -> 239[label="",style="solid", color="black", weight=3]; 130.25/78.12 205[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344) (Pos (Succ zzz4000))))",fontsize=16,color="black",shape="box"];205 -> 240[label="",style="solid", color="black", weight=3]; 130.25/78.12 206[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 False",fontsize=16,color="black",shape="box"];206 -> 241[label="",style="solid", color="black", weight=3]; 130.25/78.12 8976[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM2 zzz627 zzz628 zzz629 zzz630 zzz631 (Pos Zero) (Pos Zero < zzz627)))",fontsize=16,color="black",shape="box"];8976 -> 9188[label="",style="solid", color="black", weight=3]; 130.25/78.12 208[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM0 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) otherwise))",fontsize=16,color="black",shape="box"];208 -> 243[label="",style="solid", color="black", weight=3]; 130.25/78.12 209[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM zzz34 (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];64870[label="zzz34/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];209 -> 64870[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64870 -> 244[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64871[label="zzz34/FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344",fontsize=10,color="white",style="solid",shape="box"];209 -> 64871[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64871 -> 245[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 210[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM0 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) otherwise))",fontsize=16,color="black",shape="box"];210 -> 246[label="",style="solid", color="black", weight=3]; 130.25/78.12 211[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 True",fontsize=16,color="black",shape="box"];211 -> 247[label="",style="solid", color="black", weight=3]; 130.25/78.12 10334[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM2 zzz752 zzz753 zzz754 zzz755 zzz756 (Neg (Succ zzz747)) (primCmpInt (Neg (Succ zzz747)) zzz752 == LT)))",fontsize=16,color="burlywood",shape="box"];64872[label="zzz752/Pos zzz7520",fontsize=10,color="white",style="solid",shape="box"];10334 -> 64872[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64872 -> 10365[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64873[label="zzz752/Neg zzz7520",fontsize=10,color="white",style="solid",shape="box"];10334 -> 64873[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64873 -> 10366[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 24192[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2153)) zzz2154 zzz2155 zzz2156 zzz2157 (Neg (Succ zzz2148)) (Neg (Succ zzz2148) > Neg (Succ zzz2153))))",fontsize=16,color="black",shape="box"];24192 -> 24241[label="",style="solid", color="black", weight=3]; 130.25/78.12 24193[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM zzz2156 (Neg (Succ zzz2148))))",fontsize=16,color="burlywood",shape="triangle"];64874[label="zzz2156/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];24193 -> 64874[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64874 -> 24242[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64875[label="zzz2156/FiniteMap.Branch zzz21560 zzz21561 zzz21562 zzz21563 zzz21564",fontsize=10,color="white",style="solid",shape="box"];24193 -> 64875[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64875 -> 24243[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 222[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 False",fontsize=16,color="black",shape="box"];222 -> 259[label="",style="solid", color="black", weight=3]; 130.25/78.12 11666[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM2 zzz893 zzz894 zzz895 zzz896 zzz897 (Neg (Succ zzz888)) (Neg (Succ zzz888) < zzz893)))",fontsize=16,color="black",shape="box"];11666 -> 11804[label="",style="solid", color="black", weight=3]; 130.25/78.12 10954[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero) zzz835 zzz836 zzz837 zzz838 False",fontsize=16,color="black",shape="box"];10954 -> 11142[label="",style="solid", color="black", weight=3]; 130.25/78.12 11803[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM2 zzz908 zzz909 zzz910 zzz911 zzz912 (Neg Zero) (compare (Neg Zero) zzz908 == LT)))",fontsize=16,color="black",shape="box"];11803 -> 11965[label="",style="solid", color="black", weight=3]; 130.25/78.12 226[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM0 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) otherwise))",fontsize=16,color="black",shape="box"];226 -> 264[label="",style="solid", color="black", weight=3]; 130.25/78.12 227[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (GT == GT)))",fontsize=16,color="black",shape="box"];227 -> 265[label="",style="solid", color="black", weight=3]; 130.25/78.12 228[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM0 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) otherwise))",fontsize=16,color="black",shape="box"];228 -> 266[label="",style="solid", color="black", weight=3]; 130.25/78.12 23840[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz2088)) zzz2089 zzz2090 zzz2091 zzz2092 (Pos (Succ zzz2083)) (compare (Pos (Succ zzz2083)) (Pos (Succ zzz2088)) == GT)))",fontsize=16,color="black",shape="box"];23840 -> 23903[label="",style="solid", color="black", weight=3]; 130.25/78.12 23841[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM FiniteMap.EmptyFM (Pos (Succ zzz2083))))",fontsize=16,color="black",shape="box"];23841 -> 23904[label="",style="solid", color="black", weight=3]; 130.25/78.12 23842[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM (FiniteMap.Branch zzz20910 zzz20911 zzz20912 zzz20913 zzz20914) (Pos (Succ zzz2083))))",fontsize=16,color="black",shape="box"];23842 -> 23905[label="",style="solid", color="black", weight=3]; 130.25/78.12 238[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos (Succ zzz4000)) True))",fontsize=16,color="black",shape="box"];238 -> 278[label="",style="solid", color="black", weight=3]; 130.25/78.12 239[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Pos (Succ zzz4000))))",fontsize=16,color="black",shape="box"];239 -> 279[label="",style="solid", color="black", weight=3]; 130.25/78.12 240 -> 16425[label="",style="dashed", color="red", weight=0]; 130.25/78.12 240[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344) (Pos (Succ zzz4000))))",fontsize=16,color="magenta"];240 -> 16426[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 240 -> 16427[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 240 -> 16428[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 240 -> 16429[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 240 -> 16430[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 240 -> 16431[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 240 -> 16432[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 240 -> 16433[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 240 -> 16434[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 240 -> 16435[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 240 -> 16436[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 240 -> 16437[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 240 -> 16438[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 240 -> 16439[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 240 -> 16440[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 241[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 otherwise",fontsize=16,color="black",shape="box"];241 -> 281[label="",style="solid", color="black", weight=3]; 130.25/78.12 9188[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM2 zzz627 zzz628 zzz629 zzz630 zzz631 (Pos Zero) (compare (Pos Zero) zzz627 == LT)))",fontsize=16,color="black",shape="box"];9188 -> 9218[label="",style="solid", color="black", weight=3]; 130.25/78.12 243[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM0 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) True))",fontsize=16,color="black",shape="box"];243 -> 284[label="",style="solid", color="black", weight=3]; 130.25/78.12 244[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM FiniteMap.EmptyFM (Pos Zero)))",fontsize=16,color="black",shape="box"];244 -> 285[label="",style="solid", color="black", weight=3]; 130.25/78.12 245[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344) (Pos Zero)))",fontsize=16,color="black",shape="box"];245 -> 286[label="",style="solid", color="black", weight=3]; 130.25/78.12 246[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM0 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) True))",fontsize=16,color="black",shape="box"];246 -> 287[label="",style="solid", color="black", weight=3]; 130.25/78.12 247 -> 288[label="",style="dashed", color="red", weight=0]; 130.25/78.12 247[label="FiniteMap.glueVBal (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))) zzz43) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))) zzz44)",fontsize=16,color="magenta"];247 -> 289[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 247 -> 290[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10365[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz7520) zzz753 zzz754 zzz755 zzz756 (Neg (Succ zzz747)) (primCmpInt (Neg (Succ zzz747)) (Pos zzz7520) == LT)))",fontsize=16,color="black",shape="box"];10365 -> 10395[label="",style="solid", color="black", weight=3]; 130.25/78.12 10366[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz7520) zzz753 zzz754 zzz755 zzz756 (Neg (Succ zzz747)) (primCmpInt (Neg (Succ zzz747)) (Neg zzz7520) == LT)))",fontsize=16,color="black",shape="box"];10366 -> 10396[label="",style="solid", color="black", weight=3]; 130.25/78.12 24241[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2153)) zzz2154 zzz2155 zzz2156 zzz2157 (Neg (Succ zzz2148)) (compare (Neg (Succ zzz2148)) (Neg (Succ zzz2153)) == GT)))",fontsize=16,color="black",shape="box"];24241 -> 24276[label="",style="solid", color="black", weight=3]; 130.25/78.12 24242[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM FiniteMap.EmptyFM (Neg (Succ zzz2148))))",fontsize=16,color="black",shape="box"];24242 -> 24277[label="",style="solid", color="black", weight=3]; 130.25/78.12 24243[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM (FiniteMap.Branch zzz21560 zzz21561 zzz21562 zzz21563 zzz21564) (Neg (Succ zzz2148))))",fontsize=16,color="black",shape="box"];24243 -> 24278[label="",style="solid", color="black", weight=3]; 130.25/78.12 259[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 otherwise",fontsize=16,color="black",shape="box"];259 -> 305[label="",style="solid", color="black", weight=3]; 130.25/78.12 11804[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM2 zzz893 zzz894 zzz895 zzz896 zzz897 (Neg (Succ zzz888)) (compare (Neg (Succ zzz888)) zzz893 == LT)))",fontsize=16,color="black",shape="box"];11804 -> 11966[label="",style="solid", color="black", weight=3]; 130.25/78.12 11142[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero) zzz835 zzz836 zzz837 zzz838 otherwise",fontsize=16,color="black",shape="box"];11142 -> 11397[label="",style="solid", color="black", weight=3]; 130.25/78.12 11965[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM2 zzz908 zzz909 zzz910 zzz911 zzz912 (Neg Zero) (primCmpInt (Neg Zero) zzz908 == LT)))",fontsize=16,color="burlywood",shape="box"];64876[label="zzz908/Pos zzz9080",fontsize=10,color="white",style="solid",shape="box"];11965 -> 64876[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64876 -> 12076[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64877[label="zzz908/Neg zzz9080",fontsize=10,color="white",style="solid",shape="box"];11965 -> 64877[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64877 -> 12077[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 264[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM0 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) True))",fontsize=16,color="black",shape="box"];264 -> 313[label="",style="solid", color="black", weight=3]; 130.25/78.12 265[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34 (Neg Zero) True))",fontsize=16,color="black",shape="box"];265 -> 314[label="",style="solid", color="black", weight=3]; 130.25/78.12 266[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM0 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) True))",fontsize=16,color="black",shape="box"];266 -> 315[label="",style="solid", color="black", weight=3]; 130.25/78.12 23903[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz2088)) zzz2089 zzz2090 zzz2091 zzz2092 (Pos (Succ zzz2083)) (primCmpInt (Pos (Succ zzz2083)) (Pos (Succ zzz2088)) == GT)))",fontsize=16,color="black",shape="box"];23903 -> 23951[label="",style="solid", color="black", weight=3]; 130.25/78.12 23904[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Pos (Succ zzz2083))))",fontsize=16,color="black",shape="box"];23904 -> 23952[label="",style="solid", color="black", weight=3]; 130.25/78.12 23905[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz20910 zzz20911 zzz20912 zzz20913 zzz20914) (Pos (Succ zzz2083))))",fontsize=16,color="black",shape="box"];23905 -> 23953[label="",style="solid", color="black", weight=3]; 130.25/78.12 278[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM zzz34 (Pos (Succ zzz4000))))",fontsize=16,color="burlywood",shape="box"];64878[label="zzz34/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];278 -> 64878[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64878 -> 328[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64879[label="zzz34/FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344",fontsize=10,color="white",style="solid",shape="box"];278 -> 64879[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64879 -> 329[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 279[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust Nothing)",fontsize=16,color="black",shape="box"];279 -> 330[label="",style="solid", color="black", weight=3]; 130.25/78.12 16426[label="zzz32",fontsize=16,color="green",shape="box"];16427[label="zzz4000",fontsize=16,color="green",shape="box"];16428[label="zzz31",fontsize=16,color="green",shape="box"];16429[label="zzz43",fontsize=16,color="green",shape="box"];16430[label="zzz41",fontsize=16,color="green",shape="box"];16431[label="zzz344",fontsize=16,color="green",shape="box"];16432[label="zzz42",fontsize=16,color="green",shape="box"];16433[label="zzz342",fontsize=16,color="green",shape="box"];16434[label="FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344",fontsize=16,color="green",shape="box"];16435[label="zzz340",fontsize=16,color="green",shape="box"];16436[label="zzz341",fontsize=16,color="green",shape="box"];16437[label="zzz300",fontsize=16,color="green",shape="box"];16438[label="zzz44",fontsize=16,color="green",shape="box"];16439[label="zzz33",fontsize=16,color="green",shape="box"];16440[label="zzz343",fontsize=16,color="green",shape="box"];16425[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz1392 zzz1393 zzz1394 zzz1395 zzz1396) (Pos (Succ zzz1387))))",fontsize=16,color="black",shape="triangle"];16425 -> 16576[label="",style="solid", color="black", weight=3]; 130.25/78.12 281[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 True",fontsize=16,color="black",shape="box"];281 -> 332[label="",style="solid", color="black", weight=3]; 130.25/78.12 9218[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM2 zzz627 zzz628 zzz629 zzz630 zzz631 (Pos Zero) (primCmpInt (Pos Zero) zzz627 == LT)))",fontsize=16,color="burlywood",shape="box"];64880[label="zzz627/Pos zzz6270",fontsize=10,color="white",style="solid",shape="box"];9218 -> 64880[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64880 -> 9238[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64881[label="zzz627/Neg zzz6270",fontsize=10,color="white",style="solid",shape="box"];9218 -> 64881[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64881 -> 9239[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 284[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (Just zzz31))",fontsize=16,color="black",shape="box"];284 -> 337[label="",style="solid", color="black", weight=3]; 130.25/78.12 285[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Pos Zero)))",fontsize=16,color="black",shape="box"];285 -> 338[label="",style="solid", color="black", weight=3]; 130.25/78.12 286 -> 14732[label="",style="dashed", color="red", weight=0]; 130.25/78.12 286[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344) (Pos Zero)))",fontsize=16,color="magenta"];286 -> 14733[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 286 -> 14734[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 286 -> 14735[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 286 -> 14736[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 286 -> 14737[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 286 -> 14738[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 286 -> 14739[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 286 -> 14740[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 286 -> 14741[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 286 -> 14742[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 286 -> 14743[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 286 -> 14744[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 286 -> 14745[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 286 -> 14746[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 287[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (Just zzz31))",fontsize=16,color="black",shape="box"];287 -> 340[label="",style="solid", color="black", weight=3]; 130.25/78.12 289 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 289[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))) zzz44",fontsize=16,color="magenta"];289 -> 341[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 289 -> 342[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 290 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 290[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))) zzz43",fontsize=16,color="magenta"];290 -> 343[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 290 -> 344[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 288[label="FiniteMap.glueVBal zzz6 zzz5",fontsize=16,color="burlywood",shape="triangle"];64882[label="zzz6/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];288 -> 64882[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64882 -> 345[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64883[label="zzz6/FiniteMap.Branch zzz60 zzz61 zzz62 zzz63 zzz64",fontsize=10,color="white",style="solid",shape="box"];288 -> 64883[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64883 -> 346[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 10395[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz7520) zzz753 zzz754 zzz755 zzz756 (Neg (Succ zzz747)) (LT == LT)))",fontsize=16,color="black",shape="box"];10395 -> 10564[label="",style="solid", color="black", weight=3]; 130.25/78.12 10396[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz7520) zzz753 zzz754 zzz755 zzz756 (Neg (Succ zzz747)) (primCmpNat zzz7520 (Succ zzz747) == LT)))",fontsize=16,color="burlywood",shape="box"];64884[label="zzz7520/Succ zzz75200",fontsize=10,color="white",style="solid",shape="box"];10396 -> 64884[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64884 -> 10565[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64885[label="zzz7520/Zero",fontsize=10,color="white",style="solid",shape="box"];10396 -> 64885[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64885 -> 10566[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 24276[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2153)) zzz2154 zzz2155 zzz2156 zzz2157 (Neg (Succ zzz2148)) (primCmpInt (Neg (Succ zzz2148)) (Neg (Succ zzz2153)) == GT)))",fontsize=16,color="black",shape="box"];24276 -> 24355[label="",style="solid", color="black", weight=3]; 130.25/78.12 24277[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Neg (Succ zzz2148))))",fontsize=16,color="black",shape="box"];24277 -> 24356[label="",style="solid", color="black", weight=3]; 130.25/78.12 24278[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz21560 zzz21561 zzz21562 zzz21563 zzz21564) (Neg (Succ zzz2148))))",fontsize=16,color="black",shape="box"];24278 -> 24357[label="",style="solid", color="black", weight=3]; 130.25/78.12 305[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 True",fontsize=16,color="black",shape="box"];305 -> 362[label="",style="solid", color="black", weight=3]; 130.25/78.12 11966[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM2 zzz893 zzz894 zzz895 zzz896 zzz897 (Neg (Succ zzz888)) (primCmpInt (Neg (Succ zzz888)) zzz893 == LT)))",fontsize=16,color="burlywood",shape="box"];64886[label="zzz893/Pos zzz8930",fontsize=10,color="white",style="solid",shape="box"];11966 -> 64886[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64886 -> 12078[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64887[label="zzz893/Neg zzz8930",fontsize=10,color="white",style="solid",shape="box"];11966 -> 64887[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64887 -> 12079[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 11397[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero) zzz835 zzz836 zzz837 zzz838 True",fontsize=16,color="black",shape="box"];11397 -> 11667[label="",style="solid", color="black", weight=3]; 130.25/78.12 12076[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz9080) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (primCmpInt (Neg Zero) (Pos zzz9080) == LT)))",fontsize=16,color="burlywood",shape="box"];64888[label="zzz9080/Succ zzz90800",fontsize=10,color="white",style="solid",shape="box"];12076 -> 64888[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64888 -> 12136[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64889[label="zzz9080/Zero",fontsize=10,color="white",style="solid",shape="box"];12076 -> 64889[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64889 -> 12137[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 12077[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz9080) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (primCmpInt (Neg Zero) (Neg zzz9080) == LT)))",fontsize=16,color="burlywood",shape="box"];64890[label="zzz9080/Succ zzz90800",fontsize=10,color="white",style="solid",shape="box"];12077 -> 64890[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64890 -> 12138[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64891[label="zzz9080/Zero",fontsize=10,color="white",style="solid",shape="box"];12077 -> 64891[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64891 -> 12139[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 313[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (Just zzz31))",fontsize=16,color="black",shape="box"];313 -> 371[label="",style="solid", color="black", weight=3]; 130.25/78.12 314[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM zzz34 (Neg Zero)))",fontsize=16,color="burlywood",shape="box"];64892[label="zzz34/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];314 -> 64892[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64892 -> 372[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64893[label="zzz34/FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344",fontsize=10,color="white",style="solid",shape="box"];314 -> 64893[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64893 -> 373[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 315[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (Just zzz31))",fontsize=16,color="black",shape="box"];315 -> 374[label="",style="solid", color="black", weight=3]; 130.25/78.12 23951 -> 26944[label="",style="dashed", color="red", weight=0]; 130.25/78.12 23951[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz2088)) zzz2089 zzz2090 zzz2091 zzz2092 (Pos (Succ zzz2083)) (primCmpNat (Succ zzz2083) (Succ zzz2088) == GT)))",fontsize=16,color="magenta"];23951 -> 26945[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23951 -> 26946[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23951 -> 26947[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23951 -> 26948[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23951 -> 26949[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23951 -> 26950[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23951 -> 26951[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23951 -> 26952[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23951 -> 26953[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23951 -> 26954[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23951 -> 26955[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23951 -> 26956[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23951 -> 26957[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23951 -> 26958[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23951 -> 26959[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23951 -> 26960[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23951 -> 26961[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 23952[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust Nothing)",fontsize=16,color="black",shape="box"];23952 -> 24165[label="",style="solid", color="black", weight=3]; 130.25/78.12 23953[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 zzz20910 zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (Pos (Succ zzz2083) < zzz20910)))",fontsize=16,color="black",shape="box"];23953 -> 24166[label="",style="solid", color="black", weight=3]; 130.25/78.12 328[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM FiniteMap.EmptyFM (Pos (Succ zzz4000))))",fontsize=16,color="black",shape="box"];328 -> 388[label="",style="solid", color="black", weight=3]; 130.25/78.12 329[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344) (Pos (Succ zzz4000))))",fontsize=16,color="black",shape="box"];329 -> 389[label="",style="solid", color="black", weight=3]; 130.25/78.12 330[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 False",fontsize=16,color="black",shape="box"];330 -> 390[label="",style="solid", color="black", weight=3]; 130.25/78.12 16576[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM2 zzz1392 zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (Pos (Succ zzz1387) < zzz1392)))",fontsize=16,color="black",shape="box"];16576 -> 16821[label="",style="solid", color="black", weight=3]; 130.25/78.12 332 -> 288[label="",style="dashed", color="red", weight=0]; 130.25/78.12 332[label="FiniteMap.glueVBal (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero)) zzz43) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero)) zzz44)",fontsize=16,color="magenta"];332 -> 392[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 332 -> 393[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 9238[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz6270) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (primCmpInt (Pos Zero) (Pos zzz6270) == LT)))",fontsize=16,color="burlywood",shape="box"];64894[label="zzz6270/Succ zzz62700",fontsize=10,color="white",style="solid",shape="box"];9238 -> 64894[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64894 -> 9293[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64895[label="zzz6270/Zero",fontsize=10,color="white",style="solid",shape="box"];9238 -> 64895[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64895 -> 9294[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 9239[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz6270) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (primCmpInt (Pos Zero) (Neg zzz6270) == LT)))",fontsize=16,color="burlywood",shape="box"];64896[label="zzz6270/Succ zzz62700",fontsize=10,color="white",style="solid",shape="box"];9239 -> 64896[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64896 -> 9295[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64897[label="zzz6270/Zero",fontsize=10,color="white",style="solid",shape="box"];9239 -> 64897[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64897 -> 9296[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 337[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 True",fontsize=16,color="black",shape="box"];337 -> 398[label="",style="solid", color="black", weight=3]; 130.25/78.12 338[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust Nothing)",fontsize=16,color="black",shape="box"];338 -> 399[label="",style="solid", color="black", weight=3]; 130.25/78.12 14733[label="zzz41",fontsize=16,color="green",shape="box"];14734[label="zzz32",fontsize=16,color="green",shape="box"];14735[label="zzz42",fontsize=16,color="green",shape="box"];14736[label="zzz3000",fontsize=16,color="green",shape="box"];14737[label="zzz43",fontsize=16,color="green",shape="box"];14738[label="zzz343",fontsize=16,color="green",shape="box"];14739[label="zzz344",fontsize=16,color="green",shape="box"];14740[label="zzz33",fontsize=16,color="green",shape="box"];14741[label="zzz44",fontsize=16,color="green",shape="box"];14742[label="FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344",fontsize=16,color="green",shape="box"];14743[label="zzz340",fontsize=16,color="green",shape="box"];14744[label="zzz341",fontsize=16,color="green",shape="box"];14745[label="zzz342",fontsize=16,color="green",shape="box"];14746[label="zzz31",fontsize=16,color="green",shape="box"];14732[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz1201 zzz1202 zzz1203 zzz1204 zzz1205) (Pos Zero)))",fontsize=16,color="black",shape="triangle"];14732 -> 14817[label="",style="solid", color="black", weight=3]; 130.25/78.12 340[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero) zzz41 zzz42 zzz43 zzz44 True",fontsize=16,color="black",shape="box"];340 -> 401[label="",style="solid", color="black", weight=3]; 130.25/78.12 341[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))",fontsize=16,color="black",shape="box"];341 -> 402[label="",style="solid", color="black", weight=3]; 130.25/78.12 342[label="zzz44",fontsize=16,color="green",shape="box"];343[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))",fontsize=16,color="black",shape="box"];343 -> 403[label="",style="solid", color="black", weight=3]; 130.25/78.12 344[label="zzz43",fontsize=16,color="green",shape="box"];345[label="FiniteMap.glueVBal FiniteMap.EmptyFM zzz5",fontsize=16,color="black",shape="box"];345 -> 404[label="",style="solid", color="black", weight=3]; 130.25/78.12 346[label="FiniteMap.glueVBal (FiniteMap.Branch zzz60 zzz61 zzz62 zzz63 zzz64) zzz5",fontsize=16,color="burlywood",shape="box"];64898[label="zzz5/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];346 -> 64898[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64898 -> 405[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64899[label="zzz5/FiniteMap.Branch zzz50 zzz51 zzz52 zzz53 zzz54",fontsize=10,color="white",style="solid",shape="box"];346 -> 64899[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64899 -> 406[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 10564[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz7520) zzz753 zzz754 zzz755 zzz756 (Neg (Succ zzz747)) True))",fontsize=16,color="black",shape="box"];10564 -> 10612[label="",style="solid", color="black", weight=3]; 130.25/78.12 10565[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz75200)) zzz753 zzz754 zzz755 zzz756 (Neg (Succ zzz747)) (primCmpNat (Succ zzz75200) (Succ zzz747) == LT)))",fontsize=16,color="black",shape="box"];10565 -> 10613[label="",style="solid", color="black", weight=3]; 130.25/78.12 10566[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz753 zzz754 zzz755 zzz756 (Neg (Succ zzz747)) (primCmpNat Zero (Succ zzz747) == LT)))",fontsize=16,color="black",shape="box"];10566 -> 10614[label="",style="solid", color="black", weight=3]; 130.25/78.12 24355 -> 27134[label="",style="dashed", color="red", weight=0]; 130.25/78.12 24355[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2153)) zzz2154 zzz2155 zzz2156 zzz2157 (Neg (Succ zzz2148)) (primCmpNat (Succ zzz2153) (Succ zzz2148) == GT)))",fontsize=16,color="magenta"];24355 -> 27135[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24355 -> 27136[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24355 -> 27137[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24355 -> 27138[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24355 -> 27139[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24355 -> 27140[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24355 -> 27141[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24355 -> 27142[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24355 -> 27143[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24355 -> 27144[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24355 -> 27145[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24355 -> 27146[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24355 -> 27147[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24355 -> 27148[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24355 -> 27149[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24355 -> 27150[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24355 -> 27151[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24356[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust Nothing)",fontsize=16,color="black",shape="box"];24356 -> 24648[label="",style="solid", color="black", weight=3]; 130.25/78.12 24357[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 zzz21560 zzz21561 zzz21562 zzz21563 zzz21564 (Neg (Succ zzz2148)) (Neg (Succ zzz2148) < zzz21560)))",fontsize=16,color="black",shape="box"];24357 -> 24649[label="",style="solid", color="black", weight=3]; 130.25/78.12 362 -> 288[label="",style="dashed", color="red", weight=0]; 130.25/78.12 362[label="FiniteMap.glueVBal (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))) zzz43) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))) zzz44)",fontsize=16,color="magenta"];362 -> 425[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 362 -> 426[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12078[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz8930) zzz894 zzz895 zzz896 zzz897 (Neg (Succ zzz888)) (primCmpInt (Neg (Succ zzz888)) (Pos zzz8930) == LT)))",fontsize=16,color="black",shape="box"];12078 -> 12140[label="",style="solid", color="black", weight=3]; 130.25/78.12 12079[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz8930) zzz894 zzz895 zzz896 zzz897 (Neg (Succ zzz888)) (primCmpInt (Neg (Succ zzz888)) (Neg zzz8930) == LT)))",fontsize=16,color="black",shape="box"];12079 -> 12141[label="",style="solid", color="black", weight=3]; 130.25/78.12 11667 -> 288[label="",style="dashed", color="red", weight=0]; 130.25/78.12 11667[label="FiniteMap.glueVBal (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero)) zzz837) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero)) zzz838)",fontsize=16,color="magenta"];11667 -> 11805[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 11667 -> 11806[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12136[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz90800)) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (primCmpInt (Neg Zero) (Pos (Succ zzz90800)) == LT)))",fontsize=16,color="black",shape="box"];12136 -> 12214[label="",style="solid", color="black", weight=3]; 130.25/78.12 12137[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];12137 -> 12215[label="",style="solid", color="black", weight=3]; 130.25/78.12 12138[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz90800)) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ zzz90800)) == LT)))",fontsize=16,color="black",shape="box"];12138 -> 12216[label="",style="solid", color="black", weight=3]; 130.25/78.12 12139[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == LT)))",fontsize=16,color="black",shape="box"];12139 -> 12217[label="",style="solid", color="black", weight=3]; 130.25/78.12 371[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 True",fontsize=16,color="black",shape="box"];371 -> 438[label="",style="solid", color="black", weight=3]; 130.25/78.12 372[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM FiniteMap.EmptyFM (Neg Zero)))",fontsize=16,color="black",shape="box"];372 -> 439[label="",style="solid", color="black", weight=3]; 130.25/78.12 373[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344) (Neg Zero)))",fontsize=16,color="black",shape="box"];373 -> 440[label="",style="solid", color="black", weight=3]; 130.25/78.12 374[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero) zzz41 zzz42 zzz43 zzz44 True",fontsize=16,color="black",shape="box"];374 -> 441[label="",style="solid", color="black", weight=3]; 130.25/78.12 26945[label="zzz2079",fontsize=16,color="green",shape="box"];26946[label="zzz2090",fontsize=16,color="green",shape="box"];26947[label="zzz2086",fontsize=16,color="green",shape="box"];26948[label="Succ zzz2083",fontsize=16,color="green",shape="box"];26949[label="zzz2078",fontsize=16,color="green",shape="box"];26950[label="zzz2080",fontsize=16,color="green",shape="box"];26951[label="zzz2085",fontsize=16,color="green",shape="box"];26952[label="zzz2089",fontsize=16,color="green",shape="box"];26953[label="zzz2083",fontsize=16,color="green",shape="box"];26954[label="zzz2088",fontsize=16,color="green",shape="box"];26955[label="Succ zzz2088",fontsize=16,color="green",shape="box"];26956[label="zzz2092",fontsize=16,color="green",shape="box"];26957[label="zzz2084",fontsize=16,color="green",shape="box"];26958[label="zzz2091",fontsize=16,color="green",shape="box"];26959[label="zzz2087",fontsize=16,color="green",shape="box"];26960[label="zzz2081",fontsize=16,color="green",shape="box"];26961[label="zzz2082",fontsize=16,color="green",shape="box"];26944[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) zzz2615 zzz2616 zzz2617 zzz2618 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz2619)) zzz2620 zzz2621 zzz2622 zzz2623 (Pos (Succ zzz2614)) (primCmpNat zzz2624 zzz2625 == GT)))",fontsize=16,color="burlywood",shape="triangle"];64900[label="zzz2624/Succ zzz26240",fontsize=10,color="white",style="solid",shape="box"];26944 -> 64900[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64900 -> 27132[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64901[label="zzz2624/Zero",fontsize=10,color="white",style="solid",shape="box"];26944 -> 64901[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64901 -> 27133[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 24165[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 False",fontsize=16,color="black",shape="box"];24165 -> 24196[label="",style="solid", color="black", weight=3]; 130.25/78.12 24166[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 zzz20910 zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (compare (Pos (Succ zzz2083)) zzz20910 == LT)))",fontsize=16,color="black",shape="box"];24166 -> 24197[label="",style="solid", color="black", weight=3]; 130.25/78.12 388[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Pos (Succ zzz4000))))",fontsize=16,color="black",shape="box"];388 -> 458[label="",style="solid", color="black", weight=3]; 130.25/78.12 389[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344) (Pos (Succ zzz4000))))",fontsize=16,color="black",shape="box"];389 -> 459[label="",style="solid", color="black", weight=3]; 130.25/78.12 390[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 otherwise",fontsize=16,color="black",shape="box"];390 -> 460[label="",style="solid", color="black", weight=3]; 130.25/78.12 16821[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM2 zzz1392 zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (compare (Pos (Succ zzz1387)) zzz1392 == LT)))",fontsize=16,color="black",shape="box"];16821 -> 17229[label="",style="solid", color="black", weight=3]; 130.25/78.12 392 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 392[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero)) zzz44",fontsize=16,color="magenta"];392 -> 463[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 392 -> 464[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 393 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 393[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero)) zzz43",fontsize=16,color="magenta"];393 -> 465[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 393 -> 466[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 9293[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz62700)) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (primCmpInt (Pos Zero) (Pos (Succ zzz62700)) == LT)))",fontsize=16,color="black",shape="box"];9293 -> 9455[label="",style="solid", color="black", weight=3]; 130.25/78.12 9294[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];9294 -> 9456[label="",style="solid", color="black", weight=3]; 130.25/78.12 9295[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz62700)) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ zzz62700)) == LT)))",fontsize=16,color="black",shape="box"];9295 -> 9457[label="",style="solid", color="black", weight=3]; 130.25/78.12 9296[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == LT)))",fontsize=16,color="black",shape="box"];9296 -> 9458[label="",style="solid", color="black", weight=3]; 130.25/78.12 398 -> 4125[label="",style="dashed", color="red", weight=0]; 130.25/78.12 398[label="FiniteMap.mkVBalBranch (Pos Zero) (FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)) zzz41) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)) zzz43) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)) zzz44)",fontsize=16,color="magenta"];398 -> 4126[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 398 -> 4127[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 398 -> 4128[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 398 -> 4129[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 399[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero) zzz41 zzz42 zzz43 zzz44 False",fontsize=16,color="black",shape="box"];399 -> 474[label="",style="solid", color="black", weight=3]; 130.25/78.12 14817[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM2 zzz1201 zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (Pos Zero < zzz1201)))",fontsize=16,color="black",shape="box"];14817 -> 14841[label="",style="solid", color="black", weight=3]; 130.25/78.12 401 -> 4125[label="",style="dashed", color="red", weight=0]; 130.25/78.12 401[label="FiniteMap.mkVBalBranch (Pos Zero) (FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)) zzz41) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)) zzz43) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)) zzz44)",fontsize=16,color="magenta"];401 -> 4130[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 401 -> 4131[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 401 -> 4132[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 401 -> 4133[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 402[label="FiniteMap.splitGT (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))",fontsize=16,color="black",shape="box"];402 -> 479[label="",style="solid", color="black", weight=3]; 130.25/78.12 403[label="FiniteMap.splitLT (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))",fontsize=16,color="black",shape="triangle"];403 -> 480[label="",style="solid", color="black", weight=3]; 130.25/78.12 404[label="FiniteMap.glueVBal5 FiniteMap.EmptyFM zzz5",fontsize=16,color="black",shape="box"];404 -> 481[label="",style="solid", color="black", weight=3]; 130.25/78.12 405[label="FiniteMap.glueVBal (FiniteMap.Branch zzz60 zzz61 zzz62 zzz63 zzz64) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];405 -> 482[label="",style="solid", color="black", weight=3]; 130.25/78.12 406[label="FiniteMap.glueVBal (FiniteMap.Branch zzz60 zzz61 zzz62 zzz63 zzz64) (FiniteMap.Branch zzz50 zzz51 zzz52 zzz53 zzz54)",fontsize=16,color="black",shape="box"];406 -> 483[label="",style="solid", color="black", weight=3]; 130.25/78.12 10612[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM zzz755 (Neg (Succ zzz747))))",fontsize=16,color="burlywood",shape="triangle"];64902[label="zzz755/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];10612 -> 64902[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64902 -> 10747[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64903[label="zzz755/FiniteMap.Branch zzz7550 zzz7551 zzz7552 zzz7553 zzz7554",fontsize=10,color="white",style="solid",shape="box"];10612 -> 64903[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64903 -> 10748[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 10613 -> 16650[label="",style="dashed", color="red", weight=0]; 130.25/78.12 10613[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz75200)) zzz753 zzz754 zzz755 zzz756 (Neg (Succ zzz747)) (primCmpNat zzz75200 zzz747 == LT)))",fontsize=16,color="magenta"];10613 -> 16651[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10613 -> 16652[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10613 -> 16653[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10613 -> 16654[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10613 -> 16655[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10613 -> 16656[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10613 -> 16657[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10613 -> 16658[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10613 -> 16659[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10613 -> 16660[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10613 -> 16661[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10613 -> 16662[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10613 -> 16663[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10613 -> 16664[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10613 -> 16665[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10613 -> 16666[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10613 -> 16667[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10614[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz753 zzz754 zzz755 zzz756 (Neg (Succ zzz747)) (LT == LT)))",fontsize=16,color="black",shape="box"];10614 -> 10751[label="",style="solid", color="black", weight=3]; 130.25/78.12 27135[label="zzz2146",fontsize=16,color="green",shape="box"];27136[label="Succ zzz2148",fontsize=16,color="green",shape="box"];27137[label="zzz2156",fontsize=16,color="green",shape="box"];27138[label="zzz2143",fontsize=16,color="green",shape="box"];27139[label="zzz2147",fontsize=16,color="green",shape="box"];27140[label="zzz2148",fontsize=16,color="green",shape="box"];27141[label="zzz2152",fontsize=16,color="green",shape="box"];27142[label="zzz2149",fontsize=16,color="green",shape="box"];27143[label="zzz2153",fontsize=16,color="green",shape="box"];27144[label="zzz2151",fontsize=16,color="green",shape="box"];27145[label="zzz2155",fontsize=16,color="green",shape="box"];27146[label="zzz2157",fontsize=16,color="green",shape="box"];27147[label="zzz2144",fontsize=16,color="green",shape="box"];27148[label="zzz2154",fontsize=16,color="green",shape="box"];27149[label="Succ zzz2153",fontsize=16,color="green",shape="box"];27150[label="zzz2145",fontsize=16,color="green",shape="box"];27151[label="zzz2150",fontsize=16,color="green",shape="box"];27134[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) zzz2633 zzz2634 zzz2635 zzz2636 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2637)) zzz2638 zzz2639 zzz2640 zzz2641 (Neg (Succ zzz2632)) (primCmpNat zzz2642 zzz2643 == GT)))",fontsize=16,color="burlywood",shape="triangle"];64904[label="zzz2642/Succ zzz26420",fontsize=10,color="white",style="solid",shape="box"];27134 -> 64904[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64904 -> 27322[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64905[label="zzz2642/Zero",fontsize=10,color="white",style="solid",shape="box"];27134 -> 64905[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64905 -> 27323[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 24648[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 False",fontsize=16,color="black",shape="box"];24648 -> 24693[label="",style="solid", color="black", weight=3]; 130.25/78.12 24649[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 zzz21560 zzz21561 zzz21562 zzz21563 zzz21564 (Neg (Succ zzz2148)) (compare (Neg (Succ zzz2148)) zzz21560 == LT)))",fontsize=16,color="black",shape="box"];24649 -> 24694[label="",style="solid", color="black", weight=3]; 130.25/78.12 425 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 425[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))) zzz44",fontsize=16,color="magenta"];425 -> 507[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 425 -> 508[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 426 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 426[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))) zzz43",fontsize=16,color="magenta"];426 -> 509[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 426 -> 510[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12140[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz8930) zzz894 zzz895 zzz896 zzz897 (Neg (Succ zzz888)) (LT == LT)))",fontsize=16,color="black",shape="box"];12140 -> 12218[label="",style="solid", color="black", weight=3]; 130.25/78.12 12141[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz8930) zzz894 zzz895 zzz896 zzz897 (Neg (Succ zzz888)) (primCmpNat zzz8930 (Succ zzz888) == LT)))",fontsize=16,color="burlywood",shape="box"];64906[label="zzz8930/Succ zzz89300",fontsize=10,color="white",style="solid",shape="box"];12141 -> 64906[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64906 -> 12219[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64907[label="zzz8930/Zero",fontsize=10,color="white",style="solid",shape="box"];12141 -> 64907[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64907 -> 12220[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 11805 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 11805[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero)) zzz838",fontsize=16,color="magenta"];11805 -> 11967[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 11805 -> 11968[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 11806 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 11806[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero)) zzz837",fontsize=16,color="magenta"];11806 -> 11969[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 11806 -> 11970[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12214[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz90800)) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (LT == LT)))",fontsize=16,color="black",shape="box"];12214 -> 12270[label="",style="solid", color="black", weight=3]; 130.25/78.12 12215[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (EQ == LT)))",fontsize=16,color="black",shape="box"];12215 -> 12271[label="",style="solid", color="black", weight=3]; 130.25/78.12 12216[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz90800)) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (primCmpNat (Succ zzz90800) Zero == LT)))",fontsize=16,color="black",shape="box"];12216 -> 12272[label="",style="solid", color="black", weight=3]; 130.25/78.12 12217[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (EQ == LT)))",fontsize=16,color="black",shape="box"];12217 -> 12273[label="",style="solid", color="black", weight=3]; 130.25/78.12 438 -> 5407[label="",style="dashed", color="red", weight=0]; 130.25/78.12 438[label="FiniteMap.mkVBalBranch (Neg Zero) (FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)) zzz41) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)) zzz43) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)) zzz44)",fontsize=16,color="magenta"];438 -> 5408[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 438 -> 5409[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 438 -> 5410[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 439[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Neg Zero)))",fontsize=16,color="black",shape="box"];439 -> 523[label="",style="solid", color="black", weight=3]; 130.25/78.12 440 -> 19318[label="",style="dashed", color="red", weight=0]; 130.25/78.12 440[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344) (Neg Zero)))",fontsize=16,color="magenta"];440 -> 19319[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 440 -> 19320[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 440 -> 19321[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 440 -> 19322[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 440 -> 19323[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 440 -> 19324[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 440 -> 19325[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 440 -> 19326[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 440 -> 19327[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 440 -> 19328[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 440 -> 19329[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 440 -> 19330[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 440 -> 19331[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 440 -> 19332[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 441 -> 5407[label="",style="dashed", color="red", weight=0]; 130.25/78.12 441[label="FiniteMap.mkVBalBranch (Neg Zero) (FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)) zzz41) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)) zzz43) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)) zzz44)",fontsize=16,color="magenta"];441 -> 5411[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 441 -> 5412[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 441 -> 5413[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 27132[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) zzz2615 zzz2616 zzz2617 zzz2618 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz2619)) zzz2620 zzz2621 zzz2622 zzz2623 (Pos (Succ zzz2614)) (primCmpNat (Succ zzz26240) zzz2625 == GT)))",fontsize=16,color="burlywood",shape="box"];64908[label="zzz2625/Succ zzz26250",fontsize=10,color="white",style="solid",shape="box"];27132 -> 64908[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64908 -> 27324[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64909[label="zzz2625/Zero",fontsize=10,color="white",style="solid",shape="box"];27132 -> 64909[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64909 -> 27325[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 27133[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) zzz2615 zzz2616 zzz2617 zzz2618 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz2619)) zzz2620 zzz2621 zzz2622 zzz2623 (Pos (Succ zzz2614)) (primCmpNat Zero zzz2625 == GT)))",fontsize=16,color="burlywood",shape="box"];64910[label="zzz2625/Succ zzz26250",fontsize=10,color="white",style="solid",shape="box"];27133 -> 64910[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64910 -> 27326[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64911[label="zzz2625/Zero",fontsize=10,color="white",style="solid",shape="box"];27133 -> 64911[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64911 -> 27327[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 24196[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 otherwise",fontsize=16,color="black",shape="box"];24196 -> 24248[label="",style="solid", color="black", weight=3]; 130.25/78.12 24197[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 zzz20910 zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (primCmpInt (Pos (Succ zzz2083)) zzz20910 == LT)))",fontsize=16,color="burlywood",shape="box"];64912[label="zzz20910/Pos zzz209100",fontsize=10,color="white",style="solid",shape="box"];24197 -> 64912[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64912 -> 24249[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64913[label="zzz20910/Neg zzz209100",fontsize=10,color="white",style="solid",shape="box"];24197 -> 64913[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64913 -> 24250[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 458[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust Nothing)",fontsize=16,color="black",shape="box"];458 -> 545[label="",style="solid", color="black", weight=3]; 130.25/78.12 459 -> 27965[label="",style="dashed", color="red", weight=0]; 130.25/78.12 459[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust (FiniteMap.lookupFM2 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz4000)) (Pos (Succ zzz4000) < zzz340)))",fontsize=16,color="magenta"];459 -> 27966[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 459 -> 27967[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 459 -> 27968[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 459 -> 27969[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 459 -> 27970[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 459 -> 27971[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 459 -> 27972[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 459 -> 27973[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 459 -> 27974[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 459 -> 27975[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 459 -> 27976[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 459 -> 27977[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 459 -> 27978[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 459 -> 27979[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 460[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 True",fontsize=16,color="black",shape="box"];460 -> 547[label="",style="solid", color="black", weight=3]; 130.25/78.12 17229[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM2 zzz1392 zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (primCmpInt (Pos (Succ zzz1387)) zzz1392 == LT)))",fontsize=16,color="burlywood",shape="box"];64914[label="zzz1392/Pos zzz13920",fontsize=10,color="white",style="solid",shape="box"];17229 -> 64914[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64914 -> 17562[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64915[label="zzz1392/Neg zzz13920",fontsize=10,color="white",style="solid",shape="box"];17229 -> 64915[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64915 -> 17563[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 463[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero)",fontsize=16,color="black",shape="box"];463 -> 550[label="",style="solid", color="black", weight=3]; 130.25/78.12 464[label="zzz44",fontsize=16,color="green",shape="box"];465[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero)",fontsize=16,color="black",shape="box"];465 -> 551[label="",style="solid", color="black", weight=3]; 130.25/78.12 466[label="zzz43",fontsize=16,color="green",shape="box"];9455[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz62700)) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (primCmpNat Zero (Succ zzz62700) == LT)))",fontsize=16,color="black",shape="box"];9455 -> 9524[label="",style="solid", color="black", weight=3]; 130.25/78.12 9456[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (EQ == LT)))",fontsize=16,color="black",shape="box"];9456 -> 9525[label="",style="solid", color="black", weight=3]; 130.25/78.12 9457[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz62700)) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (GT == LT)))",fontsize=16,color="black",shape="box"];9457 -> 9526[label="",style="solid", color="black", weight=3]; 130.25/78.12 9458[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (EQ == LT)))",fontsize=16,color="black",shape="box"];9458 -> 9527[label="",style="solid", color="black", weight=3]; 130.25/78.12 4126 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 4126[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)) zzz43",fontsize=16,color="magenta"];4126 -> 4216[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 4126 -> 4217[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 4127[label="Zero",fontsize=16,color="green",shape="box"];4128 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 4128[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)) zzz44",fontsize=16,color="magenta"];4128 -> 4218[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 4128 -> 4219[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 4129[label="FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)) zzz41",fontsize=16,color="black",shape="box"];4129 -> 4220[label="",style="solid", color="black", weight=3]; 130.25/78.12 4125[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 zzz250 zzz34",fontsize=16,color="burlywood",shape="triangle"];64916[label="zzz250/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];4125 -> 64916[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64916 -> 4221[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64917[label="zzz250/FiniteMap.Branch zzz2500 zzz2501 zzz2502 zzz2503 zzz2504",fontsize=10,color="white",style="solid",shape="box"];4125 -> 64917[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64917 -> 4222[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 474[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero) zzz41 zzz42 zzz43 zzz44 otherwise",fontsize=16,color="black",shape="box"];474 -> 562[label="",style="solid", color="black", weight=3]; 130.25/78.12 14841[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM2 zzz1201 zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (compare (Pos Zero) zzz1201 == LT)))",fontsize=16,color="black",shape="box"];14841 -> 14863[label="",style="solid", color="black", weight=3]; 130.25/78.12 4130 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 4130[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)) zzz43",fontsize=16,color="magenta"];4130 -> 4223[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 4130 -> 4224[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 4131[label="Zero",fontsize=16,color="green",shape="box"];4132 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 4132[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)) zzz44",fontsize=16,color="magenta"];4132 -> 4225[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 4132 -> 4226[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 4133[label="FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)) zzz41",fontsize=16,color="black",shape="box"];4133 -> 4227[label="",style="solid", color="black", weight=3]; 130.25/78.12 479[label="FiniteMap.splitGT3 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))",fontsize=16,color="black",shape="box"];479 -> 571[label="",style="solid", color="black", weight=3]; 130.25/78.12 480[label="FiniteMap.splitLT3 (FiniteMap.Branch (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))",fontsize=16,color="black",shape="box"];480 -> 572[label="",style="solid", color="black", weight=3]; 130.25/78.12 481[label="zzz5",fontsize=16,color="green",shape="box"];482[label="FiniteMap.glueVBal4 (FiniteMap.Branch zzz60 zzz61 zzz62 zzz63 zzz64) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];482 -> 573[label="",style="solid", color="black", weight=3]; 130.25/78.12 483[label="FiniteMap.glueVBal3 (FiniteMap.Branch zzz60 zzz61 zzz62 zzz63 zzz64) (FiniteMap.Branch zzz50 zzz51 zzz52 zzz53 zzz54)",fontsize=16,color="black",shape="box"];483 -> 574[label="",style="solid", color="black", weight=3]; 130.25/78.12 10747[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM FiniteMap.EmptyFM (Neg (Succ zzz747))))",fontsize=16,color="black",shape="box"];10747 -> 10955[label="",style="solid", color="black", weight=3]; 130.25/78.12 10748[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM (FiniteMap.Branch zzz7550 zzz7551 zzz7552 zzz7553 zzz7554) (Neg (Succ zzz747))))",fontsize=16,color="black",shape="box"];10748 -> 10956[label="",style="solid", color="black", weight=3]; 130.25/78.12 16651[label="zzz743",fontsize=16,color="green",shape="box"];16652[label="zzz750",fontsize=16,color="green",shape="box"];16653[label="zzz744",fontsize=16,color="green",shape="box"];16654[label="zzz755",fontsize=16,color="green",shape="box"];16655[label="zzz747",fontsize=16,color="green",shape="box"];16656[label="zzz75200",fontsize=16,color="green",shape="box"];16657[label="zzz745",fontsize=16,color="green",shape="box"];16658[label="zzz746",fontsize=16,color="green",shape="box"];16659[label="zzz749",fontsize=16,color="green",shape="box"];16660[label="zzz75200",fontsize=16,color="green",shape="box"];16661[label="zzz753",fontsize=16,color="green",shape="box"];16662[label="zzz754",fontsize=16,color="green",shape="box"];16663[label="zzz756",fontsize=16,color="green",shape="box"];16664[label="zzz748",fontsize=16,color="green",shape="box"];16665[label="zzz747",fontsize=16,color="green",shape="box"];16666[label="zzz742",fontsize=16,color="green",shape="box"];16667[label="zzz751",fontsize=16,color="green",shape="box"];16650[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) zzz1404 zzz1405 zzz1406 zzz1407 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1408)) zzz1409 zzz1410 zzz1411 zzz1412 (Neg (Succ zzz1403)) (primCmpNat zzz1413 zzz1414 == LT)))",fontsize=16,color="burlywood",shape="triangle"];64918[label="zzz1413/Succ zzz14130",fontsize=10,color="white",style="solid",shape="box"];16650 -> 64918[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64918 -> 16822[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64919[label="zzz1413/Zero",fontsize=10,color="white",style="solid",shape="box"];16650 -> 64919[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64919 -> 16823[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 10751[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz753 zzz754 zzz755 zzz756 (Neg (Succ zzz747)) True))",fontsize=16,color="black",shape="box"];10751 -> 10961[label="",style="solid", color="black", weight=3]; 130.25/78.12 27322[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) zzz2633 zzz2634 zzz2635 zzz2636 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2637)) zzz2638 zzz2639 zzz2640 zzz2641 (Neg (Succ zzz2632)) (primCmpNat (Succ zzz26420) zzz2643 == GT)))",fontsize=16,color="burlywood",shape="box"];64920[label="zzz2643/Succ zzz26430",fontsize=10,color="white",style="solid",shape="box"];27322 -> 64920[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64920 -> 27370[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64921[label="zzz2643/Zero",fontsize=10,color="white",style="solid",shape="box"];27322 -> 64921[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64921 -> 27371[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 27323[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) zzz2633 zzz2634 zzz2635 zzz2636 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2637)) zzz2638 zzz2639 zzz2640 zzz2641 (Neg (Succ zzz2632)) (primCmpNat Zero zzz2643 == GT)))",fontsize=16,color="burlywood",shape="box"];64922[label="zzz2643/Succ zzz26430",fontsize=10,color="white",style="solid",shape="box"];27323 -> 64922[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64922 -> 27372[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64923[label="zzz2643/Zero",fontsize=10,color="white",style="solid",shape="box"];27323 -> 64923[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64923 -> 27373[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 24693[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 otherwise",fontsize=16,color="black",shape="box"];24693 -> 24739[label="",style="solid", color="black", weight=3]; 130.25/78.12 24694[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 zzz21560 zzz21561 zzz21562 zzz21563 zzz21564 (Neg (Succ zzz2148)) (primCmpInt (Neg (Succ zzz2148)) zzz21560 == LT)))",fontsize=16,color="burlywood",shape="box"];64924[label="zzz21560/Pos zzz215600",fontsize=10,color="white",style="solid",shape="box"];24694 -> 64924[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64924 -> 24740[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64925[label="zzz21560/Neg zzz215600",fontsize=10,color="white",style="solid",shape="box"];24694 -> 64925[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64925 -> 24741[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 507[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))",fontsize=16,color="black",shape="box"];507 -> 600[label="",style="solid", color="black", weight=3]; 130.25/78.12 508[label="zzz44",fontsize=16,color="green",shape="box"];509[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))",fontsize=16,color="black",shape="box"];509 -> 601[label="",style="solid", color="black", weight=3]; 130.25/78.12 510[label="zzz43",fontsize=16,color="green",shape="box"];12218[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz8930) zzz894 zzz895 zzz896 zzz897 (Neg (Succ zzz888)) True))",fontsize=16,color="black",shape="box"];12218 -> 12274[label="",style="solid", color="black", weight=3]; 130.25/78.12 12219[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz89300)) zzz894 zzz895 zzz896 zzz897 (Neg (Succ zzz888)) (primCmpNat (Succ zzz89300) (Succ zzz888) == LT)))",fontsize=16,color="black",shape="box"];12219 -> 12275[label="",style="solid", color="black", weight=3]; 130.25/78.12 12220[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz894 zzz895 zzz896 zzz897 (Neg (Succ zzz888)) (primCmpNat Zero (Succ zzz888) == LT)))",fontsize=16,color="black",shape="box"];12220 -> 12276[label="",style="solid", color="black", weight=3]; 130.25/78.12 11967[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero)",fontsize=16,color="black",shape="triangle"];11967 -> 12080[label="",style="solid", color="black", weight=3]; 130.25/78.12 11968[label="zzz838",fontsize=16,color="green",shape="box"];11969[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero)",fontsize=16,color="black",shape="triangle"];11969 -> 12081[label="",style="solid", color="black", weight=3]; 130.25/78.12 11970[label="zzz837",fontsize=16,color="green",shape="box"];12270[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz90800)) zzz909 zzz910 zzz911 zzz912 (Neg Zero) True))",fontsize=16,color="black",shape="box"];12270 -> 12369[label="",style="solid", color="black", weight=3]; 130.25/78.12 12271[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) False))",fontsize=16,color="black",shape="box"];12271 -> 12370[label="",style="solid", color="black", weight=3]; 130.25/78.12 12272[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz90800)) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (GT == LT)))",fontsize=16,color="black",shape="box"];12272 -> 12371[label="",style="solid", color="black", weight=3]; 130.25/78.12 12273[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) False))",fontsize=16,color="black",shape="box"];12273 -> 12372[label="",style="solid", color="black", weight=3]; 130.25/78.12 5408 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 5408[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)) zzz43",fontsize=16,color="magenta"];5408 -> 5440[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 5408 -> 5441[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 5409 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 5409[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)) zzz44",fontsize=16,color="magenta"];5409 -> 5442[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 5409 -> 5443[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 5410[label="FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)) zzz41",fontsize=16,color="black",shape="box"];5410 -> 5444[label="",style="solid", color="black", weight=3]; 130.25/78.12 5407[label="FiniteMap.mkVBalBranch (Neg Zero) zzz31 zzz353 zzz34",fontsize=16,color="burlywood",shape="triangle"];64926[label="zzz353/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];5407 -> 64926[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64926 -> 5445[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64927[label="zzz353/FiniteMap.Branch zzz3530 zzz3531 zzz3532 zzz3533 zzz3534",fontsize=10,color="white",style="solid",shape="box"];5407 -> 64927[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64927 -> 5446[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 523[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero) zzz41 zzz42 zzz43 zzz44 (Maybe.isJust Nothing)",fontsize=16,color="black",shape="box"];523 -> 620[label="",style="solid", color="black", weight=3]; 130.25/78.12 19319[label="zzz44",fontsize=16,color="green",shape="box"];19320[label="zzz33",fontsize=16,color="green",shape="box"];19321[label="zzz43",fontsize=16,color="green",shape="box"];19322[label="zzz343",fontsize=16,color="green",shape="box"];19323[label="zzz31",fontsize=16,color="green",shape="box"];19324[label="zzz32",fontsize=16,color="green",shape="box"];19325[label="zzz41",fontsize=16,color="green",shape="box"];19326[label="zzz42",fontsize=16,color="green",shape="box"];19327[label="zzz340",fontsize=16,color="green",shape="box"];19328[label="zzz341",fontsize=16,color="green",shape="box"];19329[label="zzz342",fontsize=16,color="green",shape="box"];19330[label="zzz344",fontsize=16,color="green",shape="box"];19331[label="FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344",fontsize=16,color="green",shape="box"];19332[label="zzz3000",fontsize=16,color="green",shape="box"];19318[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz1603 zzz1604 zzz1605 zzz1606 zzz1607) (Neg Zero)))",fontsize=16,color="black",shape="triangle"];19318 -> 19403[label="",style="solid", color="black", weight=3]; 130.25/78.12 5411 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 5411[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)) zzz43",fontsize=16,color="magenta"];5411 -> 5447[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 5411 -> 5448[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 5412 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 5412[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)) zzz44",fontsize=16,color="magenta"];5412 -> 5449[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 5412 -> 5450[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 5413[label="FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)) zzz41",fontsize=16,color="black",shape="box"];5413 -> 5451[label="",style="solid", color="black", weight=3]; 130.25/78.12 27324[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) zzz2615 zzz2616 zzz2617 zzz2618 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz2619)) zzz2620 zzz2621 zzz2622 zzz2623 (Pos (Succ zzz2614)) (primCmpNat (Succ zzz26240) (Succ zzz26250) == GT)))",fontsize=16,color="black",shape="box"];27324 -> 27374[label="",style="solid", color="black", weight=3]; 130.25/78.12 27325[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) zzz2615 zzz2616 zzz2617 zzz2618 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz2619)) zzz2620 zzz2621 zzz2622 zzz2623 (Pos (Succ zzz2614)) (primCmpNat (Succ zzz26240) Zero == GT)))",fontsize=16,color="black",shape="box"];27325 -> 27375[label="",style="solid", color="black", weight=3]; 130.25/78.12 27326[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) zzz2615 zzz2616 zzz2617 zzz2618 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz2619)) zzz2620 zzz2621 zzz2622 zzz2623 (Pos (Succ zzz2614)) (primCmpNat Zero (Succ zzz26250) == GT)))",fontsize=16,color="black",shape="box"];27326 -> 27376[label="",style="solid", color="black", weight=3]; 130.25/78.12 27327[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) zzz2615 zzz2616 zzz2617 zzz2618 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz2619)) zzz2620 zzz2621 zzz2622 zzz2623 (Pos (Succ zzz2614)) (primCmpNat Zero Zero == GT)))",fontsize=16,color="black",shape="box"];27327 -> 27377[label="",style="solid", color="black", weight=3]; 130.25/78.12 24248[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 True",fontsize=16,color="black",shape="box"];24248 -> 24283[label="",style="solid", color="black", weight=3]; 130.25/78.12 24249[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz209100) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (primCmpInt (Pos (Succ zzz2083)) (Pos zzz209100) == LT)))",fontsize=16,color="black",shape="box"];24249 -> 24284[label="",style="solid", color="black", weight=3]; 130.25/78.12 24250[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz209100) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (primCmpInt (Pos (Succ zzz2083)) (Neg zzz209100) == LT)))",fontsize=16,color="black",shape="box"];24250 -> 24285[label="",style="solid", color="black", weight=3]; 130.25/78.12 545[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 False",fontsize=16,color="black",shape="box"];545 -> 649[label="",style="solid", color="black", weight=3]; 130.25/78.12 27966[label="zzz44",fontsize=16,color="green",shape="box"];27967[label="zzz341",fontsize=16,color="green",shape="box"];27968[label="zzz41",fontsize=16,color="green",shape="box"];27969[label="zzz42",fontsize=16,color="green",shape="box"];27970[label="zzz344",fontsize=16,color="green",shape="box"];27971[label="zzz31",fontsize=16,color="green",shape="box"];27972[label="zzz32",fontsize=16,color="green",shape="box"];27973[label="zzz342",fontsize=16,color="green",shape="box"];27974[label="zzz343",fontsize=16,color="green",shape="box"];27975[label="FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344",fontsize=16,color="green",shape="box"];27976[label="zzz33",fontsize=16,color="green",shape="box"];27977[label="zzz340",fontsize=16,color="green",shape="box"];27978[label="zzz4000",fontsize=16,color="green",shape="box"];27979[label="zzz43",fontsize=16,color="green",shape="box"];27965[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM2 zzz2743 zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (Pos (Succ zzz2738) < zzz2743)))",fontsize=16,color="black",shape="triangle"];27965 -> 28134[label="",style="solid", color="black", weight=3]; 130.25/78.12 547 -> 288[label="",style="dashed", color="red", weight=0]; 130.25/78.12 547[label="FiniteMap.glueVBal (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))) zzz43) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))) zzz44)",fontsize=16,color="magenta"];547 -> 651[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 547 -> 652[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 17562[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz13920) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (primCmpInt (Pos (Succ zzz1387)) (Pos zzz13920) == LT)))",fontsize=16,color="black",shape="box"];17562 -> 17670[label="",style="solid", color="black", weight=3]; 130.25/78.12 17563[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz13920) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (primCmpInt (Pos (Succ zzz1387)) (Neg zzz13920) == LT)))",fontsize=16,color="black",shape="box"];17563 -> 17671[label="",style="solid", color="black", weight=3]; 130.25/78.12 550[label="FiniteMap.splitGT (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero)",fontsize=16,color="black",shape="box"];550 -> 656[label="",style="solid", color="black", weight=3]; 130.25/78.12 551[label="FiniteMap.splitLT (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero)",fontsize=16,color="black",shape="box"];551 -> 657[label="",style="solid", color="black", weight=3]; 130.25/78.12 9524[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz62700)) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (LT == LT)))",fontsize=16,color="black",shape="box"];9524 -> 9733[label="",style="solid", color="black", weight=3]; 130.25/78.12 9525[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) False))",fontsize=16,color="black",shape="box"];9525 -> 9734[label="",style="solid", color="black", weight=3]; 130.25/78.12 9526[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz62700)) zzz628 zzz629 zzz630 zzz631 (Pos Zero) False))",fontsize=16,color="black",shape="box"];9526 -> 9735[label="",style="solid", color="black", weight=3]; 130.25/78.12 9527[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) False))",fontsize=16,color="black",shape="box"];9527 -> 9736[label="",style="solid", color="black", weight=3]; 130.25/78.12 4216[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)",fontsize=16,color="black",shape="box"];4216 -> 4300[label="",style="solid", color="black", weight=3]; 130.25/78.12 4217[label="zzz43",fontsize=16,color="green",shape="box"];4218[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)",fontsize=16,color="black",shape="box"];4218 -> 4301[label="",style="solid", color="black", weight=3]; 130.25/78.12 4219[label="zzz44",fontsize=16,color="green",shape="box"];4220[label="zzz41",fontsize=16,color="green",shape="box"];4221[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 FiniteMap.EmptyFM zzz34",fontsize=16,color="black",shape="box"];4221 -> 4302[label="",style="solid", color="black", weight=3]; 130.25/78.12 4222[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 zzz2502 zzz2503 zzz2504) zzz34",fontsize=16,color="burlywood",shape="box"];64928[label="zzz34/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];4222 -> 64928[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64928 -> 4303[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64929[label="zzz34/FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344",fontsize=10,color="white",style="solid",shape="box"];4222 -> 64929[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64929 -> 4304[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 562[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero) zzz41 zzz42 zzz43 zzz44 True",fontsize=16,color="black",shape="box"];562 -> 667[label="",style="solid", color="black", weight=3]; 130.25/78.12 14863[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM2 zzz1201 zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (primCmpInt (Pos Zero) zzz1201 == LT)))",fontsize=16,color="burlywood",shape="box"];64930[label="zzz1201/Pos zzz12010",fontsize=10,color="white",style="solid",shape="box"];14863 -> 64930[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64930 -> 14901[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64931[label="zzz1201/Neg zzz12010",fontsize=10,color="white",style="solid",shape="box"];14863 -> 64931[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64931 -> 14902[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 4223[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)",fontsize=16,color="black",shape="box"];4223 -> 4305[label="",style="solid", color="black", weight=3]; 130.25/78.12 4224[label="zzz43",fontsize=16,color="green",shape="box"];4225[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)",fontsize=16,color="black",shape="box"];4225 -> 4306[label="",style="solid", color="black", weight=3]; 130.25/78.12 4226[label="zzz44",fontsize=16,color="green",shape="box"];4227[label="zzz41",fontsize=16,color="green",shape="box"];571[label="FiniteMap.splitGT2 (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (Neg (Succ zzz4000) > Pos zzz300)",fontsize=16,color="black",shape="box"];571 -> 677[label="",style="solid", color="black", weight=3]; 130.25/78.12 572[label="FiniteMap.splitLT2 (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (Neg (Succ zzz4000) < Pos zzz300)",fontsize=16,color="black",shape="box"];572 -> 678[label="",style="solid", color="black", weight=3]; 130.25/78.12 573[label="FiniteMap.Branch zzz60 zzz61 zzz62 zzz63 zzz64",fontsize=16,color="green",shape="box"];574 -> 62159[label="",style="dashed", color="red", weight=0]; 130.25/78.12 574[label="FiniteMap.glueVBal3GlueVBal2 zzz50 zzz51 zzz52 zzz53 zzz54 zzz60 zzz61 zzz62 zzz63 zzz64 zzz60 zzz61 zzz62 zzz63 zzz64 zzz50 zzz51 zzz52 zzz53 zzz54 (FiniteMap.sIZE_RATIO * FiniteMap.glueVBal3Size_l zzz50 zzz51 zzz52 zzz53 zzz54 zzz60 zzz61 zzz62 zzz63 zzz64 < FiniteMap.glueVBal3Size_r zzz50 zzz51 zzz52 zzz53 zzz54 zzz60 zzz61 zzz62 zzz63 zzz64)",fontsize=16,color="magenta"];574 -> 62160[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 574 -> 62161[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 574 -> 62162[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 574 -> 62163[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 574 -> 62164[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 574 -> 62165[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 574 -> 62166[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 574 -> 62167[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 574 -> 62168[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 574 -> 62169[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 574 -> 62170[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 10955[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Neg (Succ zzz747))))",fontsize=16,color="black",shape="box"];10955 -> 11143[label="",style="solid", color="black", weight=3]; 130.25/78.12 10956[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz7550 zzz7551 zzz7552 zzz7553 zzz7554) (Neg (Succ zzz747))))",fontsize=16,color="black",shape="box"];10956 -> 11144[label="",style="solid", color="black", weight=3]; 130.25/78.12 16822[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) zzz1404 zzz1405 zzz1406 zzz1407 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1408)) zzz1409 zzz1410 zzz1411 zzz1412 (Neg (Succ zzz1403)) (primCmpNat (Succ zzz14130) zzz1414 == LT)))",fontsize=16,color="burlywood",shape="box"];64932[label="zzz1414/Succ zzz14140",fontsize=10,color="white",style="solid",shape="box"];16822 -> 64932[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64932 -> 17230[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64933[label="zzz1414/Zero",fontsize=10,color="white",style="solid",shape="box"];16822 -> 64933[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64933 -> 17231[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 16823[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) zzz1404 zzz1405 zzz1406 zzz1407 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1408)) zzz1409 zzz1410 zzz1411 zzz1412 (Neg (Succ zzz1403)) (primCmpNat Zero zzz1414 == LT)))",fontsize=16,color="burlywood",shape="box"];64934[label="zzz1414/Succ zzz14140",fontsize=10,color="white",style="solid",shape="box"];16823 -> 64934[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64934 -> 17232[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64935[label="zzz1414/Zero",fontsize=10,color="white",style="solid",shape="box"];16823 -> 64935[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64935 -> 17233[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 10961 -> 10612[label="",style="dashed", color="red", weight=0]; 130.25/78.12 10961[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM zzz755 (Neg (Succ zzz747))))",fontsize=16,color="magenta"];27370[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) zzz2633 zzz2634 zzz2635 zzz2636 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2637)) zzz2638 zzz2639 zzz2640 zzz2641 (Neg (Succ zzz2632)) (primCmpNat (Succ zzz26420) (Succ zzz26430) == GT)))",fontsize=16,color="black",shape="box"];27370 -> 27472[label="",style="solid", color="black", weight=3]; 130.25/78.12 27371[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) zzz2633 zzz2634 zzz2635 zzz2636 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2637)) zzz2638 zzz2639 zzz2640 zzz2641 (Neg (Succ zzz2632)) (primCmpNat (Succ zzz26420) Zero == GT)))",fontsize=16,color="black",shape="box"];27371 -> 27473[label="",style="solid", color="black", weight=3]; 130.25/78.12 27372[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) zzz2633 zzz2634 zzz2635 zzz2636 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2637)) zzz2638 zzz2639 zzz2640 zzz2641 (Neg (Succ zzz2632)) (primCmpNat Zero (Succ zzz26430) == GT)))",fontsize=16,color="black",shape="box"];27372 -> 27474[label="",style="solid", color="black", weight=3]; 130.25/78.12 27373[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) zzz2633 zzz2634 zzz2635 zzz2636 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2637)) zzz2638 zzz2639 zzz2640 zzz2641 (Neg (Succ zzz2632)) (primCmpNat Zero Zero == GT)))",fontsize=16,color="black",shape="box"];27373 -> 27475[label="",style="solid", color="black", weight=3]; 130.25/78.12 24739[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 True",fontsize=16,color="black",shape="box"];24739 -> 24803[label="",style="solid", color="black", weight=3]; 130.25/78.12 24740[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz215600) zzz21561 zzz21562 zzz21563 zzz21564 (Neg (Succ zzz2148)) (primCmpInt (Neg (Succ zzz2148)) (Pos zzz215600) == LT)))",fontsize=16,color="black",shape="box"];24740 -> 24804[label="",style="solid", color="black", weight=3]; 130.25/78.12 24741[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz215600) zzz21561 zzz21562 zzz21563 zzz21564 (Neg (Succ zzz2148)) (primCmpInt (Neg (Succ zzz2148)) (Neg zzz215600) == LT)))",fontsize=16,color="black",shape="box"];24741 -> 24805[label="",style="solid", color="black", weight=3]; 130.25/78.12 600[label="FiniteMap.splitGT (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))",fontsize=16,color="black",shape="box"];600 -> 710[label="",style="solid", color="black", weight=3]; 130.25/78.12 601[label="FiniteMap.splitLT (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))",fontsize=16,color="black",shape="triangle"];601 -> 711[label="",style="solid", color="black", weight=3]; 130.25/78.12 12274[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM zzz896 (Neg (Succ zzz888))))",fontsize=16,color="burlywood",shape="triangle"];64936[label="zzz896/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];12274 -> 64936[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64936 -> 12373[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64937[label="zzz896/FiniteMap.Branch zzz8960 zzz8961 zzz8962 zzz8963 zzz8964",fontsize=10,color="white",style="solid",shape="box"];12274 -> 64937[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64937 -> 12374[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 12275 -> 19020[label="",style="dashed", color="red", weight=0]; 130.25/78.12 12275[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz89300)) zzz894 zzz895 zzz896 zzz897 (Neg (Succ zzz888)) (primCmpNat zzz89300 zzz888 == LT)))",fontsize=16,color="magenta"];12275 -> 19021[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12275 -> 19022[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12275 -> 19023[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12275 -> 19024[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12275 -> 19025[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12275 -> 19026[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12275 -> 19027[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12275 -> 19028[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12275 -> 19029[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12275 -> 19030[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12275 -> 19031[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12275 -> 19032[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12275 -> 19033[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12275 -> 19034[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12275 -> 19035[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12275 -> 19036[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12276[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz894 zzz895 zzz896 zzz897 (Neg (Succ zzz888)) (LT == LT)))",fontsize=16,color="black",shape="box"];12276 -> 12377[label="",style="solid", color="black", weight=3]; 130.25/78.12 12080[label="FiniteMap.splitGT (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero)",fontsize=16,color="black",shape="box"];12080 -> 12142[label="",style="solid", color="black", weight=3]; 130.25/78.12 12081[label="FiniteMap.splitLT (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero)",fontsize=16,color="black",shape="box"];12081 -> 12143[label="",style="solid", color="black", weight=3]; 130.25/78.12 12369[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM zzz911 (Neg Zero)))",fontsize=16,color="burlywood",shape="triangle"];64938[label="zzz911/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];12369 -> 64938[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64938 -> 12460[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64939[label="zzz911/FiniteMap.Branch zzz9110 zzz9111 zzz9112 zzz9113 zzz9114",fontsize=10,color="white",style="solid",shape="box"];12369 -> 64939[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64939 -> 12461[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 12370[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (Neg Zero > Pos Zero)))",fontsize=16,color="black",shape="box"];12370 -> 12462[label="",style="solid", color="black", weight=3]; 130.25/78.12 12371[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz90800)) zzz909 zzz910 zzz911 zzz912 (Neg Zero) False))",fontsize=16,color="black",shape="box"];12371 -> 12463[label="",style="solid", color="black", weight=3]; 130.25/78.12 12372[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (Neg Zero > Neg Zero)))",fontsize=16,color="black",shape="box"];12372 -> 12464[label="",style="solid", color="black", weight=3]; 130.25/78.12 5440[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)",fontsize=16,color="black",shape="box"];5440 -> 5510[label="",style="solid", color="black", weight=3]; 130.25/78.12 5441[label="zzz43",fontsize=16,color="green",shape="box"];5442[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)",fontsize=16,color="black",shape="box"];5442 -> 5511[label="",style="solid", color="black", weight=3]; 130.25/78.12 5443[label="zzz44",fontsize=16,color="green",shape="box"];5444[label="zzz41",fontsize=16,color="green",shape="box"];5445[label="FiniteMap.mkVBalBranch (Neg Zero) zzz31 FiniteMap.EmptyFM zzz34",fontsize=16,color="black",shape="box"];5445 -> 5512[label="",style="solid", color="black", weight=3]; 130.25/78.12 5446[label="FiniteMap.mkVBalBranch (Neg Zero) zzz31 (FiniteMap.Branch zzz3530 zzz3531 zzz3532 zzz3533 zzz3534) zzz34",fontsize=16,color="burlywood",shape="box"];64940[label="zzz34/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];5446 -> 64940[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64940 -> 5513[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64941[label="zzz34/FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344",fontsize=10,color="white",style="solid",shape="box"];5446 -> 64941[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64941 -> 5514[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 620[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero) zzz41 zzz42 zzz43 zzz44 False",fontsize=16,color="black",shape="box"];620 -> 731[label="",style="solid", color="black", weight=3]; 130.25/78.12 19403[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM2 zzz1603 zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (Neg Zero < zzz1603)))",fontsize=16,color="black",shape="box"];19403 -> 19542[label="",style="solid", color="black", weight=3]; 130.25/78.12 5447[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)",fontsize=16,color="black",shape="box"];5447 -> 5515[label="",style="solid", color="black", weight=3]; 130.25/78.12 5448[label="zzz43",fontsize=16,color="green",shape="box"];5449[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)",fontsize=16,color="black",shape="box"];5449 -> 5516[label="",style="solid", color="black", weight=3]; 130.25/78.12 5450[label="zzz44",fontsize=16,color="green",shape="box"];5451[label="zzz41",fontsize=16,color="green",shape="box"];27374 -> 26944[label="",style="dashed", color="red", weight=0]; 130.25/78.12 27374[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) zzz2615 zzz2616 zzz2617 zzz2618 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz2619)) zzz2620 zzz2621 zzz2622 zzz2623 (Pos (Succ zzz2614)) (primCmpNat zzz26240 zzz26250 == GT)))",fontsize=16,color="magenta"];27374 -> 27476[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 27374 -> 27477[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 27375[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) zzz2615 zzz2616 zzz2617 zzz2618 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz2619)) zzz2620 zzz2621 zzz2622 zzz2623 (Pos (Succ zzz2614)) (GT == GT)))",fontsize=16,color="black",shape="box"];27375 -> 27478[label="",style="solid", color="black", weight=3]; 130.25/78.12 27376[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) zzz2615 zzz2616 zzz2617 zzz2618 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz2619)) zzz2620 zzz2621 zzz2622 zzz2623 (Pos (Succ zzz2614)) (LT == GT)))",fontsize=16,color="black",shape="box"];27376 -> 27479[label="",style="solid", color="black", weight=3]; 130.25/78.12 27377[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) zzz2615 zzz2616 zzz2617 zzz2618 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz2619)) zzz2620 zzz2621 zzz2622 zzz2623 (Pos (Succ zzz2614)) (EQ == GT)))",fontsize=16,color="black",shape="box"];27377 -> 27480[label="",style="solid", color="black", weight=3]; 130.25/78.12 24283 -> 288[label="",style="dashed", color="red", weight=0]; 130.25/78.12 24283[label="FiniteMap.glueVBal (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083))) zzz2086) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083))) zzz2087)",fontsize=16,color="magenta"];24283 -> 24363[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24283 -> 24364[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24284[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz209100) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (primCmpNat (Succ zzz2083) zzz209100 == LT)))",fontsize=16,color="burlywood",shape="box"];64942[label="zzz209100/Succ zzz2091000",fontsize=10,color="white",style="solid",shape="box"];24284 -> 64942[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64942 -> 24365[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64943[label="zzz209100/Zero",fontsize=10,color="white",style="solid",shape="box"];24284 -> 64943[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64943 -> 24366[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 24285[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz209100) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (GT == LT)))",fontsize=16,color="black",shape="box"];24285 -> 24367[label="",style="solid", color="black", weight=3]; 130.25/78.12 649[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 otherwise",fontsize=16,color="black",shape="box"];649 -> 764[label="",style="solid", color="black", weight=3]; 130.25/78.12 28134[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM2 zzz2743 zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (compare (Pos (Succ zzz2738)) zzz2743 == LT)))",fontsize=16,color="black",shape="box"];28134 -> 28164[label="",style="solid", color="black", weight=3]; 130.25/78.12 651 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 651[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))) zzz44",fontsize=16,color="magenta"];651 -> 767[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 651 -> 768[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 652 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 652[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))) zzz43",fontsize=16,color="magenta"];652 -> 769[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 652 -> 770[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 17670[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz13920) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (primCmpNat (Succ zzz1387) zzz13920 == LT)))",fontsize=16,color="burlywood",shape="box"];64944[label="zzz13920/Succ zzz139200",fontsize=10,color="white",style="solid",shape="box"];17670 -> 64944[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64944 -> 17799[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64945[label="zzz13920/Zero",fontsize=10,color="white",style="solid",shape="box"];17670 -> 64945[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64945 -> 17800[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 17671[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz13920) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (GT == LT)))",fontsize=16,color="black",shape="box"];17671 -> 17801[label="",style="solid", color="black", weight=3]; 130.25/78.12 656[label="FiniteMap.splitGT3 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero)",fontsize=16,color="black",shape="box"];656 -> 774[label="",style="solid", color="black", weight=3]; 130.25/78.12 657[label="FiniteMap.splitLT3 (FiniteMap.Branch (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Pos Zero)",fontsize=16,color="black",shape="box"];657 -> 775[label="",style="solid", color="black", weight=3]; 130.25/78.12 9733[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz62700)) zzz628 zzz629 zzz630 zzz631 (Pos Zero) True))",fontsize=16,color="black",shape="box"];9733 -> 9885[label="",style="solid", color="black", weight=3]; 130.25/78.12 9734[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (Pos Zero > Pos Zero)))",fontsize=16,color="black",shape="box"];9734 -> 9886[label="",style="solid", color="black", weight=3]; 130.25/78.12 9735[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz62700)) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (Pos Zero > Neg (Succ zzz62700))))",fontsize=16,color="black",shape="box"];9735 -> 9887[label="",style="solid", color="black", weight=3]; 130.25/78.12 9736[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (Pos Zero > Neg Zero)))",fontsize=16,color="black",shape="box"];9736 -> 9888[label="",style="solid", color="black", weight=3]; 130.25/78.12 4300[label="FiniteMap.splitLT (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)",fontsize=16,color="black",shape="box"];4300 -> 4341[label="",style="solid", color="black", weight=3]; 130.25/78.12 4301[label="FiniteMap.splitGT (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)",fontsize=16,color="black",shape="box"];4301 -> 4342[label="",style="solid", color="black", weight=3]; 130.25/78.12 4302[label="FiniteMap.mkVBalBranch5 (Pos zzz300) zzz31 FiniteMap.EmptyFM zzz34",fontsize=16,color="black",shape="box"];4302 -> 4343[label="",style="solid", color="black", weight=3]; 130.25/78.12 4303[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 zzz2502 zzz2503 zzz2504) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];4303 -> 4344[label="",style="solid", color="black", weight=3]; 130.25/78.12 4304[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 zzz2502 zzz2503 zzz2504) (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)",fontsize=16,color="black",shape="box"];4304 -> 4345[label="",style="solid", color="black", weight=3]; 130.25/78.12 667 -> 288[label="",style="dashed", color="red", weight=0]; 130.25/78.12 667[label="FiniteMap.glueVBal (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero)) zzz43) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero)) zzz44)",fontsize=16,color="magenta"];667 -> 786[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 667 -> 787[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 14901[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz12010) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (primCmpInt (Pos Zero) (Pos zzz12010) == LT)))",fontsize=16,color="burlywood",shape="box"];64946[label="zzz12010/Succ zzz120100",fontsize=10,color="white",style="solid",shape="box"];14901 -> 64946[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64946 -> 15020[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64947[label="zzz12010/Zero",fontsize=10,color="white",style="solid",shape="box"];14901 -> 64947[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64947 -> 15021[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 14902[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz12010) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (primCmpInt (Pos Zero) (Neg zzz12010) == LT)))",fontsize=16,color="burlywood",shape="box"];64948[label="zzz12010/Succ zzz120100",fontsize=10,color="white",style="solid",shape="box"];14902 -> 64948[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64948 -> 15022[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64949[label="zzz12010/Zero",fontsize=10,color="white",style="solid",shape="box"];14902 -> 64949[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64949 -> 15023[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 4305[label="FiniteMap.splitLT (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)",fontsize=16,color="black",shape="box"];4305 -> 4346[label="",style="solid", color="black", weight=3]; 130.25/78.12 4306[label="FiniteMap.splitGT (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)",fontsize=16,color="black",shape="box"];4306 -> 4347[label="",style="solid", color="black", weight=3]; 130.25/78.12 677[label="FiniteMap.splitGT2 (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (compare (Neg (Succ zzz4000)) (Pos zzz300) == GT)",fontsize=16,color="black",shape="box"];677 -> 797[label="",style="solid", color="black", weight=3]; 130.25/78.12 678[label="FiniteMap.splitLT2 (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (compare (Neg (Succ zzz4000)) (Pos zzz300) == LT)",fontsize=16,color="black",shape="box"];678 -> 798[label="",style="solid", color="black", weight=3]; 130.25/78.12 62160[label="zzz50",fontsize=16,color="green",shape="box"];62161[label="FiniteMap.glueVBal3Size_r zzz50 zzz51 zzz52 zzz53 zzz54 zzz60 zzz61 zzz62 zzz63 zzz64",fontsize=16,color="black",shape="box"];62161 -> 62172[label="",style="solid", color="black", weight=3]; 130.25/78.12 62162[label="zzz54",fontsize=16,color="green",shape="box"];62163[label="zzz60",fontsize=16,color="green",shape="box"];62164[label="zzz53",fontsize=16,color="green",shape="box"];62165[label="zzz62",fontsize=16,color="green",shape="box"];62166[label="zzz51",fontsize=16,color="green",shape="box"];62167[label="zzz63",fontsize=16,color="green",shape="box"];62168[label="zzz64",fontsize=16,color="green",shape="box"];62169[label="zzz52",fontsize=16,color="green",shape="box"];62170[label="zzz61",fontsize=16,color="green",shape="box"];62159[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (FiniteMap.sIZE_RATIO * FiniteMap.glueVBal3Size_l zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 < zzz6319)",fontsize=16,color="black",shape="triangle"];62159 -> 62173[label="",style="solid", color="black", weight=3]; 130.25/78.12 11143[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust Nothing)",fontsize=16,color="black",shape="box"];11143 -> 11398[label="",style="solid", color="black", weight=3]; 130.25/78.12 11144 -> 10027[label="",style="dashed", color="red", weight=0]; 130.25/78.12 11144[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 (Maybe.isJust (FiniteMap.lookupFM2 zzz7550 zzz7551 zzz7552 zzz7553 zzz7554 (Neg (Succ zzz747)) (Neg (Succ zzz747) < zzz7550)))",fontsize=16,color="magenta"];11144 -> 11399[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 11144 -> 11400[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 11144 -> 11401[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 11144 -> 11402[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 11144 -> 11403[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 17230[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) zzz1404 zzz1405 zzz1406 zzz1407 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1408)) zzz1409 zzz1410 zzz1411 zzz1412 (Neg (Succ zzz1403)) (primCmpNat (Succ zzz14130) (Succ zzz14140) == LT)))",fontsize=16,color="black",shape="box"];17230 -> 17564[label="",style="solid", color="black", weight=3]; 130.25/78.12 17231[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) zzz1404 zzz1405 zzz1406 zzz1407 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1408)) zzz1409 zzz1410 zzz1411 zzz1412 (Neg (Succ zzz1403)) (primCmpNat (Succ zzz14130) Zero == LT)))",fontsize=16,color="black",shape="box"];17231 -> 17565[label="",style="solid", color="black", weight=3]; 130.25/78.12 17232[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) zzz1404 zzz1405 zzz1406 zzz1407 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1408)) zzz1409 zzz1410 zzz1411 zzz1412 (Neg (Succ zzz1403)) (primCmpNat Zero (Succ zzz14140) == LT)))",fontsize=16,color="black",shape="box"];17232 -> 17566[label="",style="solid", color="black", weight=3]; 130.25/78.12 17233[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) zzz1404 zzz1405 zzz1406 zzz1407 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1408)) zzz1409 zzz1410 zzz1411 zzz1412 (Neg (Succ zzz1403)) (primCmpNat Zero Zero == LT)))",fontsize=16,color="black",shape="box"];17233 -> 17567[label="",style="solid", color="black", weight=3]; 130.25/78.12 27472 -> 27134[label="",style="dashed", color="red", weight=0]; 130.25/78.12 27472[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) zzz2633 zzz2634 zzz2635 zzz2636 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2637)) zzz2638 zzz2639 zzz2640 zzz2641 (Neg (Succ zzz2632)) (primCmpNat zzz26420 zzz26430 == GT)))",fontsize=16,color="magenta"];27472 -> 27516[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 27472 -> 27517[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 27473[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) zzz2633 zzz2634 zzz2635 zzz2636 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2637)) zzz2638 zzz2639 zzz2640 zzz2641 (Neg (Succ zzz2632)) (GT == GT)))",fontsize=16,color="black",shape="box"];27473 -> 27518[label="",style="solid", color="black", weight=3]; 130.25/78.12 27474[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) zzz2633 zzz2634 zzz2635 zzz2636 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2637)) zzz2638 zzz2639 zzz2640 zzz2641 (Neg (Succ zzz2632)) (LT == GT)))",fontsize=16,color="black",shape="box"];27474 -> 27519[label="",style="solid", color="black", weight=3]; 130.25/78.12 27475[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) zzz2633 zzz2634 zzz2635 zzz2636 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2637)) zzz2638 zzz2639 zzz2640 zzz2641 (Neg (Succ zzz2632)) (EQ == GT)))",fontsize=16,color="black",shape="box"];27475 -> 27520[label="",style="solid", color="black", weight=3]; 130.25/78.12 24803 -> 288[label="",style="dashed", color="red", weight=0]; 130.25/78.12 24803[label="FiniteMap.glueVBal (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148))) zzz2151) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148))) zzz2152)",fontsize=16,color="magenta"];24803 -> 24877[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24803 -> 24878[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24804[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz215600) zzz21561 zzz21562 zzz21563 zzz21564 (Neg (Succ zzz2148)) (LT == LT)))",fontsize=16,color="black",shape="box"];24804 -> 24879[label="",style="solid", color="black", weight=3]; 130.25/78.12 24805[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz215600) zzz21561 zzz21562 zzz21563 zzz21564 (Neg (Succ zzz2148)) (primCmpNat zzz215600 (Succ zzz2148) == LT)))",fontsize=16,color="burlywood",shape="box"];64950[label="zzz215600/Succ zzz2156000",fontsize=10,color="white",style="solid",shape="box"];24805 -> 64950[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64950 -> 24880[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64951[label="zzz215600/Zero",fontsize=10,color="white",style="solid",shape="box"];24805 -> 64951[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64951 -> 24881[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 710[label="FiniteMap.splitGT3 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))",fontsize=16,color="black",shape="box"];710 -> 837[label="",style="solid", color="black", weight=3]; 130.25/78.12 711[label="FiniteMap.splitLT3 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34) (Neg (Succ zzz4000))",fontsize=16,color="black",shape="box"];711 -> 838[label="",style="solid", color="black", weight=3]; 130.25/78.12 12373[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM FiniteMap.EmptyFM (Neg (Succ zzz888))))",fontsize=16,color="black",shape="box"];12373 -> 12465[label="",style="solid", color="black", weight=3]; 130.25/78.12 12374[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM (FiniteMap.Branch zzz8960 zzz8961 zzz8962 zzz8963 zzz8964) (Neg (Succ zzz888))))",fontsize=16,color="black",shape="box"];12374 -> 12466[label="",style="solid", color="black", weight=3]; 130.25/78.12 19021[label="zzz888",fontsize=16,color="green",shape="box"];19022[label="zzz884",fontsize=16,color="green",shape="box"];19023[label="zzz892",fontsize=16,color="green",shape="box"];19024[label="zzz89300",fontsize=16,color="green",shape="box"];19025[label="zzz891",fontsize=16,color="green",shape="box"];19026[label="zzz886",fontsize=16,color="green",shape="box"];19027[label="zzz887",fontsize=16,color="green",shape="box"];19028[label="zzz889",fontsize=16,color="green",shape="box"];19029[label="zzz897",fontsize=16,color="green",shape="box"];19030[label="zzz89300",fontsize=16,color="green",shape="box"];19031[label="zzz895",fontsize=16,color="green",shape="box"];19032[label="zzz890",fontsize=16,color="green",shape="box"];19033[label="zzz888",fontsize=16,color="green",shape="box"];19034[label="zzz894",fontsize=16,color="green",shape="box"];19035[label="zzz885",fontsize=16,color="green",shape="box"];19036[label="zzz896",fontsize=16,color="green",shape="box"];19020[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) zzz1582 zzz1583 zzz1584 zzz1585 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1586)) zzz1587 zzz1588 zzz1589 zzz1590 (Neg (Succ zzz1581)) (primCmpNat zzz1591 zzz1592 == LT)))",fontsize=16,color="burlywood",shape="triangle"];64952[label="zzz1591/Succ zzz15910",fontsize=10,color="white",style="solid",shape="box"];19020 -> 64952[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64952 -> 19181[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64953[label="zzz1591/Zero",fontsize=10,color="white",style="solid",shape="box"];19020 -> 64953[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64953 -> 19182[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 12377[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz894 zzz895 zzz896 zzz897 (Neg (Succ zzz888)) True))",fontsize=16,color="black",shape="box"];12377 -> 12471[label="",style="solid", color="black", weight=3]; 130.25/78.12 12142[label="FiniteMap.splitGT3 (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero)",fontsize=16,color="black",shape="box"];12142 -> 12221[label="",style="solid", color="black", weight=3]; 130.25/78.12 12143[label="FiniteMap.splitLT3 (FiniteMap.Branch (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834) (Neg Zero)",fontsize=16,color="black",shape="box"];12143 -> 12222[label="",style="solid", color="black", weight=3]; 130.25/78.12 12460[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM FiniteMap.EmptyFM (Neg Zero)))",fontsize=16,color="black",shape="box"];12460 -> 12554[label="",style="solid", color="black", weight=3]; 130.25/78.12 12461[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM (FiniteMap.Branch zzz9110 zzz9111 zzz9112 zzz9113 zzz9114) (Neg Zero)))",fontsize=16,color="black",shape="box"];12461 -> 12555[label="",style="solid", color="black", weight=3]; 130.25/78.12 12462[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (compare (Neg Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];12462 -> 12556[label="",style="solid", color="black", weight=3]; 130.25/78.12 12463[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz90800)) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (Neg Zero > Neg (Succ zzz90800))))",fontsize=16,color="black",shape="box"];12463 -> 12557[label="",style="solid", color="black", weight=3]; 130.25/78.12 12464[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (compare (Neg Zero) (Neg Zero) == GT)))",fontsize=16,color="black",shape="box"];12464 -> 12558[label="",style="solid", color="black", weight=3]; 130.25/78.12 5510[label="FiniteMap.splitLT (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)",fontsize=16,color="black",shape="triangle"];5510 -> 5553[label="",style="solid", color="black", weight=3]; 130.25/78.12 5511[label="FiniteMap.splitGT (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)",fontsize=16,color="black",shape="box"];5511 -> 5554[label="",style="solid", color="black", weight=3]; 130.25/78.12 5512[label="FiniteMap.mkVBalBranch5 (Neg Zero) zzz31 FiniteMap.EmptyFM zzz34",fontsize=16,color="black",shape="box"];5512 -> 5555[label="",style="solid", color="black", weight=3]; 130.25/78.12 5513[label="FiniteMap.mkVBalBranch (Neg Zero) zzz31 (FiniteMap.Branch zzz3530 zzz3531 zzz3532 zzz3533 zzz3534) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];5513 -> 5556[label="",style="solid", color="black", weight=3]; 130.25/78.12 5514[label="FiniteMap.mkVBalBranch (Neg Zero) zzz31 (FiniteMap.Branch zzz3530 zzz3531 zzz3532 zzz3533 zzz3534) (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)",fontsize=16,color="black",shape="box"];5514 -> 5557[label="",style="solid", color="black", weight=3]; 130.25/78.12 731[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero) zzz41 zzz42 zzz43 zzz44 otherwise",fontsize=16,color="black",shape="box"];731 -> 859[label="",style="solid", color="black", weight=3]; 130.25/78.12 19542[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM2 zzz1603 zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (compare (Neg Zero) zzz1603 == LT)))",fontsize=16,color="black",shape="box"];19542 -> 19592[label="",style="solid", color="black", weight=3]; 130.25/78.12 5515[label="FiniteMap.splitLT (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)",fontsize=16,color="black",shape="triangle"];5515 -> 5558[label="",style="solid", color="black", weight=3]; 130.25/78.12 5516[label="FiniteMap.splitGT (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)",fontsize=16,color="black",shape="box"];5516 -> 5559[label="",style="solid", color="black", weight=3]; 130.25/78.12 27476[label="zzz26240",fontsize=16,color="green",shape="box"];27477[label="zzz26250",fontsize=16,color="green",shape="box"];27478[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) zzz2615 zzz2616 zzz2617 zzz2618 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz2619)) zzz2620 zzz2621 zzz2622 zzz2623 (Pos (Succ zzz2614)) True))",fontsize=16,color="black",shape="box"];27478 -> 27521[label="",style="solid", color="black", weight=3]; 130.25/78.12 27479[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) zzz2615 zzz2616 zzz2617 zzz2618 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz2619)) zzz2620 zzz2621 zzz2622 zzz2623 (Pos (Succ zzz2614)) False))",fontsize=16,color="black",shape="triangle"];27479 -> 27522[label="",style="solid", color="black", weight=3]; 130.25/78.12 27480 -> 27479[label="",style="dashed", color="red", weight=0]; 130.25/78.12 27480[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) zzz2615 zzz2616 zzz2617 zzz2618 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz2619)) zzz2620 zzz2621 zzz2622 zzz2623 (Pos (Succ zzz2614)) False))",fontsize=16,color="magenta"];24363 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 24363[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083))) zzz2087",fontsize=16,color="magenta"];24363 -> 24657[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24363 -> 24658[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24364 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 24364[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083))) zzz2086",fontsize=16,color="magenta"];24364 -> 24659[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24364 -> 24660[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24365[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz2091000)) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (primCmpNat (Succ zzz2083) (Succ zzz2091000) == LT)))",fontsize=16,color="black",shape="box"];24365 -> 24661[label="",style="solid", color="black", weight=3]; 130.25/78.12 24366[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (primCmpNat (Succ zzz2083) Zero == LT)))",fontsize=16,color="black",shape="box"];24366 -> 24662[label="",style="solid", color="black", weight=3]; 130.25/78.12 24367[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz209100) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) False))",fontsize=16,color="black",shape="box"];24367 -> 24663[label="",style="solid", color="black", weight=3]; 130.25/78.12 764[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000)) zzz41 zzz42 zzz43 zzz44 True",fontsize=16,color="black",shape="box"];764 -> 893[label="",style="solid", color="black", weight=3]; 130.25/78.12 28164[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM2 zzz2743 zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (primCmpInt (Pos (Succ zzz2738)) zzz2743 == LT)))",fontsize=16,color="burlywood",shape="box"];64954[label="zzz2743/Pos zzz27430",fontsize=10,color="white",style="solid",shape="box"];28164 -> 64954[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64954 -> 28478[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64955[label="zzz2743/Neg zzz27430",fontsize=10,color="white",style="solid",shape="box"];28164 -> 64955[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64955 -> 28479[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 767[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))",fontsize=16,color="black",shape="box"];767 -> 896[label="",style="solid", color="black", weight=3]; 130.25/78.12 768[label="zzz44",fontsize=16,color="green",shape="box"];769[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))",fontsize=16,color="black",shape="box"];769 -> 897[label="",style="solid", color="black", weight=3]; 130.25/78.12 770[label="zzz43",fontsize=16,color="green",shape="box"];17799[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz139200)) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (primCmpNat (Succ zzz1387) (Succ zzz139200) == LT)))",fontsize=16,color="black",shape="box"];17799 -> 17839[label="",style="solid", color="black", weight=3]; 130.25/78.12 17800[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (primCmpNat (Succ zzz1387) Zero == LT)))",fontsize=16,color="black",shape="box"];17800 -> 17840[label="",style="solid", color="black", weight=3]; 130.25/78.12 17801[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz13920) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) False))",fontsize=16,color="black",shape="box"];17801 -> 17841[label="",style="solid", color="black", weight=3]; 130.25/78.12 774[label="FiniteMap.splitGT2 (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Pos Zero) (Pos Zero > Pos (Succ zzz3000))",fontsize=16,color="black",shape="box"];774 -> 902[label="",style="solid", color="black", weight=3]; 130.25/78.12 775[label="FiniteMap.splitLT2 (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Pos Zero) (Pos Zero < Pos (Succ zzz3000))",fontsize=16,color="black",shape="box"];775 -> 903[label="",style="solid", color="black", weight=3]; 130.25/78.12 9885[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM zzz630 (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];64956[label="zzz630/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];9885 -> 64956[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64956 -> 9911[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64957[label="zzz630/FiniteMap.Branch zzz6300 zzz6301 zzz6302 zzz6303 zzz6304",fontsize=10,color="white",style="solid",shape="box"];9885 -> 64957[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64957 -> 9912[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 9886[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (compare (Pos Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];9886 -> 9913[label="",style="solid", color="black", weight=3]; 130.25/78.12 9887[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz62700)) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (compare (Pos Zero) (Neg (Succ zzz62700)) == GT)))",fontsize=16,color="black",shape="box"];9887 -> 9914[label="",style="solid", color="black", weight=3]; 130.25/78.12 9888[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (compare (Pos Zero) (Neg Zero) == GT)))",fontsize=16,color="black",shape="box"];9888 -> 9915[label="",style="solid", color="black", weight=3]; 130.25/78.12 4341[label="FiniteMap.splitLT3 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)",fontsize=16,color="black",shape="box"];4341 -> 4377[label="",style="solid", color="black", weight=3]; 130.25/78.12 4342[label="FiniteMap.splitGT3 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)",fontsize=16,color="black",shape="box"];4342 -> 4378[label="",style="solid", color="black", weight=3]; 130.25/78.12 4343[label="FiniteMap.addToFM zzz34 (Pos zzz300) zzz31",fontsize=16,color="black",shape="triangle"];4343 -> 4379[label="",style="solid", color="black", weight=3]; 130.25/78.12 4344[label="FiniteMap.mkVBalBranch4 (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 zzz2502 zzz2503 zzz2504) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];4344 -> 4380[label="",style="solid", color="black", weight=3]; 130.25/78.12 4345[label="FiniteMap.mkVBalBranch3 (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 zzz2502 zzz2503 zzz2504) (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)",fontsize=16,color="black",shape="box"];4345 -> 4381[label="",style="solid", color="black", weight=3]; 130.25/78.12 786 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 786[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero)) zzz44",fontsize=16,color="magenta"];786 -> 914[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 786 -> 915[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 787 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 787[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero)) zzz43",fontsize=16,color="magenta"];787 -> 916[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 787 -> 917[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 15020[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz120100)) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (primCmpInt (Pos Zero) (Pos (Succ zzz120100)) == LT)))",fontsize=16,color="black",shape="box"];15020 -> 15067[label="",style="solid", color="black", weight=3]; 130.25/78.12 15021[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];15021 -> 15068[label="",style="solid", color="black", weight=3]; 130.25/78.12 15022[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz120100)) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ zzz120100)) == LT)))",fontsize=16,color="black",shape="box"];15022 -> 15069[label="",style="solid", color="black", weight=3]; 130.25/78.12 15023[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == LT)))",fontsize=16,color="black",shape="box"];15023 -> 15070[label="",style="solid", color="black", weight=3]; 130.25/78.12 4346[label="FiniteMap.splitLT3 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)",fontsize=16,color="black",shape="box"];4346 -> 4382[label="",style="solid", color="black", weight=3]; 130.25/78.12 4347[label="FiniteMap.splitGT3 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Pos Zero)",fontsize=16,color="black",shape="box"];4347 -> 4383[label="",style="solid", color="black", weight=3]; 130.25/78.12 797[label="FiniteMap.splitGT2 (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (primCmpInt (Neg (Succ zzz4000)) (Pos zzz300) == GT)",fontsize=16,color="black",shape="box"];797 -> 927[label="",style="solid", color="black", weight=3]; 130.25/78.12 798[label="FiniteMap.splitLT2 (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (primCmpInt (Neg (Succ zzz4000)) (Pos zzz300) == LT)",fontsize=16,color="black",shape="box"];798 -> 928[label="",style="solid", color="black", weight=3]; 130.25/78.12 62172 -> 54589[label="",style="dashed", color="red", weight=0]; 130.25/78.12 62172[label="FiniteMap.sizeFM (FiniteMap.Branch zzz50 zzz51 zzz52 zzz53 zzz54)",fontsize=16,color="magenta"];62172 -> 62185[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 62173[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (compare (FiniteMap.sIZE_RATIO * FiniteMap.glueVBal3Size_l zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) zzz6319 == LT)",fontsize=16,color="black",shape="box"];62173 -> 62186[label="",style="solid", color="black", weight=3]; 130.25/78.12 11398[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 False",fontsize=16,color="black",shape="box"];11398 -> 11668[label="",style="solid", color="black", weight=3]; 130.25/78.12 11399[label="zzz7554",fontsize=16,color="green",shape="box"];11400[label="zzz7553",fontsize=16,color="green",shape="box"];11401[label="zzz7551",fontsize=16,color="green",shape="box"];11402[label="zzz7552",fontsize=16,color="green",shape="box"];11403[label="zzz7550",fontsize=16,color="green",shape="box"];17564 -> 16650[label="",style="dashed", color="red", weight=0]; 130.25/78.12 17564[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) zzz1404 zzz1405 zzz1406 zzz1407 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1408)) zzz1409 zzz1410 zzz1411 zzz1412 (Neg (Succ zzz1403)) (primCmpNat zzz14130 zzz14140 == LT)))",fontsize=16,color="magenta"];17564 -> 17672[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 17564 -> 17673[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 17565[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) zzz1404 zzz1405 zzz1406 zzz1407 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1408)) zzz1409 zzz1410 zzz1411 zzz1412 (Neg (Succ zzz1403)) (GT == LT)))",fontsize=16,color="black",shape="box"];17565 -> 17674[label="",style="solid", color="black", weight=3]; 130.25/78.12 17566[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) zzz1404 zzz1405 zzz1406 zzz1407 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1408)) zzz1409 zzz1410 zzz1411 zzz1412 (Neg (Succ zzz1403)) (LT == LT)))",fontsize=16,color="black",shape="box"];17566 -> 17675[label="",style="solid", color="black", weight=3]; 130.25/78.12 17567[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) zzz1404 zzz1405 zzz1406 zzz1407 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1408)) zzz1409 zzz1410 zzz1411 zzz1412 (Neg (Succ zzz1403)) (EQ == LT)))",fontsize=16,color="black",shape="box"];17567 -> 17676[label="",style="solid", color="black", weight=3]; 130.25/78.12 27516[label="zzz26430",fontsize=16,color="green",shape="box"];27517[label="zzz26420",fontsize=16,color="green",shape="box"];27518[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) zzz2633 zzz2634 zzz2635 zzz2636 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2637)) zzz2638 zzz2639 zzz2640 zzz2641 (Neg (Succ zzz2632)) True))",fontsize=16,color="black",shape="box"];27518 -> 27537[label="",style="solid", color="black", weight=3]; 130.25/78.12 27519[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) zzz2633 zzz2634 zzz2635 zzz2636 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2637)) zzz2638 zzz2639 zzz2640 zzz2641 (Neg (Succ zzz2632)) False))",fontsize=16,color="black",shape="triangle"];27519 -> 27538[label="",style="solid", color="black", weight=3]; 130.25/78.12 27520 -> 27519[label="",style="dashed", color="red", weight=0]; 130.25/78.12 27520[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) zzz2633 zzz2634 zzz2635 zzz2636 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2637)) zzz2638 zzz2639 zzz2640 zzz2641 (Neg (Succ zzz2632)) False))",fontsize=16,color="magenta"];24877 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 24877[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148))) zzz2152",fontsize=16,color="magenta"];24877 -> 24914[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24877 -> 24915[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24878 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.12 24878[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148))) zzz2151",fontsize=16,color="magenta"];24878 -> 24916[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24878 -> 24917[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 24879[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz215600) zzz21561 zzz21562 zzz21563 zzz21564 (Neg (Succ zzz2148)) True))",fontsize=16,color="black",shape="box"];24879 -> 24918[label="",style="solid", color="black", weight=3]; 130.25/78.12 24880[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz2156000)) zzz21561 zzz21562 zzz21563 zzz21564 (Neg (Succ zzz2148)) (primCmpNat (Succ zzz2156000) (Succ zzz2148) == LT)))",fontsize=16,color="black",shape="box"];24880 -> 24919[label="",style="solid", color="black", weight=3]; 130.25/78.12 24881[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz21561 zzz21562 zzz21563 zzz21564 (Neg (Succ zzz2148)) (primCmpNat Zero (Succ zzz2148) == LT)))",fontsize=16,color="black",shape="box"];24881 -> 24920[label="",style="solid", color="black", weight=3]; 130.25/78.12 837[label="FiniteMap.splitGT2 (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (Neg (Succ zzz4000) > Neg Zero)",fontsize=16,color="black",shape="box"];837 -> 970[label="",style="solid", color="black", weight=3]; 130.25/78.12 838[label="FiniteMap.splitLT2 (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (Neg (Succ zzz4000) < Neg Zero)",fontsize=16,color="black",shape="box"];838 -> 971[label="",style="solid", color="black", weight=3]; 130.25/78.12 12465[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Neg (Succ zzz888))))",fontsize=16,color="black",shape="box"];12465 -> 12559[label="",style="solid", color="black", weight=3]; 130.25/78.12 12466 -> 11469[label="",style="dashed", color="red", weight=0]; 130.25/78.12 12466[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz8960 zzz8961 zzz8962 zzz8963 zzz8964) (Neg (Succ zzz888))))",fontsize=16,color="magenta"];12466 -> 12560[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12466 -> 12561[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12466 -> 12562[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12466 -> 12563[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 12466 -> 12564[label="",style="dashed", color="magenta", weight=3]; 130.25/78.12 19181[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) zzz1582 zzz1583 zzz1584 zzz1585 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1586)) zzz1587 zzz1588 zzz1589 zzz1590 (Neg (Succ zzz1581)) (primCmpNat (Succ zzz15910) zzz1592 == LT)))",fontsize=16,color="burlywood",shape="box"];64958[label="zzz1592/Succ zzz15920",fontsize=10,color="white",style="solid",shape="box"];19181 -> 64958[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64958 -> 19404[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64959[label="zzz1592/Zero",fontsize=10,color="white",style="solid",shape="box"];19181 -> 64959[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64959 -> 19405[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 19182[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) zzz1582 zzz1583 zzz1584 zzz1585 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1586)) zzz1587 zzz1588 zzz1589 zzz1590 (Neg (Succ zzz1581)) (primCmpNat Zero zzz1592 == LT)))",fontsize=16,color="burlywood",shape="box"];64960[label="zzz1592/Succ zzz15920",fontsize=10,color="white",style="solid",shape="box"];19182 -> 64960[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64960 -> 19406[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 64961[label="zzz1592/Zero",fontsize=10,color="white",style="solid",shape="box"];19182 -> 64961[label="",style="solid", color="burlywood", weight=9]; 130.25/78.12 64961 -> 19407[label="",style="solid", color="burlywood", weight=3]; 130.25/78.12 12471 -> 12274[label="",style="dashed", color="red", weight=0]; 130.25/78.12 12471[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust (FiniteMap.lookupFM zzz896 (Neg (Succ zzz888))))",fontsize=16,color="magenta"];12221[label="FiniteMap.splitGT2 (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834 (Neg Zero) (Neg Zero > Pos (Succ zzz830))",fontsize=16,color="black",shape="box"];12221 -> 12277[label="",style="solid", color="black", weight=3]; 130.25/78.13 12222[label="FiniteMap.splitLT2 (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834 (Neg Zero) (Neg Zero < Pos (Succ zzz830))",fontsize=16,color="black",shape="box"];12222 -> 12278[label="",style="solid", color="black", weight=3]; 130.25/78.13 12554 -> 10691[label="",style="dashed", color="red", weight=0]; 130.25/78.13 12554[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Neg Zero)))",fontsize=16,color="magenta"];12554 -> 12633[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 12554 -> 12634[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 12554 -> 12635[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 12554 -> 12636[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 12554 -> 12637[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 12554 -> 12638[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 12554 -> 12639[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 12554 -> 12640[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 12554 -> 12641[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 12555[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz9110 zzz9111 zzz9112 zzz9113 zzz9114) (Neg Zero)))",fontsize=16,color="black",shape="box"];12555 -> 12642[label="",style="solid", color="black", weight=3]; 130.25/78.13 12556[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];12556 -> 12643[label="",style="solid", color="black", weight=3]; 130.25/78.13 12557[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz90800)) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (compare (Neg Zero) (Neg (Succ zzz90800)) == GT)))",fontsize=16,color="black",shape="box"];12557 -> 12644[label="",style="solid", color="black", weight=3]; 130.25/78.13 12558[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == GT)))",fontsize=16,color="black",shape="box"];12558 -> 12645[label="",style="solid", color="black", weight=3]; 130.25/78.13 5553[label="FiniteMap.splitLT3 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)",fontsize=16,color="black",shape="box"];5553 -> 5597[label="",style="solid", color="black", weight=3]; 130.25/78.13 5554[label="FiniteMap.splitGT3 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)",fontsize=16,color="black",shape="box"];5554 -> 5598[label="",style="solid", color="black", weight=3]; 130.25/78.13 5555[label="FiniteMap.addToFM zzz34 (Neg Zero) zzz31",fontsize=16,color="black",shape="triangle"];5555 -> 5599[label="",style="solid", color="black", weight=3]; 130.25/78.13 5556[label="FiniteMap.mkVBalBranch4 (Neg Zero) zzz31 (FiniteMap.Branch zzz3530 zzz3531 zzz3532 zzz3533 zzz3534) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];5556 -> 5600[label="",style="solid", color="black", weight=3]; 130.25/78.13 5557[label="FiniteMap.mkVBalBranch3 (Neg Zero) zzz31 (FiniteMap.Branch zzz3530 zzz3531 zzz3532 zzz3533 zzz3534) (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)",fontsize=16,color="black",shape="box"];5557 -> 5601[label="",style="solid", color="black", weight=3]; 130.25/78.13 859[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero) zzz41 zzz42 zzz43 zzz44 True",fontsize=16,color="black",shape="box"];859 -> 993[label="",style="solid", color="black", weight=3]; 130.25/78.13 19592[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM2 zzz1603 zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (primCmpInt (Neg Zero) zzz1603 == LT)))",fontsize=16,color="burlywood",shape="box"];64962[label="zzz1603/Pos zzz16030",fontsize=10,color="white",style="solid",shape="box"];19592 -> 64962[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64962 -> 19634[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 64963[label="zzz1603/Neg zzz16030",fontsize=10,color="white",style="solid",shape="box"];19592 -> 64963[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64963 -> 19635[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 5558[label="FiniteMap.splitLT3 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)",fontsize=16,color="black",shape="box"];5558 -> 5602[label="",style="solid", color="black", weight=3]; 130.25/78.13 5559[label="FiniteMap.splitGT3 (FiniteMap.Branch (Neg Zero) zzz31 zzz32 zzz33 zzz34) (Neg Zero)",fontsize=16,color="black",shape="box"];5559 -> 5603[label="",style="solid", color="black", weight=3]; 130.25/78.13 27521 -> 23586[label="",style="dashed", color="red", weight=0]; 130.25/78.13 27521[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) zzz2615 zzz2616 zzz2617 zzz2618 (Maybe.isJust (FiniteMap.lookupFM zzz2623 (Pos (Succ zzz2614))))",fontsize=16,color="magenta"];27521 -> 27539[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27521 -> 27540[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27521 -> 27541[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27521 -> 27542[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27521 -> 27543[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27521 -> 27544[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27521 -> 27545[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27521 -> 27546[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27521 -> 27547[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27521 -> 27548[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27521 -> 27549[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27522[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) zzz2615 zzz2616 zzz2617 zzz2618 (Maybe.isJust (FiniteMap.lookupFM0 (Pos (Succ zzz2619)) zzz2620 zzz2621 zzz2622 zzz2623 (Pos (Succ zzz2614)) otherwise))",fontsize=16,color="black",shape="box"];27522 -> 27550[label="",style="solid", color="black", weight=3]; 130.25/78.13 24657[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083))",fontsize=16,color="black",shape="triangle"];24657 -> 24703[label="",style="solid", color="black", weight=3]; 130.25/78.13 24658[label="zzz2087",fontsize=16,color="green",shape="box"];24659[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083))",fontsize=16,color="black",shape="triangle"];24659 -> 24704[label="",style="solid", color="black", weight=3]; 130.25/78.13 24660[label="zzz2086",fontsize=16,color="green",shape="box"];24661 -> 22809[label="",style="dashed", color="red", weight=0]; 130.25/78.13 24661[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz2091000)) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (primCmpNat zzz2083 zzz2091000 == LT)))",fontsize=16,color="magenta"];24661 -> 24705[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24661 -> 24706[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24661 -> 24707[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24661 -> 24708[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24661 -> 24709[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24661 -> 24710[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24661 -> 24711[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24662[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (GT == LT)))",fontsize=16,color="black",shape="box"];24662 -> 24712[label="",style="solid", color="black", weight=3]; 130.25/78.13 24663[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz209100) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (Pos (Succ zzz2083) > Neg zzz209100)))",fontsize=16,color="black",shape="box"];24663 -> 24713[label="",style="solid", color="black", weight=3]; 130.25/78.13 893 -> 288[label="",style="dashed", color="red", weight=0]; 130.25/78.13 893[label="FiniteMap.glueVBal (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))) zzz43) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))) zzz44)",fontsize=16,color="magenta"];893 -> 1060[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 893 -> 1061[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 28478[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz27430) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (primCmpInt (Pos (Succ zzz2738)) (Pos zzz27430) == LT)))",fontsize=16,color="black",shape="box"];28478 -> 28510[label="",style="solid", color="black", weight=3]; 130.25/78.13 28479[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz27430) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (primCmpInt (Pos (Succ zzz2738)) (Neg zzz27430) == LT)))",fontsize=16,color="black",shape="box"];28479 -> 28511[label="",style="solid", color="black", weight=3]; 130.25/78.13 896[label="FiniteMap.splitGT (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))",fontsize=16,color="black",shape="box"];896 -> 1065[label="",style="solid", color="black", weight=3]; 130.25/78.13 897[label="FiniteMap.splitLT (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))",fontsize=16,color="black",shape="box"];897 -> 1066[label="",style="solid", color="black", weight=3]; 130.25/78.13 17839 -> 22038[label="",style="dashed", color="red", weight=0]; 130.25/78.13 17839[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz139200)) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (primCmpNat zzz1387 zzz139200 == LT)))",fontsize=16,color="magenta"];17839 -> 22039[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17839 -> 22040[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17839 -> 22041[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17839 -> 22042[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17839 -> 22043[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17839 -> 22044[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17839 -> 22045[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17839 -> 22046[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17839 -> 22047[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17839 -> 22048[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17839 -> 22049[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17839 -> 22050[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17839 -> 22051[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17839 -> 22052[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17839 -> 22053[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17839 -> 22054[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17839 -> 22055[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17840[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (GT == LT)))",fontsize=16,color="black",shape="box"];17840 -> 18130[label="",style="solid", color="black", weight=3]; 130.25/78.13 17841[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz13920) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (Pos (Succ zzz1387) > Neg zzz13920)))",fontsize=16,color="black",shape="box"];17841 -> 18131[label="",style="solid", color="black", weight=3]; 130.25/78.13 902[label="FiniteMap.splitGT2 (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Pos Zero) (compare (Pos Zero) (Pos (Succ zzz3000)) == GT)",fontsize=16,color="black",shape="box"];902 -> 1073[label="",style="solid", color="black", weight=3]; 130.25/78.13 903[label="FiniteMap.splitLT2 (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Pos Zero) (compare (Pos Zero) (Pos (Succ zzz3000)) == LT)",fontsize=16,color="black",shape="box"];903 -> 1074[label="",style="solid", color="black", weight=3]; 130.25/78.13 9911[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM FiniteMap.EmptyFM (Pos Zero)))",fontsize=16,color="black",shape="box"];9911 -> 10274[label="",style="solid", color="black", weight=3]; 130.25/78.13 9912[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM (FiniteMap.Branch zzz6300 zzz6301 zzz6302 zzz6303 zzz6304) (Pos Zero)))",fontsize=16,color="black",shape="box"];9912 -> 10275[label="",style="solid", color="black", weight=3]; 130.25/78.13 9913[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];9913 -> 10276[label="",style="solid", color="black", weight=3]; 130.25/78.13 9914[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz62700)) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ zzz62700)) == GT)))",fontsize=16,color="black",shape="box"];9914 -> 10277[label="",style="solid", color="black", weight=3]; 130.25/78.13 9915[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == GT)))",fontsize=16,color="black",shape="box"];9915 -> 10278[label="",style="solid", color="black", weight=3]; 130.25/78.13 4377[label="FiniteMap.splitLT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (Pos Zero < Pos Zero)",fontsize=16,color="black",shape="box"];4377 -> 4713[label="",style="solid", color="black", weight=3]; 130.25/78.13 4378[label="FiniteMap.splitGT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (Pos Zero > Pos Zero)",fontsize=16,color="black",shape="box"];4378 -> 4714[label="",style="solid", color="black", weight=3]; 130.25/78.13 4379[label="FiniteMap.addToFM_C FiniteMap.addToFM0 zzz34 (Pos zzz300) zzz31",fontsize=16,color="burlywood",shape="triangle"];64964[label="zzz34/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];4379 -> 64964[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64964 -> 4715[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 64965[label="zzz34/FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344",fontsize=10,color="white",style="solid",shape="box"];4379 -> 64965[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64965 -> 4716[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 4380 -> 4343[label="",style="dashed", color="red", weight=0]; 130.25/78.13 4380[label="FiniteMap.addToFM (FiniteMap.Branch zzz2500 zzz2501 zzz2502 zzz2503 zzz2504) (Pos zzz300) zzz31",fontsize=16,color="magenta"];4380 -> 4717[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 4381[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344)",fontsize=16,color="black",shape="box"];4381 -> 4718[label="",style="solid", color="black", weight=3]; 130.25/78.13 914[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero)",fontsize=16,color="black",shape="box"];914 -> 1086[label="",style="solid", color="black", weight=3]; 130.25/78.13 915[label="zzz44",fontsize=16,color="green",shape="box"];916[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero)",fontsize=16,color="black",shape="box"];916 -> 1087[label="",style="solid", color="black", weight=3]; 130.25/78.13 917[label="zzz43",fontsize=16,color="green",shape="box"];15067[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz120100)) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (primCmpNat Zero (Succ zzz120100) == LT)))",fontsize=16,color="black",shape="box"];15067 -> 15118[label="",style="solid", color="black", weight=3]; 130.25/78.13 15068[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (EQ == LT)))",fontsize=16,color="black",shape="box"];15068 -> 15119[label="",style="solid", color="black", weight=3]; 130.25/78.13 15069[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz120100)) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (GT == LT)))",fontsize=16,color="black",shape="box"];15069 -> 15120[label="",style="solid", color="black", weight=3]; 130.25/78.13 15070[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (EQ == LT)))",fontsize=16,color="black",shape="box"];15070 -> 15121[label="",style="solid", color="black", weight=3]; 130.25/78.13 4382[label="FiniteMap.splitLT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (Pos Zero < Neg Zero)",fontsize=16,color="black",shape="box"];4382 -> 4719[label="",style="solid", color="black", weight=3]; 130.25/78.13 4383[label="FiniteMap.splitGT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (Pos Zero > Neg Zero)",fontsize=16,color="black",shape="box"];4383 -> 4720[label="",style="solid", color="black", weight=3]; 130.25/78.13 927[label="FiniteMap.splitGT2 (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (LT == GT)",fontsize=16,color="black",shape="box"];927 -> 1098[label="",style="solid", color="black", weight=3]; 130.25/78.13 928[label="FiniteMap.splitLT2 (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (LT == LT)",fontsize=16,color="black",shape="box"];928 -> 1099[label="",style="solid", color="black", weight=3]; 130.25/78.13 62185[label="FiniteMap.Branch zzz50 zzz51 zzz52 zzz53 zzz54",fontsize=16,color="green",shape="box"];54589[label="FiniteMap.sizeFM zzz3490",fontsize=16,color="burlywood",shape="triangle"];64966[label="zzz3490/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];54589 -> 64966[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64966 -> 55011[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 64967[label="zzz3490/FiniteMap.Branch zzz34900 zzz34901 zzz34902 zzz34903 zzz34904",fontsize=10,color="white",style="solid",shape="box"];54589 -> 64967[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64967 -> 55012[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 62186[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.glueVBal3Size_l zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) zzz6319 == LT)",fontsize=16,color="black",shape="box"];62186 -> 62192[label="",style="solid", color="black", weight=3]; 130.25/78.13 11668[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 otherwise",fontsize=16,color="black",shape="box"];11668 -> 11807[label="",style="solid", color="black", weight=3]; 130.25/78.13 17672[label="zzz14130",fontsize=16,color="green",shape="box"];17673[label="zzz14140",fontsize=16,color="green",shape="box"];17674[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) zzz1404 zzz1405 zzz1406 zzz1407 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1408)) zzz1409 zzz1410 zzz1411 zzz1412 (Neg (Succ zzz1403)) False))",fontsize=16,color="black",shape="triangle"];17674 -> 17802[label="",style="solid", color="black", weight=3]; 130.25/78.13 17675[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) zzz1404 zzz1405 zzz1406 zzz1407 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1408)) zzz1409 zzz1410 zzz1411 zzz1412 (Neg (Succ zzz1403)) True))",fontsize=16,color="black",shape="box"];17675 -> 17803[label="",style="solid", color="black", weight=3]; 130.25/78.13 17676 -> 17674[label="",style="dashed", color="red", weight=0]; 130.25/78.13 17676[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) zzz1404 zzz1405 zzz1406 zzz1407 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1408)) zzz1409 zzz1410 zzz1411 zzz1412 (Neg (Succ zzz1403)) False))",fontsize=16,color="magenta"];27537 -> 24193[label="",style="dashed", color="red", weight=0]; 130.25/78.13 27537[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) zzz2633 zzz2634 zzz2635 zzz2636 (Maybe.isJust (FiniteMap.lookupFM zzz2641 (Neg (Succ zzz2632))))",fontsize=16,color="magenta"];27537 -> 27626[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27537 -> 27627[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27537 -> 27628[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27537 -> 27629[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27537 -> 27630[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27537 -> 27631[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27537 -> 27632[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27537 -> 27633[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27537 -> 27634[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27537 -> 27635[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27537 -> 27636[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27538[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) zzz2633 zzz2634 zzz2635 zzz2636 (Maybe.isJust (FiniteMap.lookupFM0 (Neg (Succ zzz2637)) zzz2638 zzz2639 zzz2640 zzz2641 (Neg (Succ zzz2632)) otherwise))",fontsize=16,color="black",shape="box"];27538 -> 27637[label="",style="solid", color="black", weight=3]; 130.25/78.13 24914[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148))",fontsize=16,color="black",shape="triangle"];24914 -> 24958[label="",style="solid", color="black", weight=3]; 130.25/78.13 24915[label="zzz2152",fontsize=16,color="green",shape="box"];24916[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148))",fontsize=16,color="black",shape="triangle"];24916 -> 24959[label="",style="solid", color="black", weight=3]; 130.25/78.13 24917[label="zzz2151",fontsize=16,color="green",shape="box"];24918 -> 24193[label="",style="dashed", color="red", weight=0]; 130.25/78.13 24918[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM zzz21563 (Neg (Succ zzz2148))))",fontsize=16,color="magenta"];24918 -> 24960[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24919 -> 23616[label="",style="dashed", color="red", weight=0]; 130.25/78.13 24919[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz2156000)) zzz21561 zzz21562 zzz21563 zzz21564 (Neg (Succ zzz2148)) (primCmpNat zzz2156000 zzz2148 == LT)))",fontsize=16,color="magenta"];24919 -> 24961[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24919 -> 24962[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24919 -> 24963[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24919 -> 24964[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24919 -> 24965[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24919 -> 24966[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24919 -> 24967[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24920[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz21561 zzz21562 zzz21563 zzz21564 (Neg (Succ zzz2148)) (LT == LT)))",fontsize=16,color="black",shape="box"];24920 -> 24968[label="",style="solid", color="black", weight=3]; 130.25/78.13 970[label="FiniteMap.splitGT2 (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (compare (Neg (Succ zzz4000)) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];970 -> 1174[label="",style="solid", color="black", weight=3]; 130.25/78.13 971[label="FiniteMap.splitLT2 (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (compare (Neg (Succ zzz4000)) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];971 -> 1175[label="",style="solid", color="black", weight=3]; 130.25/78.13 12559[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 (Maybe.isJust Nothing)",fontsize=16,color="black",shape="box"];12559 -> 12646[label="",style="solid", color="black", weight=3]; 130.25/78.13 12560[label="zzz8963",fontsize=16,color="green",shape="box"];12561[label="zzz8961",fontsize=16,color="green",shape="box"];12562[label="zzz8962",fontsize=16,color="green",shape="box"];12563[label="zzz8960",fontsize=16,color="green",shape="box"];12564[label="zzz8964",fontsize=16,color="green",shape="box"];19404[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) zzz1582 zzz1583 zzz1584 zzz1585 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1586)) zzz1587 zzz1588 zzz1589 zzz1590 (Neg (Succ zzz1581)) (primCmpNat (Succ zzz15910) (Succ zzz15920) == LT)))",fontsize=16,color="black",shape="box"];19404 -> 19543[label="",style="solid", color="black", weight=3]; 130.25/78.13 19405[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) zzz1582 zzz1583 zzz1584 zzz1585 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1586)) zzz1587 zzz1588 zzz1589 zzz1590 (Neg (Succ zzz1581)) (primCmpNat (Succ zzz15910) Zero == LT)))",fontsize=16,color="black",shape="box"];19405 -> 19544[label="",style="solid", color="black", weight=3]; 130.25/78.13 19406[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) zzz1582 zzz1583 zzz1584 zzz1585 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1586)) zzz1587 zzz1588 zzz1589 zzz1590 (Neg (Succ zzz1581)) (primCmpNat Zero (Succ zzz15920) == LT)))",fontsize=16,color="black",shape="box"];19406 -> 19545[label="",style="solid", color="black", weight=3]; 130.25/78.13 19407[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) zzz1582 zzz1583 zzz1584 zzz1585 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1586)) zzz1587 zzz1588 zzz1589 zzz1590 (Neg (Succ zzz1581)) (primCmpNat Zero Zero == LT)))",fontsize=16,color="black",shape="box"];19407 -> 19546[label="",style="solid", color="black", weight=3]; 130.25/78.13 12277[label="FiniteMap.splitGT2 (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834 (Neg Zero) (compare (Neg Zero) (Pos (Succ zzz830)) == GT)",fontsize=16,color="black",shape="box"];12277 -> 12378[label="",style="solid", color="black", weight=3]; 130.25/78.13 12278[label="FiniteMap.splitLT2 (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834 (Neg Zero) (compare (Neg Zero) (Pos (Succ zzz830)) == LT)",fontsize=16,color="black",shape="box"];12278 -> 12379[label="",style="solid", color="black", weight=3]; 130.25/78.13 12633[label="zzz900",fontsize=16,color="green",shape="box"];12634[label="zzz904",fontsize=16,color="green",shape="box"];12635[label="zzz899",fontsize=16,color="green",shape="box"];12636[label="zzz901",fontsize=16,color="green",shape="box"];12637[label="zzz907",fontsize=16,color="green",shape="box"];12638[label="zzz903",fontsize=16,color="green",shape="box"];12639[label="zzz905",fontsize=16,color="green",shape="box"];12640[label="zzz902",fontsize=16,color="green",shape="box"];12641[label="zzz906",fontsize=16,color="green",shape="box"];12642 -> 11718[label="",style="dashed", color="red", weight=0]; 130.25/78.13 12642[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM2 zzz9110 zzz9111 zzz9112 zzz9113 zzz9114 (Neg Zero) (Neg Zero < zzz9110)))",fontsize=16,color="magenta"];12642 -> 12918[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 12642 -> 12919[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 12642 -> 12920[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 12642 -> 12921[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 12642 -> 12922[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 12643[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (EQ == GT)))",fontsize=16,color="black",shape="box"];12643 -> 12923[label="",style="solid", color="black", weight=3]; 130.25/78.13 12644[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz90800)) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ zzz90800)) == GT)))",fontsize=16,color="black",shape="box"];12644 -> 12924[label="",style="solid", color="black", weight=3]; 130.25/78.13 12645[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (EQ == GT)))",fontsize=16,color="black",shape="box"];12645 -> 12925[label="",style="solid", color="black", weight=3]; 130.25/78.13 5597[label="FiniteMap.splitLT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (Neg Zero < Pos Zero)",fontsize=16,color="black",shape="box"];5597 -> 5850[label="",style="solid", color="black", weight=3]; 130.25/78.13 5598[label="FiniteMap.splitGT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (Neg Zero > Pos Zero)",fontsize=16,color="black",shape="box"];5598 -> 5851[label="",style="solid", color="black", weight=3]; 130.25/78.13 5599 -> 12360[label="",style="dashed", color="red", weight=0]; 130.25/78.13 5599[label="FiniteMap.addToFM_C FiniteMap.addToFM0 zzz34 (Neg Zero) zzz31",fontsize=16,color="magenta"];5599 -> 12361[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 5599 -> 12362[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 5600 -> 5555[label="",style="dashed", color="red", weight=0]; 130.25/78.13 5600[label="FiniteMap.addToFM (FiniteMap.Branch zzz3530 zzz3531 zzz3532 zzz3533 zzz3534) (Neg Zero) zzz31",fontsize=16,color="magenta"];5600 -> 5854[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 5601[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344)",fontsize=16,color="black",shape="box"];5601 -> 5855[label="",style="solid", color="black", weight=3]; 130.25/78.13 993 -> 288[label="",style="dashed", color="red", weight=0]; 130.25/78.13 993[label="FiniteMap.glueVBal (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero)) zzz43) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero)) zzz44)",fontsize=16,color="magenta"];993 -> 1200[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 993 -> 1201[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 19634[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz16030) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (primCmpInt (Neg Zero) (Pos zzz16030) == LT)))",fontsize=16,color="burlywood",shape="box"];64968[label="zzz16030/Succ zzz160300",fontsize=10,color="white",style="solid",shape="box"];19634 -> 64968[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64968 -> 19769[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 64969[label="zzz16030/Zero",fontsize=10,color="white",style="solid",shape="box"];19634 -> 64969[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64969 -> 19770[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 19635[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz16030) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (primCmpInt (Neg Zero) (Neg zzz16030) == LT)))",fontsize=16,color="burlywood",shape="box"];64970[label="zzz16030/Succ zzz160300",fontsize=10,color="white",style="solid",shape="box"];19635 -> 64970[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64970 -> 19771[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 64971[label="zzz16030/Zero",fontsize=10,color="white",style="solid",shape="box"];19635 -> 64971[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64971 -> 19772[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 5602[label="FiniteMap.splitLT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (Neg Zero < Neg Zero)",fontsize=16,color="black",shape="box"];5602 -> 5856[label="",style="solid", color="black", weight=3]; 130.25/78.13 5603[label="FiniteMap.splitGT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (Neg Zero > Neg Zero)",fontsize=16,color="black",shape="box"];5603 -> 5857[label="",style="solid", color="black", weight=3]; 130.25/78.13 27539[label="zzz2618",fontsize=16,color="green",shape="box"];27540[label="zzz2610",fontsize=16,color="green",shape="box"];27541[label="zzz2611",fontsize=16,color="green",shape="box"];27542[label="zzz2617",fontsize=16,color="green",shape="box"];27543[label="zzz2612",fontsize=16,color="green",shape="box"];27544[label="zzz2614",fontsize=16,color="green",shape="box"];27545[label="zzz2613",fontsize=16,color="green",shape="box"];27546[label="zzz2615",fontsize=16,color="green",shape="box"];27547[label="zzz2623",fontsize=16,color="green",shape="box"];27548[label="zzz2616",fontsize=16,color="green",shape="box"];27549[label="zzz2609",fontsize=16,color="green",shape="box"];27550[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) zzz2615 zzz2616 zzz2617 zzz2618 (Maybe.isJust (FiniteMap.lookupFM0 (Pos (Succ zzz2619)) zzz2620 zzz2621 zzz2622 zzz2623 (Pos (Succ zzz2614)) True))",fontsize=16,color="black",shape="box"];27550 -> 27638[label="",style="solid", color="black", weight=3]; 130.25/78.13 24703 -> 19598[label="",style="dashed", color="red", weight=0]; 130.25/78.13 24703[label="FiniteMap.splitGT (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083))",fontsize=16,color="magenta"];24703 -> 24749[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24703 -> 24750[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24704 -> 23112[label="",style="dashed", color="red", weight=0]; 130.25/78.13 24704[label="FiniteMap.splitLT (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083))",fontsize=16,color="magenta"];24704 -> 24751[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24704 -> 24752[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24705[label="zzz2091000",fontsize=16,color="green",shape="box"];24706[label="zzz2083",fontsize=16,color="green",shape="box"];24707[label="zzz20911",fontsize=16,color="green",shape="box"];24708[label="zzz2091000",fontsize=16,color="green",shape="box"];24709[label="zzz20912",fontsize=16,color="green",shape="box"];24710[label="zzz20914",fontsize=16,color="green",shape="box"];24711[label="zzz20913",fontsize=16,color="green",shape="box"];24712[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) False))",fontsize=16,color="black",shape="box"];24712 -> 24753[label="",style="solid", color="black", weight=3]; 130.25/78.13 24713[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz209100) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (compare (Pos (Succ zzz2083)) (Neg zzz209100) == GT)))",fontsize=16,color="black",shape="box"];24713 -> 24754[label="",style="solid", color="black", weight=3]; 130.25/78.13 1060 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.13 1060[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))) zzz44",fontsize=16,color="magenta"];1060 -> 1302[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 1060 -> 1303[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 1061 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.13 1061[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))) zzz43",fontsize=16,color="magenta"];1061 -> 1304[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 1061 -> 1305[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 28510[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM2 (Pos zzz27430) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (primCmpNat (Succ zzz2738) zzz27430 == LT)))",fontsize=16,color="burlywood",shape="box"];64972[label="zzz27430/Succ zzz274300",fontsize=10,color="white",style="solid",shape="box"];28510 -> 64972[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64972 -> 28522[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 64973[label="zzz27430/Zero",fontsize=10,color="white",style="solid",shape="box"];28510 -> 64973[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64973 -> 28523[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 28511[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz27430) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (GT == LT)))",fontsize=16,color="black",shape="box"];28511 -> 28524[label="",style="solid", color="black", weight=3]; 130.25/78.13 1065[label="FiniteMap.splitGT3 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))",fontsize=16,color="black",shape="box"];1065 -> 1309[label="",style="solid", color="black", weight=3]; 130.25/78.13 1066[label="FiniteMap.splitLT3 (FiniteMap.Branch (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))",fontsize=16,color="black",shape="box"];1066 -> 1310[label="",style="solid", color="black", weight=3]; 130.25/78.13 22039[label="zzz1387",fontsize=16,color="green",shape="box"];22040[label="zzz1391",fontsize=16,color="green",shape="box"];22041[label="zzz1388",fontsize=16,color="green",shape="box"];22042[label="zzz1386",fontsize=16,color="green",shape="box"];22043[label="zzz1390",fontsize=16,color="green",shape="box"];22044[label="zzz1394",fontsize=16,color="green",shape="box"];22045[label="zzz1395",fontsize=16,color="green",shape="box"];22046[label="zzz1384",fontsize=16,color="green",shape="box"];22047[label="zzz1383",fontsize=16,color="green",shape="box"];22048[label="zzz1387",fontsize=16,color="green",shape="box"];22049[label="zzz139200",fontsize=16,color="green",shape="box"];22050[label="zzz1396",fontsize=16,color="green",shape="box"];22051[label="zzz1393",fontsize=16,color="green",shape="box"];22052[label="zzz1382",fontsize=16,color="green",shape="box"];22053[label="zzz1385",fontsize=16,color="green",shape="box"];22054[label="zzz139200",fontsize=16,color="green",shape="box"];22055[label="zzz1389",fontsize=16,color="green",shape="box"];22038[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) zzz1983 zzz1984 zzz1985 zzz1986 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz1987)) zzz1988 zzz1989 zzz1990 zzz1991 (Pos (Succ zzz1982)) (primCmpNat zzz1992 zzz1993 == LT)))",fontsize=16,color="burlywood",shape="triangle"];64974[label="zzz1992/Succ zzz19920",fontsize=10,color="white",style="solid",shape="box"];22038 -> 64974[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64974 -> 22209[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 64975[label="zzz1992/Zero",fontsize=10,color="white",style="solid",shape="box"];22038 -> 64975[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64975 -> 22210[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 18130[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) False))",fontsize=16,color="black",shape="box"];18130 -> 18159[label="",style="solid", color="black", weight=3]; 130.25/78.13 18131[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz13920) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (compare (Pos (Succ zzz1387)) (Neg zzz13920) == GT)))",fontsize=16,color="black",shape="box"];18131 -> 18160[label="",style="solid", color="black", weight=3]; 130.25/78.13 1073[label="FiniteMap.splitGT2 (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Pos (Succ zzz3000)) == GT)",fontsize=16,color="black",shape="box"];1073 -> 1317[label="",style="solid", color="black", weight=3]; 130.25/78.13 1074[label="FiniteMap.splitLT2 (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Pos (Succ zzz3000)) == LT)",fontsize=16,color="black",shape="box"];1074 -> 1318[label="",style="solid", color="black", weight=3]; 130.25/78.13 10274[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Pos Zero)))",fontsize=16,color="black",shape="box"];10274 -> 10337[label="",style="solid", color="black", weight=3]; 130.25/78.13 10275 -> 8891[label="",style="dashed", color="red", weight=0]; 130.25/78.13 10275[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz6300 zzz6301 zzz6302 zzz6303 zzz6304) (Pos Zero)))",fontsize=16,color="magenta"];10275 -> 10338[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 10275 -> 10339[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 10275 -> 10340[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 10275 -> 10341[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 10275 -> 10342[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 10276[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (EQ == GT)))",fontsize=16,color="black",shape="box"];10276 -> 10343[label="",style="solid", color="black", weight=3]; 130.25/78.13 10277[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz62700)) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (GT == GT)))",fontsize=16,color="black",shape="box"];10277 -> 10344[label="",style="solid", color="black", weight=3]; 130.25/78.13 10278[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) (EQ == GT)))",fontsize=16,color="black",shape="box"];10278 -> 10345[label="",style="solid", color="black", weight=3]; 130.25/78.13 4713[label="FiniteMap.splitLT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (compare (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];4713 -> 4917[label="",style="solid", color="black", weight=3]; 130.25/78.13 4714[label="FiniteMap.splitGT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (compare (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];4714 -> 4918[label="",style="solid", color="black", weight=3]; 130.25/78.13 4715[label="FiniteMap.addToFM_C FiniteMap.addToFM0 FiniteMap.EmptyFM (Pos zzz300) zzz31",fontsize=16,color="black",shape="box"];4715 -> 4919[label="",style="solid", color="black", weight=3]; 130.25/78.13 4716[label="FiniteMap.addToFM_C FiniteMap.addToFM0 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344) (Pos zzz300) zzz31",fontsize=16,color="black",shape="box"];4716 -> 4920[label="",style="solid", color="black", weight=3]; 130.25/78.13 4717[label="FiniteMap.Branch zzz2500 zzz2501 zzz2502 zzz2503 zzz2504",fontsize=16,color="green",shape="box"];4718[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];4718 -> 4921[label="",style="solid", color="black", weight=3]; 130.25/78.13 1086[label="FiniteMap.splitGT (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero)",fontsize=16,color="black",shape="box"];1086 -> 1329[label="",style="solid", color="black", weight=3]; 130.25/78.13 1087[label="FiniteMap.splitLT (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero)",fontsize=16,color="black",shape="box"];1087 -> 1330[label="",style="solid", color="black", weight=3]; 130.25/78.13 15118[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz120100)) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (LT == LT)))",fontsize=16,color="black",shape="box"];15118 -> 15169[label="",style="solid", color="black", weight=3]; 130.25/78.13 15119[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) False))",fontsize=16,color="black",shape="box"];15119 -> 15170[label="",style="solid", color="black", weight=3]; 130.25/78.13 15120[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz120100)) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) False))",fontsize=16,color="black",shape="box"];15120 -> 15171[label="",style="solid", color="black", weight=3]; 130.25/78.13 15121[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) False))",fontsize=16,color="black",shape="box"];15121 -> 15172[label="",style="solid", color="black", weight=3]; 130.25/78.13 4719[label="FiniteMap.splitLT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (compare (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];4719 -> 4922[label="",style="solid", color="black", weight=3]; 130.25/78.13 4720[label="FiniteMap.splitGT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (compare (Pos Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];4720 -> 4923[label="",style="solid", color="black", weight=3]; 130.25/78.13 1098[label="FiniteMap.splitGT2 (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) False",fontsize=16,color="black",shape="box"];1098 -> 1340[label="",style="solid", color="black", weight=3]; 130.25/78.13 1099[label="FiniteMap.splitLT2 (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) True",fontsize=16,color="black",shape="box"];1099 -> 1341[label="",style="solid", color="black", weight=3]; 130.25/78.13 55011[label="FiniteMap.sizeFM FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];55011 -> 55810[label="",style="solid", color="black", weight=3]; 130.25/78.13 55012[label="FiniteMap.sizeFM (FiniteMap.Branch zzz34900 zzz34901 zzz34902 zzz34903 zzz34904)",fontsize=16,color="black",shape="box"];55012 -> 55811[label="",style="solid", color="black", weight=3]; 130.25/78.13 62192[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.glueVBal3Size_l zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464)) zzz6319 == LT)",fontsize=16,color="black",shape="box"];62192 -> 62449[label="",style="solid", color="black", weight=3]; 130.25/78.13 11807[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747)) zzz748 zzz749 zzz750 zzz751 True",fontsize=16,color="black",shape="box"];11807 -> 11971[label="",style="solid", color="black", weight=3]; 130.25/78.13 17802[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) zzz1404 zzz1405 zzz1406 zzz1407 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz1408)) zzz1409 zzz1410 zzz1411 zzz1412 (Neg (Succ zzz1403)) (Neg (Succ zzz1403) > Neg (Succ zzz1408))))",fontsize=16,color="black",shape="box"];17802 -> 17842[label="",style="solid", color="black", weight=3]; 130.25/78.13 17803 -> 10612[label="",style="dashed", color="red", weight=0]; 130.25/78.13 17803[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) zzz1404 zzz1405 zzz1406 zzz1407 (Maybe.isJust (FiniteMap.lookupFM zzz1411 (Neg (Succ zzz1403))))",fontsize=16,color="magenta"];17803 -> 17843[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17803 -> 17844[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17803 -> 17845[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17803 -> 17846[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17803 -> 17847[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17803 -> 17848[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17803 -> 17849[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17803 -> 17850[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17803 -> 17851[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17803 -> 17852[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17803 -> 17853[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 27626[label="zzz2641",fontsize=16,color="green",shape="box"];27627[label="zzz2636",fontsize=16,color="green",shape="box"];27628[label="zzz2629",fontsize=16,color="green",shape="box"];27629[label="zzz2631",fontsize=16,color="green",shape="box"];27630[label="zzz2628",fontsize=16,color="green",shape="box"];27631[label="zzz2630",fontsize=16,color="green",shape="box"];27632[label="zzz2635",fontsize=16,color="green",shape="box"];27633[label="zzz2632",fontsize=16,color="green",shape="box"];27634[label="zzz2627",fontsize=16,color="green",shape="box"];27635[label="zzz2634",fontsize=16,color="green",shape="box"];27636[label="zzz2633",fontsize=16,color="green",shape="box"];27637[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) zzz2633 zzz2634 zzz2635 zzz2636 (Maybe.isJust (FiniteMap.lookupFM0 (Neg (Succ zzz2637)) zzz2638 zzz2639 zzz2640 zzz2641 (Neg (Succ zzz2632)) True))",fontsize=16,color="black",shape="box"];27637 -> 27718[label="",style="solid", color="black", weight=3]; 130.25/78.13 24958 -> 14393[label="",style="dashed", color="red", weight=0]; 130.25/78.13 24958[label="FiniteMap.splitGT (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148))",fontsize=16,color="magenta"];24958 -> 25008[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24958 -> 25009[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24959 -> 13018[label="",style="dashed", color="red", weight=0]; 130.25/78.13 24959[label="FiniteMap.splitLT (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148))",fontsize=16,color="magenta"];24959 -> 25010[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24959 -> 25011[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 24960[label="zzz21563",fontsize=16,color="green",shape="box"];24961[label="zzz21563",fontsize=16,color="green",shape="box"];24962[label="zzz21564",fontsize=16,color="green",shape="box"];24963[label="zzz21562",fontsize=16,color="green",shape="box"];24964[label="zzz2156000",fontsize=16,color="green",shape="box"];24965[label="zzz2156000",fontsize=16,color="green",shape="box"];24966[label="zzz2148",fontsize=16,color="green",shape="box"];24967[label="zzz21561",fontsize=16,color="green",shape="box"];24968[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz21561 zzz21562 zzz21563 zzz21564 (Neg (Succ zzz2148)) True))",fontsize=16,color="black",shape="box"];24968 -> 25012[label="",style="solid", color="black", weight=3]; 130.25/78.13 1174[label="FiniteMap.splitGT2 (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (primCmpInt (Neg (Succ zzz4000)) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];1174 -> 1443[label="",style="solid", color="black", weight=3]; 130.25/78.13 1175[label="FiniteMap.splitLT2 (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (primCmpInt (Neg (Succ zzz4000)) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];1175 -> 1444[label="",style="solid", color="black", weight=3]; 130.25/78.13 12646[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 False",fontsize=16,color="black",shape="box"];12646 -> 12926[label="",style="solid", color="black", weight=3]; 130.25/78.13 19543 -> 19020[label="",style="dashed", color="red", weight=0]; 130.25/78.13 19543[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) zzz1582 zzz1583 zzz1584 zzz1585 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1586)) zzz1587 zzz1588 zzz1589 zzz1590 (Neg (Succ zzz1581)) (primCmpNat zzz15910 zzz15920 == LT)))",fontsize=16,color="magenta"];19543 -> 19593[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 19543 -> 19594[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 19544[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) zzz1582 zzz1583 zzz1584 zzz1585 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1586)) zzz1587 zzz1588 zzz1589 zzz1590 (Neg (Succ zzz1581)) (GT == LT)))",fontsize=16,color="black",shape="box"];19544 -> 19595[label="",style="solid", color="black", weight=3]; 130.25/78.13 19545[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) zzz1582 zzz1583 zzz1584 zzz1585 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1586)) zzz1587 zzz1588 zzz1589 zzz1590 (Neg (Succ zzz1581)) (LT == LT)))",fontsize=16,color="black",shape="box"];19545 -> 19596[label="",style="solid", color="black", weight=3]; 130.25/78.13 19546[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) zzz1582 zzz1583 zzz1584 zzz1585 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1586)) zzz1587 zzz1588 zzz1589 zzz1590 (Neg (Succ zzz1581)) (EQ == LT)))",fontsize=16,color="black",shape="box"];19546 -> 19597[label="",style="solid", color="black", weight=3]; 130.25/78.13 12378[label="FiniteMap.splitGT2 (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834 (Neg Zero) (primCmpInt (Neg Zero) (Pos (Succ zzz830)) == GT)",fontsize=16,color="black",shape="box"];12378 -> 12472[label="",style="solid", color="black", weight=3]; 130.25/78.13 12379[label="FiniteMap.splitLT2 (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834 (Neg Zero) (primCmpInt (Neg Zero) (Pos (Succ zzz830)) == LT)",fontsize=16,color="black",shape="box"];12379 -> 12473[label="",style="solid", color="black", weight=3]; 130.25/78.13 12918[label="zzz9111",fontsize=16,color="green",shape="box"];12919[label="zzz9113",fontsize=16,color="green",shape="box"];12920[label="zzz9112",fontsize=16,color="green",shape="box"];12921[label="zzz9110",fontsize=16,color="green",shape="box"];12922[label="zzz9114",fontsize=16,color="green",shape="box"];12923[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) False))",fontsize=16,color="black",shape="box"];12923 -> 12959[label="",style="solid", color="black", weight=3]; 130.25/78.13 12924[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz90800)) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (primCmpNat (Succ zzz90800) Zero == GT)))",fontsize=16,color="black",shape="box"];12924 -> 12960[label="",style="solid", color="black", weight=3]; 130.25/78.13 12925[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) False))",fontsize=16,color="black",shape="box"];12925 -> 12961[label="",style="solid", color="black", weight=3]; 130.25/78.13 5850[label="FiniteMap.splitLT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (compare (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];5850 -> 6027[label="",style="solid", color="black", weight=3]; 130.25/78.13 5851[label="FiniteMap.splitGT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (compare (Neg Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];5851 -> 6028[label="",style="solid", color="black", weight=3]; 130.25/78.13 12361[label="zzz34",fontsize=16,color="green",shape="box"];12362[label="Zero",fontsize=16,color="green",shape="box"];12360[label="FiniteMap.addToFM_C FiniteMap.addToFM0 zzz982 (Neg zzz300) zzz31",fontsize=16,color="burlywood",shape="triangle"];64976[label="zzz982/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];12360 -> 64976[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64976 -> 12380[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 64977[label="zzz982/FiniteMap.Branch zzz9820 zzz9821 zzz9822 zzz9823 zzz9824",fontsize=10,color="white",style="solid",shape="box"];12360 -> 64977[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64977 -> 12381[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 5854[label="FiniteMap.Branch zzz3530 zzz3531 zzz3532 zzz3533 zzz3534",fontsize=16,color="green",shape="box"];5855[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];5855 -> 6031[label="",style="solid", color="black", weight=3]; 130.25/78.13 1200 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.13 1200[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero)) zzz44",fontsize=16,color="magenta"];1200 -> 1471[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 1200 -> 1472[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 1201 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.13 1201[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero)) zzz43",fontsize=16,color="magenta"];1201 -> 1473[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 1201 -> 1474[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 19769[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz160300)) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (primCmpInt (Neg Zero) (Pos (Succ zzz160300)) == LT)))",fontsize=16,color="black",shape="box"];19769 -> 19804[label="",style="solid", color="black", weight=3]; 130.25/78.13 19770[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];19770 -> 19805[label="",style="solid", color="black", weight=3]; 130.25/78.13 19771[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz160300)) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ zzz160300)) == LT)))",fontsize=16,color="black",shape="box"];19771 -> 19806[label="",style="solid", color="black", weight=3]; 130.25/78.13 19772[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == LT)))",fontsize=16,color="black",shape="box"];19772 -> 19807[label="",style="solid", color="black", weight=3]; 130.25/78.13 5856[label="FiniteMap.splitLT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (compare (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];5856 -> 6032[label="",style="solid", color="black", weight=3]; 130.25/78.13 5857[label="FiniteMap.splitGT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (compare (Neg Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];5857 -> 6033[label="",style="solid", color="black", weight=3]; 130.25/78.13 27638[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) zzz2615 zzz2616 zzz2617 zzz2618 (Maybe.isJust (Just zzz2620))",fontsize=16,color="black",shape="box"];27638 -> 27719[label="",style="solid", color="black", weight=3]; 130.25/78.13 24749[label="FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082",fontsize=16,color="green",shape="box"];24750[label="zzz2083",fontsize=16,color="green",shape="box"];19598[label="FiniteMap.splitGT zzz1612 (Pos (Succ zzz1613))",fontsize=16,color="burlywood",shape="triangle"];64978[label="zzz1612/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];19598 -> 64978[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64978 -> 19638[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 64979[label="zzz1612/FiniteMap.Branch zzz16120 zzz16121 zzz16122 zzz16123 zzz16124",fontsize=10,color="white",style="solid",shape="box"];19598 -> 64979[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64979 -> 19639[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 24751[label="zzz2083",fontsize=16,color="green",shape="box"];24752[label="FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082",fontsize=16,color="green",shape="box"];23112[label="FiniteMap.splitLT zzz1974 (Pos (Succ zzz1975))",fontsize=16,color="burlywood",shape="triangle"];64980[label="zzz1974/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];23112 -> 64980[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64980 -> 23292[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 64981[label="zzz1974/FiniteMap.Branch zzz19740 zzz19741 zzz19742 zzz19743 zzz19744",fontsize=10,color="white",style="solid",shape="box"];23112 -> 64981[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64981 -> 23293[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 24753[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (Pos (Succ zzz2083) > Pos Zero)))",fontsize=16,color="black",shape="box"];24753 -> 24814[label="",style="solid", color="black", weight=3]; 130.25/78.13 24754[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz209100) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (primCmpInt (Pos (Succ zzz2083)) (Neg zzz209100) == GT)))",fontsize=16,color="black",shape="box"];24754 -> 24815[label="",style="solid", color="black", weight=3]; 130.25/78.13 1302[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))",fontsize=16,color="black",shape="box"];1302 -> 1537[label="",style="solid", color="black", weight=3]; 130.25/78.13 1303[label="zzz44",fontsize=16,color="green",shape="box"];1304[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))",fontsize=16,color="black",shape="box"];1304 -> 1538[label="",style="solid", color="black", weight=3]; 130.25/78.13 1305[label="zzz43",fontsize=16,color="green",shape="box"];28522[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz274300)) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (primCmpNat (Succ zzz2738) (Succ zzz274300) == LT)))",fontsize=16,color="black",shape="box"];28522 -> 28535[label="",style="solid", color="black", weight=3]; 130.25/78.13 28523[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (primCmpNat (Succ zzz2738) Zero == LT)))",fontsize=16,color="black",shape="box"];28523 -> 28536[label="",style="solid", color="black", weight=3]; 130.25/78.13 28524[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM2 (Neg zzz27430) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) False))",fontsize=16,color="black",shape="box"];28524 -> 28537[label="",style="solid", color="black", weight=3]; 130.25/78.13 1309[label="FiniteMap.splitGT2 (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos (Succ zzz4000)) (Pos (Succ zzz4000) > Neg zzz300)",fontsize=16,color="black",shape="box"];1309 -> 1543[label="",style="solid", color="black", weight=3]; 130.25/78.13 1310[label="FiniteMap.splitLT2 (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos (Succ zzz4000)) (Pos (Succ zzz4000) < Neg zzz300)",fontsize=16,color="black",shape="box"];1310 -> 1544[label="",style="solid", color="black", weight=3]; 130.25/78.13 22209[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) zzz1983 zzz1984 zzz1985 zzz1986 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz1987)) zzz1988 zzz1989 zzz1990 zzz1991 (Pos (Succ zzz1982)) (primCmpNat (Succ zzz19920) zzz1993 == LT)))",fontsize=16,color="burlywood",shape="box"];64982[label="zzz1993/Succ zzz19930",fontsize=10,color="white",style="solid",shape="box"];22209 -> 64982[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64982 -> 22241[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 64983[label="zzz1993/Zero",fontsize=10,color="white",style="solid",shape="box"];22209 -> 64983[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64983 -> 22242[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 22210[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) zzz1983 zzz1984 zzz1985 zzz1986 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz1987)) zzz1988 zzz1989 zzz1990 zzz1991 (Pos (Succ zzz1982)) (primCmpNat Zero zzz1993 == LT)))",fontsize=16,color="burlywood",shape="box"];64984[label="zzz1993/Succ zzz19930",fontsize=10,color="white",style="solid",shape="box"];22210 -> 64984[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64984 -> 22243[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 64985[label="zzz1993/Zero",fontsize=10,color="white",style="solid",shape="box"];22210 -> 64985[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64985 -> 22244[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 18159[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (Pos (Succ zzz1387) > Pos Zero)))",fontsize=16,color="black",shape="box"];18159 -> 18188[label="",style="solid", color="black", weight=3]; 130.25/78.13 18160[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz13920) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (primCmpInt (Pos (Succ zzz1387)) (Neg zzz13920) == GT)))",fontsize=16,color="black",shape="box"];18160 -> 18189[label="",style="solid", color="black", weight=3]; 130.25/78.13 1317[label="FiniteMap.splitGT2 (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Pos Zero) (primCmpNat Zero (Succ zzz3000) == GT)",fontsize=16,color="black",shape="box"];1317 -> 1552[label="",style="solid", color="black", weight=3]; 130.25/78.13 1318[label="FiniteMap.splitLT2 (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Pos Zero) (primCmpNat Zero (Succ zzz3000) == LT)",fontsize=16,color="black",shape="box"];1318 -> 1553[label="",style="solid", color="black", weight=3]; 130.25/78.13 10337[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust Nothing)",fontsize=16,color="black",shape="box"];10337 -> 10370[label="",style="solid", color="black", weight=3]; 130.25/78.13 10338[label="zzz6303",fontsize=16,color="green",shape="box"];10339[label="zzz6302",fontsize=16,color="green",shape="box"];10340[label="zzz6301",fontsize=16,color="green",shape="box"];10341[label="zzz6304",fontsize=16,color="green",shape="box"];10342[label="zzz6300",fontsize=16,color="green",shape="box"];10343[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) False))",fontsize=16,color="black",shape="box"];10343 -> 10371[label="",style="solid", color="black", weight=3]; 130.25/78.13 10344[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz62700)) zzz628 zzz629 zzz630 zzz631 (Pos Zero) True))",fontsize=16,color="black",shape="box"];10344 -> 10372[label="",style="solid", color="black", weight=3]; 130.25/78.13 10345[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) False))",fontsize=16,color="black",shape="box"];10345 -> 10373[label="",style="solid", color="black", weight=3]; 130.25/78.13 4917[label="FiniteMap.splitLT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];4917 -> 4942[label="",style="solid", color="black", weight=3]; 130.25/78.13 4918[label="FiniteMap.splitGT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];4918 -> 4943[label="",style="solid", color="black", weight=3]; 130.25/78.13 4919[label="FiniteMap.addToFM_C4 FiniteMap.addToFM0 FiniteMap.EmptyFM (Pos zzz300) zzz31",fontsize=16,color="black",shape="box"];4919 -> 4944[label="",style="solid", color="black", weight=3]; 130.25/78.13 4920[label="FiniteMap.addToFM_C3 FiniteMap.addToFM0 (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344) (Pos zzz300) zzz31",fontsize=16,color="black",shape="box"];4920 -> 4945[label="",style="solid", color="black", weight=3]; 130.25/78.13 4921[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];4921 -> 4946[label="",style="solid", color="black", weight=3]; 130.25/78.13 1329[label="FiniteMap.splitGT3 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero)",fontsize=16,color="black",shape="box"];1329 -> 1565[label="",style="solid", color="black", weight=3]; 130.25/78.13 1330[label="FiniteMap.splitLT3 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos Zero)",fontsize=16,color="black",shape="box"];1330 -> 1566[label="",style="solid", color="black", weight=3]; 130.25/78.13 15169[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz120100)) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) True))",fontsize=16,color="black",shape="box"];15169 -> 15403[label="",style="solid", color="black", weight=3]; 130.25/78.13 15170[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (Pos Zero > Pos Zero)))",fontsize=16,color="black",shape="box"];15170 -> 15404[label="",style="solid", color="black", weight=3]; 130.25/78.13 15171[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz120100)) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (Pos Zero > Neg (Succ zzz120100))))",fontsize=16,color="black",shape="box"];15171 -> 15405[label="",style="solid", color="black", weight=3]; 130.25/78.13 15172[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (Pos Zero > Neg Zero)))",fontsize=16,color="black",shape="box"];15172 -> 15406[label="",style="solid", color="black", weight=3]; 130.25/78.13 4922[label="FiniteMap.splitLT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];4922 -> 4947[label="",style="solid", color="black", weight=3]; 130.25/78.13 4923[label="FiniteMap.splitGT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];4923 -> 4948[label="",style="solid", color="black", weight=3]; 130.25/78.13 1340[label="FiniteMap.splitGT1 (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (Neg (Succ zzz4000) < Pos zzz300)",fontsize=16,color="black",shape="box"];1340 -> 1577[label="",style="solid", color="black", weight=3]; 130.25/78.13 1341[label="FiniteMap.splitLT FiniteMap.EmptyFM (Neg (Succ zzz4000))",fontsize=16,color="black",shape="triangle"];1341 -> 1578[label="",style="solid", color="black", weight=3]; 130.25/78.13 55810[label="Pos Zero",fontsize=16,color="green",shape="box"];55811[label="zzz34902",fontsize=16,color="green",shape="box"];62449 -> 62469[label="",style="dashed", color="red", weight=0]; 130.25/78.13 62449[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.glueVBal3Size_l zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464)) zzz6319 == LT)",fontsize=16,color="magenta"];62449 -> 62470[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 11971 -> 288[label="",style="dashed", color="red", weight=0]; 130.25/78.13 11971[label="FiniteMap.glueVBal (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747))) zzz750) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747))) zzz751)",fontsize=16,color="magenta"];11971 -> 12082[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 11971 -> 12083[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 17842[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) zzz1404 zzz1405 zzz1406 zzz1407 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz1408)) zzz1409 zzz1410 zzz1411 zzz1412 (Neg (Succ zzz1403)) (compare (Neg (Succ zzz1403)) (Neg (Succ zzz1408)) == GT)))",fontsize=16,color="black",shape="box"];17842 -> 18132[label="",style="solid", color="black", weight=3]; 130.25/78.13 17843[label="zzz1400",fontsize=16,color="green",shape="box"];17844[label="zzz1405",fontsize=16,color="green",shape="box"];17845[label="zzz1401",fontsize=16,color="green",shape="box"];17846[label="zzz1407",fontsize=16,color="green",shape="box"];17847[label="zzz1404",fontsize=16,color="green",shape="box"];17848[label="zzz1402",fontsize=16,color="green",shape="box"];17849[label="zzz1406",fontsize=16,color="green",shape="box"];17850[label="zzz1398",fontsize=16,color="green",shape="box"];17851[label="zzz1399",fontsize=16,color="green",shape="box"];17852[label="zzz1403",fontsize=16,color="green",shape="box"];17853[label="zzz1411",fontsize=16,color="green",shape="box"];27718[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) zzz2633 zzz2634 zzz2635 zzz2636 (Maybe.isJust (Just zzz2638))",fontsize=16,color="black",shape="box"];27718 -> 27849[label="",style="solid", color="black", weight=3]; 130.25/78.13 25008[label="FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147",fontsize=16,color="green",shape="box"];25009[label="zzz2148",fontsize=16,color="green",shape="box"];14393[label="FiniteMap.splitGT zzz745 (Neg (Succ zzz747))",fontsize=16,color="burlywood",shape="triangle"];64986[label="zzz745/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];14393 -> 64986[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64986 -> 14464[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 64987[label="zzz745/FiniteMap.Branch zzz7450 zzz7451 zzz7452 zzz7453 zzz7454",fontsize=10,color="white",style="solid",shape="box"];14393 -> 64987[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64987 -> 14465[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 25010[label="FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147",fontsize=16,color="green",shape="box"];25011[label="zzz2148",fontsize=16,color="green",shape="box"];13018[label="FiniteMap.splitLT zzz745 (Neg (Succ zzz747))",fontsize=16,color="burlywood",shape="triangle"];64988[label="zzz745/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];13018 -> 64988[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64988 -> 13269[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 64989[label="zzz745/FiniteMap.Branch zzz7450 zzz7451 zzz7452 zzz7453 zzz7454",fontsize=10,color="white",style="solid",shape="box"];13018 -> 64989[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64989 -> 13270[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 25012 -> 24193[label="",style="dashed", color="red", weight=0]; 130.25/78.13 25012[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2143)) zzz2144 zzz2145 zzz2146 zzz2147) (Neg (Succ zzz2148)) zzz2149 zzz2150 zzz2151 zzz2152 (Maybe.isJust (FiniteMap.lookupFM zzz21563 (Neg (Succ zzz2148))))",fontsize=16,color="magenta"];25012 -> 25143[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 1443[label="FiniteMap.splitGT2 (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (primCmpNat Zero (Succ zzz4000) == GT)",fontsize=16,color="black",shape="box"];1443 -> 1644[label="",style="solid", color="black", weight=3]; 130.25/78.13 1444[label="FiniteMap.splitLT2 (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (primCmpNat Zero (Succ zzz4000) == LT)",fontsize=16,color="black",shape="box"];1444 -> 1645[label="",style="solid", color="black", weight=3]; 130.25/78.13 12926[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 otherwise",fontsize=16,color="black",shape="box"];12926 -> 12962[label="",style="solid", color="black", weight=3]; 130.25/78.13 19593[label="zzz15910",fontsize=16,color="green",shape="box"];19594[label="zzz15920",fontsize=16,color="green",shape="box"];19595[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) zzz1582 zzz1583 zzz1584 zzz1585 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1586)) zzz1587 zzz1588 zzz1589 zzz1590 (Neg (Succ zzz1581)) False))",fontsize=16,color="black",shape="triangle"];19595 -> 19636[label="",style="solid", color="black", weight=3]; 130.25/78.13 19596[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) zzz1582 zzz1583 zzz1584 zzz1585 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1586)) zzz1587 zzz1588 zzz1589 zzz1590 (Neg (Succ zzz1581)) True))",fontsize=16,color="black",shape="box"];19596 -> 19637[label="",style="solid", color="black", weight=3]; 130.25/78.13 19597 -> 19595[label="",style="dashed", color="red", weight=0]; 130.25/78.13 19597[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) zzz1582 zzz1583 zzz1584 zzz1585 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz1586)) zzz1587 zzz1588 zzz1589 zzz1590 (Neg (Succ zzz1581)) False))",fontsize=16,color="magenta"];12472[label="FiniteMap.splitGT2 (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834 (Neg Zero) (LT == GT)",fontsize=16,color="black",shape="triangle"];12472 -> 12569[label="",style="solid", color="black", weight=3]; 130.25/78.13 12473[label="FiniteMap.splitLT2 (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834 (Neg Zero) (LT == LT)",fontsize=16,color="black",shape="triangle"];12473 -> 12570[label="",style="solid", color="black", weight=3]; 130.25/78.13 12959[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM0 (Pos Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) otherwise))",fontsize=16,color="black",shape="box"];12959 -> 12991[label="",style="solid", color="black", weight=3]; 130.25/78.13 12960[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz90800)) zzz909 zzz910 zzz911 zzz912 (Neg Zero) (GT == GT)))",fontsize=16,color="black",shape="box"];12960 -> 12992[label="",style="solid", color="black", weight=3]; 130.25/78.13 12961[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM0 (Neg Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) otherwise))",fontsize=16,color="black",shape="box"];12961 -> 12993[label="",style="solid", color="black", weight=3]; 130.25/78.13 6027[label="FiniteMap.splitLT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];6027 -> 6083[label="",style="solid", color="black", weight=3]; 130.25/78.13 6028[label="FiniteMap.splitGT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];6028 -> 6084[label="",style="solid", color="black", weight=3]; 130.25/78.13 12380[label="FiniteMap.addToFM_C FiniteMap.addToFM0 FiniteMap.EmptyFM (Neg zzz300) zzz31",fontsize=16,color="black",shape="box"];12380 -> 12474[label="",style="solid", color="black", weight=3]; 130.25/78.13 12381[label="FiniteMap.addToFM_C FiniteMap.addToFM0 (FiniteMap.Branch zzz9820 zzz9821 zzz9822 zzz9823 zzz9824) (Neg zzz300) zzz31",fontsize=16,color="black",shape="box"];12381 -> 12475[label="",style="solid", color="black", weight=3]; 130.25/78.13 6031[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];6031 -> 6087[label="",style="solid", color="black", weight=3]; 130.25/78.13 1471[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero)",fontsize=16,color="black",shape="box"];1471 -> 1675[label="",style="solid", color="black", weight=3]; 130.25/78.13 1472[label="zzz44",fontsize=16,color="green",shape="box"];1473[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero)",fontsize=16,color="black",shape="box"];1473 -> 1676[label="",style="solid", color="black", weight=3]; 130.25/78.13 1474[label="zzz43",fontsize=16,color="green",shape="box"];19804[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz160300)) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (LT == LT)))",fontsize=16,color="black",shape="box"];19804 -> 19861[label="",style="solid", color="black", weight=3]; 130.25/78.13 19805[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (EQ == LT)))",fontsize=16,color="black",shape="box"];19805 -> 19862[label="",style="solid", color="black", weight=3]; 130.25/78.13 19806[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz160300)) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (primCmpNat (Succ zzz160300) Zero == LT)))",fontsize=16,color="black",shape="box"];19806 -> 19863[label="",style="solid", color="black", weight=3]; 130.25/78.13 19807[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (EQ == LT)))",fontsize=16,color="black",shape="box"];19807 -> 19864[label="",style="solid", color="black", weight=3]; 130.25/78.13 6032[label="FiniteMap.splitLT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];6032 -> 6088[label="",style="solid", color="black", weight=3]; 130.25/78.13 6033[label="FiniteMap.splitGT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];6033 -> 6089[label="",style="solid", color="black", weight=3]; 130.25/78.13 27719[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614)) zzz2615 zzz2616 zzz2617 zzz2618 True",fontsize=16,color="black",shape="box"];27719 -> 27850[label="",style="solid", color="black", weight=3]; 130.25/78.13 19638[label="FiniteMap.splitGT FiniteMap.EmptyFM (Pos (Succ zzz1613))",fontsize=16,color="black",shape="box"];19638 -> 19785[label="",style="solid", color="black", weight=3]; 130.25/78.13 19639[label="FiniteMap.splitGT (FiniteMap.Branch zzz16120 zzz16121 zzz16122 zzz16123 zzz16124) (Pos (Succ zzz1613))",fontsize=16,color="black",shape="box"];19639 -> 19786[label="",style="solid", color="black", weight=3]; 130.25/78.13 23292[label="FiniteMap.splitLT FiniteMap.EmptyFM (Pos (Succ zzz1975))",fontsize=16,color="black",shape="box"];23292 -> 23410[label="",style="solid", color="black", weight=3]; 130.25/78.13 23293[label="FiniteMap.splitLT (FiniteMap.Branch zzz19740 zzz19741 zzz19742 zzz19743 zzz19744) (Pos (Succ zzz1975))",fontsize=16,color="black",shape="box"];23293 -> 23411[label="",style="solid", color="black", weight=3]; 130.25/78.13 24814[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (compare (Pos (Succ zzz2083)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];24814 -> 24891[label="",style="solid", color="black", weight=3]; 130.25/78.13 24815[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz209100) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (GT == GT)))",fontsize=16,color="black",shape="box"];24815 -> 24892[label="",style="solid", color="black", weight=3]; 130.25/78.13 1537[label="FiniteMap.splitGT (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))",fontsize=16,color="black",shape="box"];1537 -> 1719[label="",style="solid", color="black", weight=3]; 130.25/78.13 1538[label="FiniteMap.splitLT (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))",fontsize=16,color="black",shape="box"];1538 -> 1720[label="",style="solid", color="black", weight=3]; 130.25/78.13 28535 -> 30437[label="",style="dashed", color="red", weight=0]; 130.25/78.13 28535[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz274300)) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (primCmpNat zzz2738 zzz274300 == LT)))",fontsize=16,color="magenta"];28535 -> 30438[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 28535 -> 30439[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 28535 -> 30440[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 28535 -> 30441[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 28535 -> 30442[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 28535 -> 30443[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 28535 -> 30444[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 28535 -> 30445[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 28535 -> 30446[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 28535 -> 30447[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 28535 -> 30448[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 28535 -> 30449[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 28535 -> 30450[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 28535 -> 30451[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 28535 -> 30452[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 28535 -> 30453[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 28536[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (GT == LT)))",fontsize=16,color="black",shape="box"];28536 -> 28561[label="",style="solid", color="black", weight=3]; 130.25/78.13 28537[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz27430) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (Pos (Succ zzz2738) > Neg zzz27430)))",fontsize=16,color="black",shape="box"];28537 -> 28562[label="",style="solid", color="black", weight=3]; 130.25/78.13 1543[label="FiniteMap.splitGT2 (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos (Succ zzz4000)) (compare (Pos (Succ zzz4000)) (Neg zzz300) == GT)",fontsize=16,color="black",shape="box"];1543 -> 1727[label="",style="solid", color="black", weight=3]; 130.25/78.13 1544 -> 21896[label="",style="dashed", color="red", weight=0]; 130.25/78.13 1544[label="FiniteMap.splitLT2 (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos (Succ zzz4000)) (compare (Pos (Succ zzz4000)) (Neg zzz300) == LT)",fontsize=16,color="magenta"];1544 -> 21897[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 1544 -> 21898[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 1544 -> 21899[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 1544 -> 21900[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 1544 -> 21901[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 1544 -> 21902[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 22241[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) zzz1983 zzz1984 zzz1985 zzz1986 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz1987)) zzz1988 zzz1989 zzz1990 zzz1991 (Pos (Succ zzz1982)) (primCmpNat (Succ zzz19920) (Succ zzz19930) == LT)))",fontsize=16,color="black",shape="box"];22241 -> 22271[label="",style="solid", color="black", weight=3]; 130.25/78.13 22242[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) zzz1983 zzz1984 zzz1985 zzz1986 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz1987)) zzz1988 zzz1989 zzz1990 zzz1991 (Pos (Succ zzz1982)) (primCmpNat (Succ zzz19920) Zero == LT)))",fontsize=16,color="black",shape="box"];22242 -> 22272[label="",style="solid", color="black", weight=3]; 130.25/78.13 22243[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) zzz1983 zzz1984 zzz1985 zzz1986 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz1987)) zzz1988 zzz1989 zzz1990 zzz1991 (Pos (Succ zzz1982)) (primCmpNat Zero (Succ zzz19930) == LT)))",fontsize=16,color="black",shape="box"];22243 -> 22273[label="",style="solid", color="black", weight=3]; 130.25/78.13 22244[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) zzz1983 zzz1984 zzz1985 zzz1986 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz1987)) zzz1988 zzz1989 zzz1990 zzz1991 (Pos (Succ zzz1982)) (primCmpNat Zero Zero == LT)))",fontsize=16,color="black",shape="box"];22244 -> 22274[label="",style="solid", color="black", weight=3]; 130.25/78.13 18188[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (compare (Pos (Succ zzz1387)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];18188 -> 18232[label="",style="solid", color="black", weight=3]; 130.25/78.13 18189[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz13920) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (GT == GT)))",fontsize=16,color="black",shape="box"];18189 -> 18233[label="",style="solid", color="black", weight=3]; 130.25/78.13 1552[label="FiniteMap.splitGT2 (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Pos Zero) (LT == GT)",fontsize=16,color="black",shape="box"];1552 -> 1738[label="",style="solid", color="black", weight=3]; 130.25/78.13 1553[label="FiniteMap.splitLT2 (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Pos Zero) (LT == LT)",fontsize=16,color="black",shape="box"];1553 -> 1739[label="",style="solid", color="black", weight=3]; 130.25/78.13 10370[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 False",fontsize=16,color="black",shape="box"];10370 -> 10400[label="",style="solid", color="black", weight=3]; 130.25/78.13 10371[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM0 (Pos Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) otherwise))",fontsize=16,color="black",shape="box"];10371 -> 10401[label="",style="solid", color="black", weight=3]; 130.25/78.13 10372 -> 9885[label="",style="dashed", color="red", weight=0]; 130.25/78.13 10372[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM zzz631 (Pos Zero)))",fontsize=16,color="magenta"];10372 -> 10402[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 10373[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM0 (Neg Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) otherwise))",fontsize=16,color="black",shape="box"];10373 -> 10403[label="",style="solid", color="black", weight=3]; 130.25/78.13 4942[label="FiniteMap.splitLT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (EQ == LT)",fontsize=16,color="black",shape="triangle"];4942 -> 5094[label="",style="solid", color="black", weight=3]; 130.25/78.13 4943[label="FiniteMap.splitGT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (EQ == GT)",fontsize=16,color="black",shape="triangle"];4943 -> 5095[label="",style="solid", color="black", weight=3]; 130.25/78.13 4944[label="FiniteMap.unitFM (Pos zzz300) zzz31",fontsize=16,color="black",shape="box"];4944 -> 5096[label="",style="solid", color="black", weight=3]; 130.25/78.13 4945[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 (Pos zzz300 < zzz340)",fontsize=16,color="black",shape="box"];4945 -> 5097[label="",style="solid", color="black", weight=3]; 130.25/78.13 4946[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];4946 -> 5098[label="",style="solid", color="black", weight=3]; 130.25/78.13 1565[label="FiniteMap.splitGT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos Zero) (Pos Zero > Neg (Succ zzz3000))",fontsize=16,color="black",shape="box"];1565 -> 1752[label="",style="solid", color="black", weight=3]; 130.25/78.13 1566[label="FiniteMap.splitLT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos Zero) (Pos Zero < Neg (Succ zzz3000))",fontsize=16,color="black",shape="box"];1566 -> 1753[label="",style="solid", color="black", weight=3]; 130.25/78.13 15403[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM zzz1204 (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];64990[label="zzz1204/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];15403 -> 64990[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64990 -> 15580[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 64991[label="zzz1204/FiniteMap.Branch zzz12040 zzz12041 zzz12042 zzz12043 zzz12044",fontsize=10,color="white",style="solid",shape="box"];15403 -> 64991[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64991 -> 15581[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 15404[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (compare (Pos Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];15404 -> 15582[label="",style="solid", color="black", weight=3]; 130.25/78.13 15405[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz120100)) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (compare (Pos Zero) (Neg (Succ zzz120100)) == GT)))",fontsize=16,color="black",shape="box"];15405 -> 15583[label="",style="solid", color="black", weight=3]; 130.25/78.13 15406[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (compare (Pos Zero) (Neg Zero) == GT)))",fontsize=16,color="black",shape="box"];15406 -> 15584[label="",style="solid", color="black", weight=3]; 130.25/78.13 4947[label="FiniteMap.splitLT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (EQ == LT)",fontsize=16,color="black",shape="triangle"];4947 -> 5099[label="",style="solid", color="black", weight=3]; 130.25/78.13 4948[label="FiniteMap.splitGT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (EQ == GT)",fontsize=16,color="black",shape="triangle"];4948 -> 5100[label="",style="solid", color="black", weight=3]; 130.25/78.13 1577[label="FiniteMap.splitGT1 (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (compare (Neg (Succ zzz4000)) (Pos zzz300) == LT)",fontsize=16,color="black",shape="box"];1577 -> 1764[label="",style="solid", color="black", weight=3]; 130.25/78.13 1578[label="FiniteMap.splitLT4 FiniteMap.EmptyFM (Neg (Succ zzz4000))",fontsize=16,color="black",shape="triangle"];1578 -> 1765[label="",style="solid", color="black", weight=3]; 130.25/78.13 62470[label="FiniteMap.glueVBal3Size_l zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464",fontsize=16,color="black",shape="triangle"];62470 -> 62472[label="",style="solid", color="black", weight=3]; 130.25/78.13 62469[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz6337) zzz6319 == LT)",fontsize=16,color="burlywood",shape="triangle"];64992[label="zzz6337/Pos zzz63370",fontsize=10,color="white",style="solid",shape="box"];62469 -> 64992[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64992 -> 62473[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 64993[label="zzz6337/Neg zzz63370",fontsize=10,color="white",style="solid",shape="box"];62469 -> 64993[label="",style="solid", color="burlywood", weight=9]; 130.25/78.13 64993 -> 62474[label="",style="solid", color="burlywood", weight=3]; 130.25/78.13 12082 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.13 12082[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747))) zzz751",fontsize=16,color="magenta"];12082 -> 12144[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 12082 -> 12145[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 12083 -> 5[label="",style="dashed", color="red", weight=0]; 130.25/78.13 12083[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747))) zzz750",fontsize=16,color="magenta"];12083 -> 12146[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 12083 -> 12147[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 18132[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) zzz1404 zzz1405 zzz1406 zzz1407 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz1408)) zzz1409 zzz1410 zzz1411 zzz1412 (Neg (Succ zzz1403)) (primCmpInt (Neg (Succ zzz1403)) (Neg (Succ zzz1408)) == GT)))",fontsize=16,color="black",shape="box"];18132 -> 18161[label="",style="solid", color="black", weight=3]; 130.25/78.13 27849[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632)) zzz2633 zzz2634 zzz2635 zzz2636 True",fontsize=16,color="black",shape="box"];27849 -> 27891[label="",style="solid", color="black", weight=3]; 130.25/78.13 14464[label="FiniteMap.splitGT FiniteMap.EmptyFM (Neg (Succ zzz747))",fontsize=16,color="black",shape="box"];14464 -> 14963[label="",style="solid", color="black", weight=3]; 130.25/78.13 14465[label="FiniteMap.splitGT (FiniteMap.Branch zzz7450 zzz7451 zzz7452 zzz7453 zzz7454) (Neg (Succ zzz747))",fontsize=16,color="black",shape="box"];14465 -> 14964[label="",style="solid", color="black", weight=3]; 130.25/78.13 13269[label="FiniteMap.splitLT FiniteMap.EmptyFM (Neg (Succ zzz747))",fontsize=16,color="black",shape="box"];13269 -> 13471[label="",style="solid", color="black", weight=3]; 130.25/78.13 13270[label="FiniteMap.splitLT (FiniteMap.Branch zzz7450 zzz7451 zzz7452 zzz7453 zzz7454) (Neg (Succ zzz747))",fontsize=16,color="black",shape="box"];13270 -> 13472[label="",style="solid", color="black", weight=3]; 130.25/78.13 25143[label="zzz21563",fontsize=16,color="green",shape="box"];1644[label="FiniteMap.splitGT2 (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (LT == GT)",fontsize=16,color="black",shape="box"];1644 -> 1825[label="",style="solid", color="black", weight=3]; 130.25/78.13 1645[label="FiniteMap.splitLT2 (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (LT == LT)",fontsize=16,color="black",shape="box"];1645 -> 1826[label="",style="solid", color="black", weight=3]; 130.25/78.13 12962[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888)) zzz889 zzz890 zzz891 zzz892 True",fontsize=16,color="black",shape="box"];12962 -> 12994[label="",style="solid", color="black", weight=3]; 130.25/78.13 19636[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) zzz1582 zzz1583 zzz1584 zzz1585 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz1586)) zzz1587 zzz1588 zzz1589 zzz1590 (Neg (Succ zzz1581)) (Neg (Succ zzz1581) > Neg (Succ zzz1586))))",fontsize=16,color="black",shape="box"];19636 -> 19773[label="",style="solid", color="black", weight=3]; 130.25/78.13 19637 -> 12274[label="",style="dashed", color="red", weight=0]; 130.25/78.13 19637[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) zzz1582 zzz1583 zzz1584 zzz1585 (Maybe.isJust (FiniteMap.lookupFM zzz1589 (Neg (Succ zzz1581))))",fontsize=16,color="magenta"];19637 -> 19774[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 19637 -> 19775[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 19637 -> 19776[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 19637 -> 19777[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 19637 -> 19778[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 19637 -> 19779[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 19637 -> 19780[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 19637 -> 19781[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 19637 -> 19782[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 19637 -> 19783[label="",style="dashed", color="magenta", weight=3]; 130.25/78.13 12569[label="FiniteMap.splitGT2 (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834 (Neg Zero) False",fontsize=16,color="black",shape="box"];12569 -> 12652[label="",style="solid", color="black", weight=3]; 130.29/78.13 12570[label="FiniteMap.splitLT2 (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834 (Neg Zero) True",fontsize=16,color="black",shape="box"];12570 -> 12653[label="",style="solid", color="black", weight=3]; 130.29/78.13 12991[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM0 (Pos Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) True))",fontsize=16,color="black",shape="box"];12991 -> 13234[label="",style="solid", color="black", weight=3]; 130.29/78.13 12992[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz90800)) zzz909 zzz910 zzz911 zzz912 (Neg Zero) True))",fontsize=16,color="black",shape="box"];12992 -> 13235[label="",style="solid", color="black", weight=3]; 130.29/78.13 12993[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM0 (Neg Zero) zzz909 zzz910 zzz911 zzz912 (Neg Zero) True))",fontsize=16,color="black",shape="box"];12993 -> 13236[label="",style="solid", color="black", weight=3]; 130.29/78.13 6083[label="FiniteMap.splitLT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (EQ == LT)",fontsize=16,color="black",shape="triangle"];6083 -> 6278[label="",style="solid", color="black", weight=3]; 130.29/78.13 6084[label="FiniteMap.splitGT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (EQ == GT)",fontsize=16,color="black",shape="triangle"];6084 -> 6279[label="",style="solid", color="black", weight=3]; 130.29/78.13 12474[label="FiniteMap.addToFM_C4 FiniteMap.addToFM0 FiniteMap.EmptyFM (Neg zzz300) zzz31",fontsize=16,color="black",shape="box"];12474 -> 12571[label="",style="solid", color="black", weight=3]; 130.29/78.13 12475[label="FiniteMap.addToFM_C3 FiniteMap.addToFM0 (FiniteMap.Branch zzz9820 zzz9821 zzz9822 zzz9823 zzz9824) (Neg zzz300) zzz31",fontsize=16,color="black",shape="box"];12475 -> 12572[label="",style="solid", color="black", weight=3]; 130.29/78.13 6087[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];6087 -> 6282[label="",style="solid", color="black", weight=3]; 130.29/78.13 1675[label="FiniteMap.splitGT (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero)",fontsize=16,color="black",shape="box"];1675 -> 1863[label="",style="solid", color="black", weight=3]; 130.29/78.13 1676[label="FiniteMap.splitLT (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero)",fontsize=16,color="black",shape="box"];1676 -> 1864[label="",style="solid", color="black", weight=3]; 130.29/78.13 19861[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz160300)) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) True))",fontsize=16,color="black",shape="box"];19861 -> 19884[label="",style="solid", color="black", weight=3]; 130.29/78.13 19862[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) False))",fontsize=16,color="black",shape="box"];19862 -> 19885[label="",style="solid", color="black", weight=3]; 130.29/78.13 19863[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz160300)) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (GT == LT)))",fontsize=16,color="black",shape="box"];19863 -> 19886[label="",style="solid", color="black", weight=3]; 130.29/78.13 19864[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM2 (Neg Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) False))",fontsize=16,color="black",shape="box"];19864 -> 19887[label="",style="solid", color="black", weight=3]; 130.29/78.13 6088[label="FiniteMap.splitLT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (EQ == LT)",fontsize=16,color="black",shape="triangle"];6088 -> 6283[label="",style="solid", color="black", weight=3]; 130.29/78.13 6089[label="FiniteMap.splitGT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (EQ == GT)",fontsize=16,color="black",shape="triangle"];6089 -> 6284[label="",style="solid", color="black", weight=3]; 130.29/78.13 27850 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.13 27850[label="FiniteMap.mkVBalBranch (Pos (Succ zzz2614)) (FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614))) zzz2615) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614))) zzz2617) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614))) zzz2618)",fontsize=16,color="magenta"];27850 -> 27892[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 27850 -> 27893[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 27850 -> 27894[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 27850 -> 27895[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 19785 -> 3302[label="",style="dashed", color="red", weight=0]; 130.29/78.13 19785[label="FiniteMap.splitGT4 FiniteMap.EmptyFM (Pos (Succ zzz1613))",fontsize=16,color="magenta"];19785 -> 19810[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 19786[label="FiniteMap.splitGT3 (FiniteMap.Branch zzz16120 zzz16121 zzz16122 zzz16123 zzz16124) (Pos (Succ zzz1613))",fontsize=16,color="black",shape="box"];19786 -> 19811[label="",style="solid", color="black", weight=3]; 130.29/78.13 23410 -> 7671[label="",style="dashed", color="red", weight=0]; 130.29/78.13 23410[label="FiniteMap.splitLT4 FiniteMap.EmptyFM (Pos (Succ zzz1975))",fontsize=16,color="magenta"];23410 -> 23610[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 23411 -> 23126[label="",style="dashed", color="red", weight=0]; 130.29/78.13 23411[label="FiniteMap.splitLT3 (FiniteMap.Branch zzz19740 zzz19741 zzz19742 zzz19743 zzz19744) (Pos (Succ zzz1975))",fontsize=16,color="magenta"];24891[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (primCmpInt (Pos (Succ zzz2083)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];24891 -> 24932[label="",style="solid", color="black", weight=3]; 130.29/78.13 24892[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz209100) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) True))",fontsize=16,color="black",shape="box"];24892 -> 24933[label="",style="solid", color="black", weight=3]; 130.29/78.13 1719[label="FiniteMap.splitGT3 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))",fontsize=16,color="black",shape="box"];1719 -> 2035[label="",style="solid", color="black", weight=3]; 130.29/78.13 1720[label="FiniteMap.splitLT3 (FiniteMap.Branch (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Pos (Succ zzz4000))",fontsize=16,color="black",shape="box"];1720 -> 2036[label="",style="solid", color="black", weight=3]; 130.29/78.13 30438[label="zzz2741",fontsize=16,color="green",shape="box"];30439[label="zzz2738",fontsize=16,color="green",shape="box"];30440[label="zzz2746",fontsize=16,color="green",shape="box"];30441[label="zzz2745",fontsize=16,color="green",shape="box"];30442[label="zzz2735",fontsize=16,color="green",shape="box"];30443[label="zzz2744",fontsize=16,color="green",shape="box"];30444[label="zzz2736",fontsize=16,color="green",shape="box"];30445[label="zzz2747",fontsize=16,color="green",shape="box"];30446[label="zzz2739",fontsize=16,color="green",shape="box"];30447[label="zzz2737",fontsize=16,color="green",shape="box"];30448[label="zzz2742",fontsize=16,color="green",shape="box"];30449[label="zzz274300",fontsize=16,color="green",shape="box"];30450[label="zzz2738",fontsize=16,color="green",shape="box"];30451[label="zzz274300",fontsize=16,color="green",shape="box"];30452[label="zzz2740",fontsize=16,color="green",shape="box"];30453[label="zzz2734",fontsize=16,color="green",shape="box"];30437[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) zzz3073 zzz3074 zzz3075 zzz3076 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3077)) zzz3078 zzz3079 zzz3080 zzz3081 (Pos (Succ zzz3072)) (primCmpNat zzz3082 zzz3083 == LT)))",fontsize=16,color="burlywood",shape="triangle"];64994[label="zzz3082/Succ zzz30820",fontsize=10,color="white",style="solid",shape="box"];30437 -> 64994[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 64994 -> 30598[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 64995[label="zzz3082/Zero",fontsize=10,color="white",style="solid",shape="box"];30437 -> 64995[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 64995 -> 30599[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 28561[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM2 (Pos Zero) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) False))",fontsize=16,color="black",shape="box"];28561 -> 28575[label="",style="solid", color="black", weight=3]; 130.29/78.13 28562[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz27430) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (compare (Pos (Succ zzz2738)) (Neg zzz27430) == GT)))",fontsize=16,color="black",shape="box"];28562 -> 28576[label="",style="solid", color="black", weight=3]; 130.29/78.13 1727[label="FiniteMap.splitGT2 (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos (Succ zzz4000)) (primCmpInt (Pos (Succ zzz4000)) (Neg zzz300) == GT)",fontsize=16,color="black",shape="box"];1727 -> 2043[label="",style="solid", color="black", weight=3]; 130.29/78.13 21897[label="zzz33",fontsize=16,color="green",shape="box"];21898[label="Neg zzz300",fontsize=16,color="green",shape="box"];21899[label="zzz4000",fontsize=16,color="green",shape="box"];21900[label="FiniteMap.EmptyFM",fontsize=16,color="green",shape="box"];21901[label="zzz32",fontsize=16,color="green",shape="box"];21902[label="zzz31",fontsize=16,color="green",shape="box"];21896[label="FiniteMap.splitLT2 zzz1970 zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) (compare (Pos (Succ zzz1975)) zzz1970 == LT)",fontsize=16,color="black",shape="triangle"];21896 -> 21951[label="",style="solid", color="black", weight=3]; 130.29/78.13 22271 -> 22038[label="",style="dashed", color="red", weight=0]; 130.29/78.13 22271[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) zzz1983 zzz1984 zzz1985 zzz1986 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz1987)) zzz1988 zzz1989 zzz1990 zzz1991 (Pos (Succ zzz1982)) (primCmpNat zzz19920 zzz19930 == LT)))",fontsize=16,color="magenta"];22271 -> 22304[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22271 -> 22305[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22272[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) zzz1983 zzz1984 zzz1985 zzz1986 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz1987)) zzz1988 zzz1989 zzz1990 zzz1991 (Pos (Succ zzz1982)) (GT == LT)))",fontsize=16,color="black",shape="box"];22272 -> 22306[label="",style="solid", color="black", weight=3]; 130.29/78.13 22273[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) zzz1983 zzz1984 zzz1985 zzz1986 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz1987)) zzz1988 zzz1989 zzz1990 zzz1991 (Pos (Succ zzz1982)) (LT == LT)))",fontsize=16,color="black",shape="box"];22273 -> 22307[label="",style="solid", color="black", weight=3]; 130.29/78.13 22274[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) zzz1983 zzz1984 zzz1985 zzz1986 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz1987)) zzz1988 zzz1989 zzz1990 zzz1991 (Pos (Succ zzz1982)) (EQ == LT)))",fontsize=16,color="black",shape="box"];22274 -> 22308[label="",style="solid", color="black", weight=3]; 130.29/78.13 18232[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (primCmpInt (Pos (Succ zzz1387)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];18232 -> 18274[label="",style="solid", color="black", weight=3]; 130.29/78.13 18233[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz13920) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) True))",fontsize=16,color="black",shape="box"];18233 -> 18275[label="",style="solid", color="black", weight=3]; 130.29/78.13 1738[label="FiniteMap.splitGT2 (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Pos Zero) False",fontsize=16,color="black",shape="box"];1738 -> 2056[label="",style="solid", color="black", weight=3]; 130.29/78.13 1739[label="FiniteMap.splitLT2 (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Pos Zero) True",fontsize=16,color="black",shape="box"];1739 -> 2057[label="",style="solid", color="black", weight=3]; 130.29/78.13 10400[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 otherwise",fontsize=16,color="black",shape="box"];10400 -> 10571[label="",style="solid", color="black", weight=3]; 130.29/78.13 10401[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM0 (Pos Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) True))",fontsize=16,color="black",shape="box"];10401 -> 10572[label="",style="solid", color="black", weight=3]; 130.29/78.13 10402[label="zzz631",fontsize=16,color="green",shape="box"];10403[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (FiniteMap.lookupFM0 (Neg Zero) zzz628 zzz629 zzz630 zzz631 (Pos Zero) True))",fontsize=16,color="black",shape="box"];10403 -> 10573[label="",style="solid", color="black", weight=3]; 130.29/78.13 5094[label="FiniteMap.splitLT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) False",fontsize=16,color="black",shape="box"];5094 -> 5369[label="",style="solid", color="black", weight=3]; 130.29/78.13 5095[label="FiniteMap.splitGT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) False",fontsize=16,color="black",shape="box"];5095 -> 5370[label="",style="solid", color="black", weight=3]; 130.29/78.13 5096[label="FiniteMap.Branch (Pos zzz300) zzz31 (Pos (Succ Zero)) FiniteMap.emptyFM FiniteMap.emptyFM",fontsize=16,color="green",shape="box"];5096 -> 5371[label="",style="dashed", color="green", weight=3]; 130.29/78.13 5096 -> 5372[label="",style="dashed", color="green", weight=3]; 130.29/78.13 5097[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 (compare (Pos zzz300) zzz340 == LT)",fontsize=16,color="black",shape="box"];5097 -> 5373[label="",style="solid", color="black", weight=3]; 130.29/78.13 5098[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];5098 -> 5374[label="",style="solid", color="black", weight=3]; 130.29/78.13 1752[label="FiniteMap.splitGT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos Zero) (compare (Pos Zero) (Neg (Succ zzz3000)) == GT)",fontsize=16,color="black",shape="box"];1752 -> 2074[label="",style="solid", color="black", weight=3]; 130.29/78.13 1753[label="FiniteMap.splitLT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos Zero) (compare (Pos Zero) (Neg (Succ zzz3000)) == LT)",fontsize=16,color="black",shape="box"];1753 -> 2075[label="",style="solid", color="black", weight=3]; 130.29/78.13 15580[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM FiniteMap.EmptyFM (Pos Zero)))",fontsize=16,color="black",shape="box"];15580 -> 15939[label="",style="solid", color="black", weight=3]; 130.29/78.13 15581[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM (FiniteMap.Branch zzz12040 zzz12041 zzz12042 zzz12043 zzz12044) (Pos Zero)))",fontsize=16,color="black",shape="box"];15581 -> 15940[label="",style="solid", color="black", weight=3]; 130.29/78.13 15582[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];15582 -> 15941[label="",style="solid", color="black", weight=3]; 130.29/78.13 15583[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz120100)) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ zzz120100)) == GT)))",fontsize=16,color="black",shape="box"];15583 -> 15942[label="",style="solid", color="black", weight=3]; 130.29/78.13 15584[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == GT)))",fontsize=16,color="black",shape="box"];15584 -> 15943[label="",style="solid", color="black", weight=3]; 130.29/78.13 5099[label="FiniteMap.splitLT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) False",fontsize=16,color="black",shape="box"];5099 -> 5375[label="",style="solid", color="black", weight=3]; 130.29/78.13 5100[label="FiniteMap.splitGT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) False",fontsize=16,color="black",shape="box"];5100 -> 5376[label="",style="solid", color="black", weight=3]; 130.29/78.13 1764[label="FiniteMap.splitGT1 (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (primCmpInt (Neg (Succ zzz4000)) (Pos zzz300) == LT)",fontsize=16,color="black",shape="box"];1764 -> 2088[label="",style="solid", color="black", weight=3]; 130.29/78.13 1765 -> 11[label="",style="dashed", color="red", weight=0]; 130.29/78.13 1765[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];62472 -> 54589[label="",style="dashed", color="red", weight=0]; 130.29/78.13 62472[label="FiniteMap.sizeFM (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464)",fontsize=16,color="magenta"];62472 -> 62486[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 62473[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos zzz63370)) zzz6319 == LT)",fontsize=16,color="black",shape="box"];62473 -> 62487[label="",style="solid", color="black", weight=3]; 130.29/78.13 62474[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg zzz63370)) zzz6319 == LT)",fontsize=16,color="black",shape="box"];62474 -> 62488[label="",style="solid", color="black", weight=3]; 130.29/78.13 12144[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747))",fontsize=16,color="black",shape="triangle"];12144 -> 12223[label="",style="solid", color="black", weight=3]; 130.29/78.13 12145[label="zzz751",fontsize=16,color="green",shape="box"];12146[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747))",fontsize=16,color="black",shape="triangle"];12146 -> 12224[label="",style="solid", color="black", weight=3]; 130.29/78.13 12147[label="zzz750",fontsize=16,color="green",shape="box"];18161 -> 28290[label="",style="dashed", color="red", weight=0]; 130.29/78.13 18161[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz1398) zzz1399 zzz1400 zzz1401 zzz1402) (Neg (Succ zzz1403)) zzz1404 zzz1405 zzz1406 zzz1407 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz1408)) zzz1409 zzz1410 zzz1411 zzz1412 (Neg (Succ zzz1403)) (primCmpNat (Succ zzz1408) (Succ zzz1403) == GT)))",fontsize=16,color="magenta"];18161 -> 28291[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18161 -> 28292[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18161 -> 28293[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18161 -> 28294[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18161 -> 28295[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18161 -> 28296[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18161 -> 28297[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18161 -> 28298[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18161 -> 28299[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18161 -> 28300[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18161 -> 28301[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18161 -> 28302[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18161 -> 28303[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18161 -> 28304[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18161 -> 28305[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18161 -> 28306[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18161 -> 28307[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 27891 -> 6244[label="",style="dashed", color="red", weight=0]; 130.29/78.13 27891[label="FiniteMap.mkVBalBranch (Neg (Succ zzz2632)) (FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632))) zzz2633) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632))) zzz2635) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632))) zzz2636)",fontsize=16,color="magenta"];27891 -> 28135[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 27891 -> 28136[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 27891 -> 28137[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 27891 -> 28138[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 14963 -> 4258[label="",style="dashed", color="red", weight=0]; 130.29/78.13 14963[label="FiniteMap.splitGT4 FiniteMap.EmptyFM (Neg (Succ zzz747))",fontsize=16,color="magenta"];14963 -> 16648[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 14964[label="FiniteMap.splitGT3 (FiniteMap.Branch zzz7450 zzz7451 zzz7452 zzz7453 zzz7454) (Neg (Succ zzz747))",fontsize=16,color="black",shape="triangle"];14964 -> 16649[label="",style="solid", color="black", weight=3]; 130.29/78.13 13471 -> 1578[label="",style="dashed", color="red", weight=0]; 130.29/78.13 13471[label="FiniteMap.splitLT4 FiniteMap.EmptyFM (Neg (Succ zzz747))",fontsize=16,color="magenta"];13471 -> 13543[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 13472[label="FiniteMap.splitLT3 (FiniteMap.Branch zzz7450 zzz7451 zzz7452 zzz7453 zzz7454) (Neg (Succ zzz747))",fontsize=16,color="black",shape="box"];13472 -> 13544[label="",style="solid", color="black", weight=3]; 130.29/78.13 1825[label="FiniteMap.splitGT2 (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) False",fontsize=16,color="black",shape="box"];1825 -> 2238[label="",style="solid", color="black", weight=3]; 130.29/78.13 1826[label="FiniteMap.splitLT2 (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) True",fontsize=16,color="black",shape="box"];1826 -> 2239[label="",style="solid", color="black", weight=3]; 130.29/78.13 12994 -> 288[label="",style="dashed", color="red", weight=0]; 130.29/78.13 12994[label="FiniteMap.glueVBal (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888))) zzz891) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888))) zzz892)",fontsize=16,color="magenta"];12994 -> 13237[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 12994 -> 13238[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 19773[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) zzz1582 zzz1583 zzz1584 zzz1585 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz1586)) zzz1587 zzz1588 zzz1589 zzz1590 (Neg (Succ zzz1581)) (compare (Neg (Succ zzz1581)) (Neg (Succ zzz1586)) == GT)))",fontsize=16,color="black",shape="box"];19773 -> 19808[label="",style="solid", color="black", weight=3]; 130.29/78.13 19774[label="zzz1578",fontsize=16,color="green",shape="box"];19775[label="zzz1577",fontsize=16,color="green",shape="box"];19776[label="zzz1589",fontsize=16,color="green",shape="box"];19777[label="zzz1585",fontsize=16,color="green",shape="box"];19778[label="zzz1583",fontsize=16,color="green",shape="box"];19779[label="zzz1584",fontsize=16,color="green",shape="box"];19780[label="zzz1579",fontsize=16,color="green",shape="box"];19781[label="zzz1582",fontsize=16,color="green",shape="box"];19782[label="zzz1581",fontsize=16,color="green",shape="box"];19783[label="zzz1580",fontsize=16,color="green",shape="box"];12652[label="FiniteMap.splitGT1 (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834 (Neg Zero) (Neg Zero < Pos (Succ zzz830))",fontsize=16,color="black",shape="box"];12652 -> 12934[label="",style="solid", color="black", weight=3]; 130.29/78.13 12653[label="FiniteMap.splitLT zzz833 (Neg Zero)",fontsize=16,color="burlywood",shape="triangle"];64996[label="zzz833/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];12653 -> 64996[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 64996 -> 12935[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 64997[label="zzz833/FiniteMap.Branch zzz8330 zzz8331 zzz8332 zzz8333 zzz8334",fontsize=10,color="white",style="solid",shape="box"];12653 -> 64997[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 64997 -> 12936[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 13234[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (Just zzz909))",fontsize=16,color="black",shape="triangle"];13234 -> 13435[label="",style="solid", color="black", weight=3]; 130.29/78.13 13235 -> 12369[label="",style="dashed", color="red", weight=0]; 130.29/78.13 13235[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (FiniteMap.lookupFM zzz912 (Neg Zero)))",fontsize=16,color="magenta"];13235 -> 13436[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 13236 -> 13234[label="",style="dashed", color="red", weight=0]; 130.29/78.13 13236[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 (Maybe.isJust (Just zzz909))",fontsize=16,color="magenta"];6278[label="FiniteMap.splitLT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) False",fontsize=16,color="black",shape="box"];6278 -> 6330[label="",style="solid", color="black", weight=3]; 130.29/78.13 6279[label="FiniteMap.splitGT2 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) False",fontsize=16,color="black",shape="box"];6279 -> 6331[label="",style="solid", color="black", weight=3]; 130.29/78.13 12571[label="FiniteMap.unitFM (Neg zzz300) zzz31",fontsize=16,color="black",shape="box"];12571 -> 12654[label="",style="solid", color="black", weight=3]; 130.29/78.13 12572[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 zzz9820 zzz9821 zzz9822 zzz9823 zzz9824 (Neg zzz300) zzz31 (Neg zzz300 < zzz9820)",fontsize=16,color="black",shape="box"];12572 -> 12655[label="",style="solid", color="black", weight=3]; 130.29/78.13 6282[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];6282 -> 6335[label="",style="solid", color="black", weight=3]; 130.29/78.13 1863[label="FiniteMap.splitGT3 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero)",fontsize=16,color="black",shape="box"];1863 -> 2283[label="",style="solid", color="black", weight=3]; 130.29/78.13 1864[label="FiniteMap.splitLT3 (FiniteMap.Branch (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM) (Neg Zero)",fontsize=16,color="black",shape="box"];1864 -> 2284[label="",style="solid", color="black", weight=3]; 130.29/78.13 19884[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM zzz1606 (Neg Zero)))",fontsize=16,color="burlywood",shape="triangle"];64998[label="zzz1606/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];19884 -> 64998[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 64998 -> 19959[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 64999[label="zzz1606/FiniteMap.Branch zzz16060 zzz16061 zzz16062 zzz16063 zzz16064",fontsize=10,color="white",style="solid",shape="box"];19884 -> 64999[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 64999 -> 19960[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 19885[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (Neg Zero > Pos Zero)))",fontsize=16,color="black",shape="box"];19885 -> 19961[label="",style="solid", color="black", weight=3]; 130.29/78.13 19886[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM2 (Neg (Succ zzz160300)) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) False))",fontsize=16,color="black",shape="box"];19886 -> 19962[label="",style="solid", color="black", weight=3]; 130.29/78.13 19887[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (Neg Zero > Neg Zero)))",fontsize=16,color="black",shape="box"];19887 -> 19963[label="",style="solid", color="black", weight=3]; 130.29/78.13 6283[label="FiniteMap.splitLT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) False",fontsize=16,color="black",shape="box"];6283 -> 6336[label="",style="solid", color="black", weight=3]; 130.29/78.13 6284[label="FiniteMap.splitGT2 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) False",fontsize=16,color="black",shape="box"];6284 -> 6337[label="",style="solid", color="black", weight=3]; 130.29/78.13 27892 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.13 27892[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614))) zzz2617",fontsize=16,color="magenta"];27892 -> 28139[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 27892 -> 28140[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 27893[label="Succ zzz2614",fontsize=16,color="green",shape="box"];27894 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.13 27894[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614))) zzz2618",fontsize=16,color="magenta"];27894 -> 28141[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 27894 -> 28142[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 27895[label="FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614))) zzz2615",fontsize=16,color="black",shape="box"];27895 -> 28143[label="",style="solid", color="black", weight=3]; 130.29/78.13 19810[label="zzz1613",fontsize=16,color="green",shape="box"];3302[label="FiniteMap.splitGT4 FiniteMap.EmptyFM (Pos (Succ zzz4000))",fontsize=16,color="black",shape="triangle"];3302 -> 3712[label="",style="solid", color="black", weight=3]; 130.29/78.13 19811[label="FiniteMap.splitGT2 zzz16120 zzz16121 zzz16122 zzz16123 zzz16124 (Pos (Succ zzz1613)) (Pos (Succ zzz1613) > zzz16120)",fontsize=16,color="black",shape="box"];19811 -> 19867[label="",style="solid", color="black", weight=3]; 130.29/78.13 23610[label="zzz1975",fontsize=16,color="green",shape="box"];7671[label="FiniteMap.splitLT4 FiniteMap.EmptyFM (Pos (Succ zzz4000))",fontsize=16,color="black",shape="triangle"];7671 -> 7785[label="",style="solid", color="black", weight=3]; 130.29/78.13 23126[label="FiniteMap.splitLT3 (FiniteMap.Branch zzz19740 zzz19741 zzz19742 zzz19743 zzz19744) (Pos (Succ zzz1975))",fontsize=16,color="black",shape="triangle"];23126 -> 23298[label="",style="solid", color="black", weight=3]; 130.29/78.13 24932[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (primCmpNat (Succ zzz2083) Zero == GT)))",fontsize=16,color="black",shape="box"];24932 -> 24982[label="",style="solid", color="black", weight=3]; 130.29/78.13 24933 -> 23586[label="",style="dashed", color="red", weight=0]; 130.29/78.13 24933[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM zzz20914 (Pos (Succ zzz2083))))",fontsize=16,color="magenta"];24933 -> 24983[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 2035[label="FiniteMap.splitGT2 (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos (Succ zzz4000)) (Pos (Succ zzz4000) > Pos Zero)",fontsize=16,color="black",shape="box"];2035 -> 2379[label="",style="solid", color="black", weight=3]; 130.29/78.13 2036[label="FiniteMap.splitLT2 (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos (Succ zzz4000)) (Pos (Succ zzz4000) < Pos Zero)",fontsize=16,color="black",shape="box"];2036 -> 2380[label="",style="solid", color="black", weight=3]; 130.29/78.13 30598[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) zzz3073 zzz3074 zzz3075 zzz3076 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3077)) zzz3078 zzz3079 zzz3080 zzz3081 (Pos (Succ zzz3072)) (primCmpNat (Succ zzz30820) zzz3083 == LT)))",fontsize=16,color="burlywood",shape="box"];65000[label="zzz3083/Succ zzz30830",fontsize=10,color="white",style="solid",shape="box"];30598 -> 65000[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65000 -> 30766[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65001[label="zzz3083/Zero",fontsize=10,color="white",style="solid",shape="box"];30598 -> 65001[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65001 -> 30767[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 30599[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) zzz3073 zzz3074 zzz3075 zzz3076 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3077)) zzz3078 zzz3079 zzz3080 zzz3081 (Pos (Succ zzz3072)) (primCmpNat Zero zzz3083 == LT)))",fontsize=16,color="burlywood",shape="box"];65002[label="zzz3083/Succ zzz30830",fontsize=10,color="white",style="solid",shape="box"];30599 -> 65002[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65002 -> 30768[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65003[label="zzz3083/Zero",fontsize=10,color="white",style="solid",shape="box"];30599 -> 65003[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65003 -> 30769[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 28575[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (Pos (Succ zzz2738) > Pos Zero)))",fontsize=16,color="black",shape="box"];28575 -> 28599[label="",style="solid", color="black", weight=3]; 130.29/78.13 28576[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz27430) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (primCmpInt (Pos (Succ zzz2738)) (Neg zzz27430) == GT)))",fontsize=16,color="black",shape="box"];28576 -> 28600[label="",style="solid", color="black", weight=3]; 130.29/78.13 2043[label="FiniteMap.splitGT2 (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos (Succ zzz4000)) (GT == GT)",fontsize=16,color="black",shape="box"];2043 -> 2388[label="",style="solid", color="black", weight=3]; 130.29/78.13 21951[label="FiniteMap.splitLT2 zzz1970 zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) (primCmpInt (Pos (Succ zzz1975)) zzz1970 == LT)",fontsize=16,color="burlywood",shape="box"];65004[label="zzz1970/Pos zzz19700",fontsize=10,color="white",style="solid",shape="box"];21951 -> 65004[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65004 -> 22211[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65005[label="zzz1970/Neg zzz19700",fontsize=10,color="white",style="solid",shape="box"];21951 -> 65005[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65005 -> 22212[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 22304[label="zzz19920",fontsize=16,color="green",shape="box"];22305[label="zzz19930",fontsize=16,color="green",shape="box"];22306[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) zzz1983 zzz1984 zzz1985 zzz1986 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz1987)) zzz1988 zzz1989 zzz1990 zzz1991 (Pos (Succ zzz1982)) False))",fontsize=16,color="black",shape="triangle"];22306 -> 22430[label="",style="solid", color="black", weight=3]; 130.29/78.13 22307[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) zzz1983 zzz1984 zzz1985 zzz1986 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz1987)) zzz1988 zzz1989 zzz1990 zzz1991 (Pos (Succ zzz1982)) True))",fontsize=16,color="black",shape="box"];22307 -> 22431[label="",style="solid", color="black", weight=3]; 130.29/78.13 22308 -> 22306[label="",style="dashed", color="red", weight=0]; 130.29/78.13 22308[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) zzz1983 zzz1984 zzz1985 zzz1986 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz1987)) zzz1988 zzz1989 zzz1990 zzz1991 (Pos (Succ zzz1982)) False))",fontsize=16,color="magenta"];18274[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (primCmpNat (Succ zzz1387) Zero == GT)))",fontsize=16,color="black",shape="box"];18274 -> 18314[label="",style="solid", color="black", weight=3]; 130.29/78.13 18275[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM zzz1396 (Pos (Succ zzz1387))))",fontsize=16,color="burlywood",shape="triangle"];65006[label="zzz1396/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];18275 -> 65006[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65006 -> 18315[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65007[label="zzz1396/FiniteMap.Branch zzz13960 zzz13961 zzz13962 zzz13963 zzz13964",fontsize=10,color="white",style="solid",shape="box"];18275 -> 65007[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65007 -> 18316[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 2056[label="FiniteMap.splitGT1 (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Pos Zero) (Pos Zero < Pos (Succ zzz3000))",fontsize=16,color="black",shape="box"];2056 -> 2402[label="",style="solid", color="black", weight=3]; 130.29/78.13 2057[label="FiniteMap.splitLT FiniteMap.EmptyFM (Pos Zero)",fontsize=16,color="black",shape="triangle"];2057 -> 2403[label="",style="solid", color="black", weight=3]; 130.29/78.13 10571[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 True",fontsize=16,color="black",shape="box"];10571 -> 10619[label="",style="solid", color="black", weight=3]; 130.29/78.13 10572[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (Just zzz628))",fontsize=16,color="black",shape="triangle"];10572 -> 10620[label="",style="solid", color="black", weight=3]; 130.29/78.13 10573 -> 10572[label="",style="dashed", color="red", weight=0]; 130.29/78.13 10573[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 (Maybe.isJust (Just zzz628))",fontsize=16,color="magenta"];5369[label="FiniteMap.splitLT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (Pos Zero > Pos Zero)",fontsize=16,color="black",shape="box"];5369 -> 5454[label="",style="solid", color="black", weight=3]; 130.29/78.13 5370[label="FiniteMap.splitGT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (Pos Zero < Pos Zero)",fontsize=16,color="black",shape="box"];5370 -> 5455[label="",style="solid", color="black", weight=3]; 130.29/78.13 5371 -> 11[label="",style="dashed", color="red", weight=0]; 130.29/78.13 5371[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];5372 -> 11[label="",style="dashed", color="red", weight=0]; 130.29/78.13 5372[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];5373[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 (primCmpInt (Pos zzz300) zzz340 == LT)",fontsize=16,color="burlywood",shape="box"];65008[label="zzz300/Succ zzz3000",fontsize=10,color="white",style="solid",shape="box"];5373 -> 65008[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65008 -> 5456[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65009[label="zzz300/Zero",fontsize=10,color="white",style="solid",shape="box"];5373 -> 65009[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65009 -> 5457[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 5374[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 zzz2502 zzz2503 zzz2504))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];5374 -> 5458[label="",style="solid", color="black", weight=3]; 130.29/78.13 2074[label="FiniteMap.splitGT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ zzz3000)) == GT)",fontsize=16,color="black",shape="box"];2074 -> 2480[label="",style="solid", color="black", weight=3]; 130.29/78.13 2075[label="FiniteMap.splitLT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ zzz3000)) == LT)",fontsize=16,color="black",shape="box"];2075 -> 2481[label="",style="solid", color="black", weight=3]; 130.29/78.13 15939[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Pos Zero)))",fontsize=16,color="black",shape="box"];15939 -> 16229[label="",style="solid", color="black", weight=3]; 130.29/78.13 15940 -> 14732[label="",style="dashed", color="red", weight=0]; 130.29/78.13 15940[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz12040 zzz12041 zzz12042 zzz12043 zzz12044) (Pos Zero)))",fontsize=16,color="magenta"];15940 -> 16230[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 15940 -> 16231[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 15940 -> 16232[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 15940 -> 16233[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 15940 -> 16234[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 15941[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (EQ == GT)))",fontsize=16,color="black",shape="box"];15941 -> 16235[label="",style="solid", color="black", weight=3]; 130.29/78.13 15942[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz120100)) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (GT == GT)))",fontsize=16,color="black",shape="box"];15942 -> 16236[label="",style="solid", color="black", weight=3]; 130.29/78.13 15943[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) (EQ == GT)))",fontsize=16,color="black",shape="box"];15943 -> 16237[label="",style="solid", color="black", weight=3]; 130.29/78.13 5375[label="FiniteMap.splitLT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (Pos Zero > Neg Zero)",fontsize=16,color="black",shape="box"];5375 -> 5459[label="",style="solid", color="black", weight=3]; 130.29/78.13 5376[label="FiniteMap.splitGT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (Pos Zero < Neg Zero)",fontsize=16,color="black",shape="box"];5376 -> 5460[label="",style="solid", color="black", weight=3]; 130.29/78.13 2088[label="FiniteMap.splitGT1 (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (LT == LT)",fontsize=16,color="black",shape="box"];2088 -> 2490[label="",style="solid", color="black", weight=3]; 130.29/78.13 62486[label="FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464",fontsize=16,color="green",shape="box"];62487 -> 62523[label="",style="dashed", color="red", weight=0]; 130.29/78.13 62487[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz63370)) zzz6319 == LT)",fontsize=16,color="magenta"];62487 -> 62524[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 62488 -> 62531[label="",style="dashed", color="red", weight=0]; 130.29/78.13 62488[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz63370)) zzz6319 == LT)",fontsize=16,color="magenta"];62488 -> 62532[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 12223[label="FiniteMap.splitGT (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747))",fontsize=16,color="black",shape="box"];12223 -> 12279[label="",style="solid", color="black", weight=3]; 130.29/78.13 12224[label="FiniteMap.splitLT (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747))",fontsize=16,color="black",shape="box"];12224 -> 12280[label="",style="solid", color="black", weight=3]; 130.29/78.13 28291[label="zzz1398",fontsize=16,color="green",shape="box"];28292[label="Succ zzz1403",fontsize=16,color="green",shape="box"];28293[label="zzz1408",fontsize=16,color="green",shape="box"];28294[label="zzz1411",fontsize=16,color="green",shape="box"];28295[label="zzz1412",fontsize=16,color="green",shape="box"];28296[label="zzz1402",fontsize=16,color="green",shape="box"];28297[label="zzz1400",fontsize=16,color="green",shape="box"];28298[label="zzz1405",fontsize=16,color="green",shape="box"];28299[label="zzz1410",fontsize=16,color="green",shape="box"];28300[label="zzz1399",fontsize=16,color="green",shape="box"];28301[label="zzz1403",fontsize=16,color="green",shape="box"];28302[label="zzz1406",fontsize=16,color="green",shape="box"];28303[label="zzz1404",fontsize=16,color="green",shape="box"];28304[label="zzz1407",fontsize=16,color="green",shape="box"];28305[label="zzz1409",fontsize=16,color="green",shape="box"];28306[label="zzz1401",fontsize=16,color="green",shape="box"];28307[label="Succ zzz1408",fontsize=16,color="green",shape="box"];28290[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) zzz2761 zzz2762 zzz2763 zzz2764 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2765)) zzz2766 zzz2767 zzz2768 zzz2769 (Neg (Succ zzz2760)) (primCmpNat zzz2770 zzz2771 == GT)))",fontsize=16,color="burlywood",shape="triangle"];65010[label="zzz2770/Succ zzz27700",fontsize=10,color="white",style="solid",shape="box"];28290 -> 65010[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65010 -> 28480[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65011[label="zzz2770/Zero",fontsize=10,color="white",style="solid",shape="box"];28290 -> 65011[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65011 -> 28481[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 28135[label="zzz2632",fontsize=16,color="green",shape="box"];28136 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.13 28136[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632))) zzz2636",fontsize=16,color="magenta"];28136 -> 28165[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28136 -> 28166[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28137 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.13 28137[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632))) zzz2635",fontsize=16,color="magenta"];28137 -> 28167[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28137 -> 28168[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28138[label="FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632))) zzz2633",fontsize=16,color="black",shape="box"];28138 -> 28169[label="",style="solid", color="black", weight=3]; 130.29/78.13 6244[label="FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 zzz33 zzz426",fontsize=16,color="burlywood",shape="triangle"];65012[label="zzz33/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];6244 -> 65012[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65012 -> 6297[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65013[label="zzz33/FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334",fontsize=10,color="white",style="solid",shape="box"];6244 -> 65013[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65013 -> 6298[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 16648[label="zzz747",fontsize=16,color="green",shape="box"];4258[label="FiniteMap.splitGT4 FiniteMap.EmptyFM (Neg (Succ zzz4000))",fontsize=16,color="black",shape="triangle"];4258 -> 4319[label="",style="solid", color="black", weight=3]; 130.29/78.13 16649[label="FiniteMap.splitGT2 zzz7450 zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (Neg (Succ zzz747) > zzz7450)",fontsize=16,color="black",shape="box"];16649 -> 17952[label="",style="solid", color="black", weight=3]; 130.29/78.13 13543[label="zzz747",fontsize=16,color="green",shape="box"];13544[label="FiniteMap.splitLT2 zzz7450 zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (Neg (Succ zzz747) < zzz7450)",fontsize=16,color="black",shape="box"];13544 -> 13838[label="",style="solid", color="black", weight=3]; 130.29/78.13 2238[label="FiniteMap.splitGT1 (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (Neg (Succ zzz4000) < Neg Zero)",fontsize=16,color="black",shape="box"];2238 -> 2562[label="",style="solid", color="black", weight=3]; 130.29/78.13 2239 -> 1341[label="",style="dashed", color="red", weight=0]; 130.29/78.13 2239[label="FiniteMap.splitLT FiniteMap.EmptyFM (Neg (Succ zzz4000))",fontsize=16,color="magenta"];13237 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.13 13237[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888))) zzz892",fontsize=16,color="magenta"];13237 -> 13437[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 13237 -> 13438[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 13238 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.13 13238[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888))) zzz891",fontsize=16,color="magenta"];13238 -> 13439[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 13238 -> 13440[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 19808[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) zzz1582 zzz1583 zzz1584 zzz1585 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz1586)) zzz1587 zzz1588 zzz1589 zzz1590 (Neg (Succ zzz1581)) (primCmpInt (Neg (Succ zzz1581)) (Neg (Succ zzz1586)) == GT)))",fontsize=16,color="black",shape="box"];19808 -> 19865[label="",style="solid", color="black", weight=3]; 130.29/78.13 12934[label="FiniteMap.splitGT1 (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834 (Neg Zero) (compare (Neg Zero) (Pos (Succ zzz830)) == LT)",fontsize=16,color="black",shape="box"];12934 -> 12970[label="",style="solid", color="black", weight=3]; 130.29/78.13 12935[label="FiniteMap.splitLT FiniteMap.EmptyFM (Neg Zero)",fontsize=16,color="black",shape="box"];12935 -> 12971[label="",style="solid", color="black", weight=3]; 130.29/78.13 12936[label="FiniteMap.splitLT (FiniteMap.Branch zzz8330 zzz8331 zzz8332 zzz8333 zzz8334) (Neg Zero)",fontsize=16,color="black",shape="box"];12936 -> 12972[label="",style="solid", color="black", weight=3]; 130.29/78.13 13435[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero) zzz904 zzz905 zzz906 zzz907 True",fontsize=16,color="black",shape="box"];13435 -> 13509[label="",style="solid", color="black", weight=3]; 130.29/78.13 13436[label="zzz912",fontsize=16,color="green",shape="box"];6330[label="FiniteMap.splitLT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (Neg Zero > Pos Zero)",fontsize=16,color="black",shape="box"];6330 -> 6542[label="",style="solid", color="black", weight=3]; 130.29/78.13 6331[label="FiniteMap.splitGT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (Neg Zero < Pos Zero)",fontsize=16,color="black",shape="box"];6331 -> 6543[label="",style="solid", color="black", weight=3]; 130.29/78.13 12654[label="FiniteMap.Branch (Neg zzz300) zzz31 (Pos (Succ Zero)) FiniteMap.emptyFM FiniteMap.emptyFM",fontsize=16,color="green",shape="box"];12654 -> 12937[label="",style="dashed", color="green", weight=3]; 130.29/78.13 12654 -> 12938[label="",style="dashed", color="green", weight=3]; 130.29/78.13 12655[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 zzz9820 zzz9821 zzz9822 zzz9823 zzz9824 (Neg zzz300) zzz31 (compare (Neg zzz300) zzz9820 == LT)",fontsize=16,color="black",shape="box"];12655 -> 12939[label="",style="solid", color="black", weight=3]; 130.29/78.13 6335[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz3530 zzz3531 zzz3532 zzz3533 zzz3534))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];6335 -> 6546[label="",style="solid", color="black", weight=3]; 130.29/78.13 2283[label="FiniteMap.splitGT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Neg Zero) (Neg Zero > Neg (Succ zzz3000))",fontsize=16,color="black",shape="box"];2283 -> 2777[label="",style="solid", color="black", weight=3]; 130.29/78.13 2284[label="FiniteMap.splitLT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Neg Zero) (Neg Zero < Neg (Succ zzz3000))",fontsize=16,color="black",shape="box"];2284 -> 2778[label="",style="solid", color="black", weight=3]; 130.29/78.13 19959[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM FiniteMap.EmptyFM (Neg Zero)))",fontsize=16,color="black",shape="box"];19959 -> 20081[label="",style="solid", color="black", weight=3]; 130.29/78.13 19960[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM (FiniteMap.Branch zzz16060 zzz16061 zzz16062 zzz16063 zzz16064) (Neg Zero)))",fontsize=16,color="black",shape="box"];19960 -> 20082[label="",style="solid", color="black", weight=3]; 130.29/78.13 19961[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (compare (Neg Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];19961 -> 20083[label="",style="solid", color="black", weight=3]; 130.29/78.13 19962[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz160300)) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (Neg Zero > Neg (Succ zzz160300))))",fontsize=16,color="black",shape="box"];19962 -> 20084[label="",style="solid", color="black", weight=3]; 130.29/78.13 19963[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (compare (Neg Zero) (Neg Zero) == GT)))",fontsize=16,color="black",shape="box"];19963 -> 20085[label="",style="solid", color="black", weight=3]; 130.29/78.13 6336[label="FiniteMap.splitLT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (Neg Zero > Neg Zero)",fontsize=16,color="black",shape="box"];6336 -> 6547[label="",style="solid", color="black", weight=3]; 130.29/78.13 6337[label="FiniteMap.splitGT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (Neg Zero < Neg Zero)",fontsize=16,color="black",shape="box"];6337 -> 6548[label="",style="solid", color="black", weight=3]; 130.29/78.13 28139 -> 24659[label="",style="dashed", color="red", weight=0]; 130.29/78.13 28139[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614))",fontsize=16,color="magenta"];28139 -> 28170[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28139 -> 28171[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28139 -> 28172[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28139 -> 28173[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28139 -> 28174[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28139 -> 28175[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28140[label="zzz2617",fontsize=16,color="green",shape="box"];28141 -> 24657[label="",style="dashed", color="red", weight=0]; 130.29/78.13 28141[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz2609)) zzz2610 zzz2611 zzz2612 zzz2613) (Pos (Succ zzz2614))",fontsize=16,color="magenta"];28141 -> 28176[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28141 -> 28177[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28141 -> 28178[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28141 -> 28179[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28141 -> 28180[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28141 -> 28181[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28142[label="zzz2618",fontsize=16,color="green",shape="box"];28143[label="zzz2615",fontsize=16,color="green",shape="box"];3712 -> 11[label="",style="dashed", color="red", weight=0]; 130.29/78.13 3712[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];19867[label="FiniteMap.splitGT2 zzz16120 zzz16121 zzz16122 zzz16123 zzz16124 (Pos (Succ zzz1613)) (compare (Pos (Succ zzz1613)) zzz16120 == GT)",fontsize=16,color="black",shape="triangle"];19867 -> 19906[label="",style="solid", color="black", weight=3]; 130.29/78.13 7785 -> 11[label="",style="dashed", color="red", weight=0]; 130.29/78.13 7785[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];23298[label="FiniteMap.splitLT2 zzz19740 zzz19741 zzz19742 zzz19743 zzz19744 (Pos (Succ zzz1975)) (Pos (Succ zzz1975) < zzz19740)",fontsize=16,color="black",shape="box"];23298 -> 23412[label="",style="solid", color="black", weight=3]; 130.29/78.13 24982[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) (GT == GT)))",fontsize=16,color="black",shape="box"];24982 -> 25024[label="",style="solid", color="black", weight=3]; 130.29/78.13 24983[label="zzz20914",fontsize=16,color="green",shape="box"];2379[label="FiniteMap.splitGT2 (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos (Succ zzz4000)) (compare (Pos (Succ zzz4000)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];2379 -> 2816[label="",style="solid", color="black", weight=3]; 130.29/78.13 2380 -> 21896[label="",style="dashed", color="red", weight=0]; 130.29/78.13 2380[label="FiniteMap.splitLT2 (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos (Succ zzz4000)) (compare (Pos (Succ zzz4000)) (Pos Zero) == LT)",fontsize=16,color="magenta"];2380 -> 21909[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 2380 -> 21910[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 2380 -> 21911[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 2380 -> 21912[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 2380 -> 21913[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 2380 -> 21914[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 30766[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) zzz3073 zzz3074 zzz3075 zzz3076 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3077)) zzz3078 zzz3079 zzz3080 zzz3081 (Pos (Succ zzz3072)) (primCmpNat (Succ zzz30820) (Succ zzz30830) == LT)))",fontsize=16,color="black",shape="box"];30766 -> 30794[label="",style="solid", color="black", weight=3]; 130.29/78.13 30767[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) zzz3073 zzz3074 zzz3075 zzz3076 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3077)) zzz3078 zzz3079 zzz3080 zzz3081 (Pos (Succ zzz3072)) (primCmpNat (Succ zzz30820) Zero == LT)))",fontsize=16,color="black",shape="box"];30767 -> 30795[label="",style="solid", color="black", weight=3]; 130.29/78.13 30768[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) zzz3073 zzz3074 zzz3075 zzz3076 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3077)) zzz3078 zzz3079 zzz3080 zzz3081 (Pos (Succ zzz3072)) (primCmpNat Zero (Succ zzz30830) == LT)))",fontsize=16,color="black",shape="box"];30768 -> 30796[label="",style="solid", color="black", weight=3]; 130.29/78.13 30769[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) zzz3073 zzz3074 zzz3075 zzz3076 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3077)) zzz3078 zzz3079 zzz3080 zzz3081 (Pos (Succ zzz3072)) (primCmpNat Zero Zero == LT)))",fontsize=16,color="black",shape="box"];30769 -> 30797[label="",style="solid", color="black", weight=3]; 130.29/78.13 28599[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (compare (Pos (Succ zzz2738)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];28599 -> 28680[label="",style="solid", color="black", weight=3]; 130.29/78.13 28600[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz27430) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (GT == GT)))",fontsize=16,color="black",shape="box"];28600 -> 28681[label="",style="solid", color="black", weight=3]; 130.29/78.13 2388[label="FiniteMap.splitGT2 (Neg zzz300) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos (Succ zzz4000)) True",fontsize=16,color="black",shape="box"];2388 -> 2827[label="",style="solid", color="black", weight=3]; 130.29/78.13 22211[label="FiniteMap.splitLT2 (Pos zzz19700) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) (primCmpInt (Pos (Succ zzz1975)) (Pos zzz19700) == LT)",fontsize=16,color="black",shape="box"];22211 -> 22245[label="",style="solid", color="black", weight=3]; 130.29/78.13 22212[label="FiniteMap.splitLT2 (Neg zzz19700) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) (primCmpInt (Pos (Succ zzz1975)) (Neg zzz19700) == LT)",fontsize=16,color="black",shape="box"];22212 -> 22246[label="",style="solid", color="black", weight=3]; 130.29/78.13 22430[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) zzz1983 zzz1984 zzz1985 zzz1986 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz1987)) zzz1988 zzz1989 zzz1990 zzz1991 (Pos (Succ zzz1982)) (Pos (Succ zzz1982) > Pos (Succ zzz1987))))",fontsize=16,color="black",shape="box"];22430 -> 22460[label="",style="solid", color="black", weight=3]; 130.29/78.13 22431 -> 18275[label="",style="dashed", color="red", weight=0]; 130.29/78.13 22431[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) zzz1983 zzz1984 zzz1985 zzz1986 (Maybe.isJust (FiniteMap.lookupFM zzz1990 (Pos (Succ zzz1982))))",fontsize=16,color="magenta"];22431 -> 22461[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22431 -> 22462[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22431 -> 22463[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22431 -> 22464[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22431 -> 22465[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22431 -> 22466[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22431 -> 22467[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22431 -> 22468[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22431 -> 22469[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22431 -> 22470[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22431 -> 22471[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18314[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) (GT == GT)))",fontsize=16,color="black",shape="box"];18314 -> 18395[label="",style="solid", color="black", weight=3]; 130.29/78.13 18315[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM FiniteMap.EmptyFM (Pos (Succ zzz1387))))",fontsize=16,color="black",shape="box"];18315 -> 18396[label="",style="solid", color="black", weight=3]; 130.29/78.13 18316[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM (FiniteMap.Branch zzz13960 zzz13961 zzz13962 zzz13963 zzz13964) (Pos (Succ zzz1387))))",fontsize=16,color="black",shape="box"];18316 -> 18397[label="",style="solid", color="black", weight=3]; 130.29/78.13 2402[label="FiniteMap.splitGT1 (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Pos Zero) (compare (Pos Zero) (Pos (Succ zzz3000)) == LT)",fontsize=16,color="black",shape="box"];2402 -> 2843[label="",style="solid", color="black", weight=3]; 130.29/78.13 2403[label="FiniteMap.splitLT4 FiniteMap.EmptyFM (Pos Zero)",fontsize=16,color="black",shape="triangle"];2403 -> 2844[label="",style="solid", color="black", weight=3]; 130.29/78.13 10619 -> 288[label="",style="dashed", color="red", weight=0]; 130.29/78.13 10619[label="FiniteMap.glueVBal (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero)) zzz625) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero)) zzz626)",fontsize=16,color="magenta"];10619 -> 10759[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 10619 -> 10760[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 10620[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero) zzz623 zzz624 zzz625 zzz626 True",fontsize=16,color="black",shape="box"];10620 -> 10761[label="",style="solid", color="black", weight=3]; 130.29/78.13 5454[label="FiniteMap.splitLT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (compare (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];5454 -> 5519[label="",style="solid", color="black", weight=3]; 130.29/78.13 5455[label="FiniteMap.splitGT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (compare (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];5455 -> 5520[label="",style="solid", color="black", weight=3]; 130.29/78.13 5456[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 (primCmpInt (Pos (Succ zzz3000)) zzz340 == LT)",fontsize=16,color="burlywood",shape="box"];65014[label="zzz340/Pos zzz3400",fontsize=10,color="white",style="solid",shape="box"];5456 -> 65014[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65014 -> 5521[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65015[label="zzz340/Neg zzz3400",fontsize=10,color="white",style="solid",shape="box"];5456 -> 65015[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65015 -> 5522[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 5457[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (primCmpInt (Pos Zero) zzz340 == LT)",fontsize=16,color="burlywood",shape="box"];65016[label="zzz340/Pos zzz3400",fontsize=10,color="white",style="solid",shape="box"];5457 -> 65016[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65016 -> 5523[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65017[label="zzz340/Neg zzz3400",fontsize=10,color="white",style="solid",shape="box"];5457 -> 65017[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65017 -> 5524[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 5458[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz2502) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 zzz2502 zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="burlywood",shape="box"];65018[label="zzz2502/Pos zzz25020",fontsize=10,color="white",style="solid",shape="box"];5458 -> 65018[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65018 -> 5525[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65019[label="zzz2502/Neg zzz25020",fontsize=10,color="white",style="solid",shape="box"];5458 -> 65019[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65019 -> 5526[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 2480[label="FiniteMap.splitGT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos Zero) (GT == GT)",fontsize=16,color="black",shape="box"];2480 -> 2901[label="",style="solid", color="black", weight=3]; 130.29/78.13 2481[label="FiniteMap.splitLT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos Zero) (GT == LT)",fontsize=16,color="black",shape="box"];2481 -> 2902[label="",style="solid", color="black", weight=3]; 130.29/78.13 16229[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust Nothing)",fontsize=16,color="black",shape="box"];16229 -> 16280[label="",style="solid", color="black", weight=3]; 130.29/78.13 16230[label="zzz12043",fontsize=16,color="green",shape="box"];16231[label="zzz12044",fontsize=16,color="green",shape="box"];16232[label="zzz12040",fontsize=16,color="green",shape="box"];16233[label="zzz12041",fontsize=16,color="green",shape="box"];16234[label="zzz12042",fontsize=16,color="green",shape="box"];16235[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) False))",fontsize=16,color="black",shape="box"];16235 -> 16281[label="",style="solid", color="black", weight=3]; 130.29/78.13 16236[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz120100)) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) True))",fontsize=16,color="black",shape="box"];16236 -> 16282[label="",style="solid", color="black", weight=3]; 130.29/78.13 16237[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) False))",fontsize=16,color="black",shape="box"];16237 -> 16283[label="",style="solid", color="black", weight=3]; 130.29/78.13 5459[label="FiniteMap.splitLT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (compare (Pos Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];5459 -> 5527[label="",style="solid", color="black", weight=3]; 130.29/78.13 5460[label="FiniteMap.splitGT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (compare (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];5460 -> 5528[label="",style="solid", color="black", weight=3]; 130.29/78.13 2490[label="FiniteMap.splitGT1 (Pos zzz300) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) True",fontsize=16,color="black",shape="box"];2490 -> 2911[label="",style="solid", color="black", weight=3]; 130.29/78.13 62524[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz63370",fontsize=16,color="burlywood",shape="triangle"];65020[label="zzz63370/Succ zzz633700",fontsize=10,color="white",style="solid",shape="box"];62524 -> 65020[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65020 -> 62527[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65021[label="zzz63370/Zero",fontsize=10,color="white",style="solid",shape="box"];62524 -> 65021[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65021 -> 62528[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 62523[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos zzz6338) zzz6319 == LT)",fontsize=16,color="burlywood",shape="triangle"];65022[label="zzz6338/Succ zzz63380",fontsize=10,color="white",style="solid",shape="box"];62523 -> 65022[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65022 -> 62529[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65023[label="zzz6338/Zero",fontsize=10,color="white",style="solid",shape="box"];62523 -> 65023[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65023 -> 62530[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 62532 -> 62524[label="",style="dashed", color="red", weight=0]; 130.29/78.13 62532[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz63370",fontsize=16,color="magenta"];62532 -> 62535[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 62531[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg zzz6340) zzz6319 == LT)",fontsize=16,color="burlywood",shape="triangle"];65024[label="zzz6340/Succ zzz63400",fontsize=10,color="white",style="solid",shape="box"];62531 -> 65024[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65024 -> 62536[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65025[label="zzz6340/Zero",fontsize=10,color="white",style="solid",shape="box"];62531 -> 65025[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65025 -> 62537[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 12279[label="FiniteMap.splitGT3 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747))",fontsize=16,color="black",shape="box"];12279 -> 12382[label="",style="solid", color="black", weight=3]; 130.29/78.13 12280[label="FiniteMap.splitLT3 (FiniteMap.Branch (Pos zzz742) zzz743 zzz744 zzz745 zzz746) (Neg (Succ zzz747))",fontsize=16,color="black",shape="box"];12280 -> 12383[label="",style="solid", color="black", weight=3]; 130.29/78.13 28480[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) zzz2761 zzz2762 zzz2763 zzz2764 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2765)) zzz2766 zzz2767 zzz2768 zzz2769 (Neg (Succ zzz2760)) (primCmpNat (Succ zzz27700) zzz2771 == GT)))",fontsize=16,color="burlywood",shape="box"];65026[label="zzz2771/Succ zzz27710",fontsize=10,color="white",style="solid",shape="box"];28480 -> 65026[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65026 -> 28512[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65027[label="zzz2771/Zero",fontsize=10,color="white",style="solid",shape="box"];28480 -> 65027[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65027 -> 28513[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 28481[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) zzz2761 zzz2762 zzz2763 zzz2764 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2765)) zzz2766 zzz2767 zzz2768 zzz2769 (Neg (Succ zzz2760)) (primCmpNat Zero zzz2771 == GT)))",fontsize=16,color="burlywood",shape="box"];65028[label="zzz2771/Succ zzz27710",fontsize=10,color="white",style="solid",shape="box"];28481 -> 65028[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65028 -> 28514[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65029[label="zzz2771/Zero",fontsize=10,color="white",style="solid",shape="box"];28481 -> 65029[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65029 -> 28515[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 28165 -> 24914[label="",style="dashed", color="red", weight=0]; 130.29/78.13 28165[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632))",fontsize=16,color="magenta"];28165 -> 28482[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28165 -> 28483[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28165 -> 28484[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28165 -> 28485[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28165 -> 28486[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28165 -> 28487[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28166[label="zzz2636",fontsize=16,color="green",shape="box"];28167 -> 24916[label="",style="dashed", color="red", weight=0]; 130.29/78.13 28167[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz2627)) zzz2628 zzz2629 zzz2630 zzz2631) (Neg (Succ zzz2632))",fontsize=16,color="magenta"];28167 -> 28488[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28167 -> 28489[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28167 -> 28490[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28167 -> 28491[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28167 -> 28492[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28167 -> 28493[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28168[label="zzz2635",fontsize=16,color="green",shape="box"];28169[label="zzz2633",fontsize=16,color="green",shape="box"];6297[label="FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 FiniteMap.EmptyFM zzz426",fontsize=16,color="black",shape="box"];6297 -> 6358[label="",style="solid", color="black", weight=3]; 130.29/78.13 6298[label="FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz426",fontsize=16,color="burlywood",shape="box"];65030[label="zzz426/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];6298 -> 65030[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65030 -> 6359[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65031[label="zzz426/FiniteMap.Branch zzz4260 zzz4261 zzz4262 zzz4263 zzz4264",fontsize=10,color="white",style="solid",shape="box"];6298 -> 65031[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65031 -> 6360[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 4319 -> 11[label="",style="dashed", color="red", weight=0]; 130.29/78.13 4319[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];17952[label="FiniteMap.splitGT2 zzz7450 zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (compare (Neg (Succ zzz747)) zzz7450 == GT)",fontsize=16,color="black",shape="box"];17952 -> 18498[label="",style="solid", color="black", weight=3]; 130.29/78.13 13838[label="FiniteMap.splitLT2 zzz7450 zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (compare (Neg (Succ zzz747)) zzz7450 == LT)",fontsize=16,color="black",shape="box"];13838 -> 14052[label="",style="solid", color="black", weight=3]; 130.29/78.13 2562[label="FiniteMap.splitGT1 (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (compare (Neg (Succ zzz4000)) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];2562 -> 3023[label="",style="solid", color="black", weight=3]; 130.29/78.13 13437[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888))",fontsize=16,color="black",shape="triangle"];13437 -> 13510[label="",style="solid", color="black", weight=3]; 130.29/78.13 13438[label="zzz892",fontsize=16,color="green",shape="box"];13439[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888))",fontsize=16,color="black",shape="triangle"];13439 -> 13511[label="",style="solid", color="black", weight=3]; 130.29/78.13 13440[label="zzz891",fontsize=16,color="green",shape="box"];19865 -> 29406[label="",style="dashed", color="red", weight=0]; 130.29/78.13 19865[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz1577 zzz1578 zzz1579 zzz1580) (Neg (Succ zzz1581)) zzz1582 zzz1583 zzz1584 zzz1585 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz1586)) zzz1587 zzz1588 zzz1589 zzz1590 (Neg (Succ zzz1581)) (primCmpNat (Succ zzz1586) (Succ zzz1581) == GT)))",fontsize=16,color="magenta"];19865 -> 29407[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 19865 -> 29408[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 19865 -> 29409[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 19865 -> 29410[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 19865 -> 29411[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 19865 -> 29412[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 19865 -> 29413[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 19865 -> 29414[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 19865 -> 29415[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 19865 -> 29416[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 19865 -> 29417[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 19865 -> 29418[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 19865 -> 29419[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 19865 -> 29420[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 19865 -> 29421[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 19865 -> 29422[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 12970[label="FiniteMap.splitGT1 (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834 (Neg Zero) (primCmpInt (Neg Zero) (Pos (Succ zzz830)) == LT)",fontsize=16,color="black",shape="box"];12970 -> 13002[label="",style="solid", color="black", weight=3]; 130.29/78.13 12971[label="FiniteMap.splitLT4 FiniteMap.EmptyFM (Neg Zero)",fontsize=16,color="black",shape="box"];12971 -> 13003[label="",style="solid", color="black", weight=3]; 130.29/78.13 12972[label="FiniteMap.splitLT3 (FiniteMap.Branch zzz8330 zzz8331 zzz8332 zzz8333 zzz8334) (Neg Zero)",fontsize=16,color="black",shape="box"];12972 -> 13004[label="",style="solid", color="black", weight=3]; 130.29/78.13 13509 -> 5407[label="",style="dashed", color="red", weight=0]; 130.29/78.13 13509[label="FiniteMap.mkVBalBranch (Neg Zero) (FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero)) zzz904) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero)) zzz906) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero)) zzz907)",fontsize=16,color="magenta"];13509 -> 13797[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 13509 -> 13798[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 13509 -> 13799[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 6542[label="FiniteMap.splitLT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (compare (Neg Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];6542 -> 6635[label="",style="solid", color="black", weight=3]; 130.29/78.13 6543[label="FiniteMap.splitGT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (compare (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];6543 -> 6636[label="",style="solid", color="black", weight=3]; 130.29/78.13 12937 -> 11[label="",style="dashed", color="red", weight=0]; 130.29/78.13 12937[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];12938 -> 11[label="",style="dashed", color="red", weight=0]; 130.29/78.13 12938[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];12939[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 zzz9820 zzz9821 zzz9822 zzz9823 zzz9824 (Neg zzz300) zzz31 (primCmpInt (Neg zzz300) zzz9820 == LT)",fontsize=16,color="burlywood",shape="box"];65032[label="zzz300/Succ zzz3000",fontsize=10,color="white",style="solid",shape="box"];12939 -> 65032[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65032 -> 12973[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65033[label="zzz300/Zero",fontsize=10,color="white",style="solid",shape="box"];12939 -> 65033[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65033 -> 12974[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 6546[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz3532) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 zzz3532 zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="burlywood",shape="box"];65034[label="zzz3532/Pos zzz35320",fontsize=10,color="white",style="solid",shape="box"];6546 -> 65034[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65034 -> 6641[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65035[label="zzz3532/Neg zzz35320",fontsize=10,color="white",style="solid",shape="box"];6546 -> 65035[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65035 -> 6642[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 2777[label="FiniteMap.splitGT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Neg Zero) (compare (Neg Zero) (Neg (Succ zzz3000)) == GT)",fontsize=16,color="black",shape="box"];2777 -> 3083[label="",style="solid", color="black", weight=3]; 130.29/78.13 2778[label="FiniteMap.splitLT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Neg Zero) (compare (Neg Zero) (Neg (Succ zzz3000)) == LT)",fontsize=16,color="black",shape="box"];2778 -> 3084[label="",style="solid", color="black", weight=3]; 130.29/78.13 20081[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Neg Zero)))",fontsize=16,color="black",shape="box"];20081 -> 20116[label="",style="solid", color="black", weight=3]; 130.29/78.13 20082 -> 19318[label="",style="dashed", color="red", weight=0]; 130.29/78.13 20082[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz16060 zzz16061 zzz16062 zzz16063 zzz16064) (Neg Zero)))",fontsize=16,color="magenta"];20082 -> 20117[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 20082 -> 20118[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 20082 -> 20119[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 20082 -> 20120[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 20082 -> 20121[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 20083[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];20083 -> 20122[label="",style="solid", color="black", weight=3]; 130.29/78.13 20084[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz160300)) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (compare (Neg Zero) (Neg (Succ zzz160300)) == GT)))",fontsize=16,color="black",shape="box"];20084 -> 20123[label="",style="solid", color="black", weight=3]; 130.29/78.13 20085[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == GT)))",fontsize=16,color="black",shape="box"];20085 -> 20124[label="",style="solid", color="black", weight=3]; 130.29/78.13 6547[label="FiniteMap.splitLT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (compare (Neg Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];6547 -> 6643[label="",style="solid", color="black", weight=3]; 130.29/78.13 6548[label="FiniteMap.splitGT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (compare (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];6548 -> 6644[label="",style="solid", color="black", weight=3]; 130.29/78.13 28170[label="zzz2610",fontsize=16,color="green",shape="box"];28171[label="zzz2611",fontsize=16,color="green",shape="box"];28172[label="zzz2612",fontsize=16,color="green",shape="box"];28173[label="zzz2614",fontsize=16,color="green",shape="box"];28174[label="zzz2613",fontsize=16,color="green",shape="box"];28175[label="zzz2609",fontsize=16,color="green",shape="box"];28176[label="zzz2610",fontsize=16,color="green",shape="box"];28177[label="zzz2611",fontsize=16,color="green",shape="box"];28178[label="zzz2612",fontsize=16,color="green",shape="box"];28179[label="zzz2614",fontsize=16,color="green",shape="box"];28180[label="zzz2613",fontsize=16,color="green",shape="box"];28181[label="zzz2609",fontsize=16,color="green",shape="box"];19906[label="FiniteMap.splitGT2 zzz16120 zzz16121 zzz16122 zzz16123 zzz16124 (Pos (Succ zzz1613)) (primCmpInt (Pos (Succ zzz1613)) zzz16120 == GT)",fontsize=16,color="burlywood",shape="box"];65036[label="zzz16120/Pos zzz161200",fontsize=10,color="white",style="solid",shape="box"];19906 -> 65036[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65036 -> 19975[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65037[label="zzz16120/Neg zzz161200",fontsize=10,color="white",style="solid",shape="box"];19906 -> 65037[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65037 -> 19976[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 23412 -> 21896[label="",style="dashed", color="red", weight=0]; 130.29/78.13 23412[label="FiniteMap.splitLT2 zzz19740 zzz19741 zzz19742 zzz19743 zzz19744 (Pos (Succ zzz1975)) (compare (Pos (Succ zzz1975)) zzz19740 == LT)",fontsize=16,color="magenta"];23412 -> 23611[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 23412 -> 23612[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 23412 -> 23613[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 23412 -> 23614[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 23412 -> 23615[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 25024[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz20911 zzz20912 zzz20913 zzz20914 (Pos (Succ zzz2083)) True))",fontsize=16,color="black",shape="box"];25024 -> 25155[label="",style="solid", color="black", weight=3]; 130.29/78.13 2816[label="FiniteMap.splitGT2 (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos (Succ zzz4000)) (primCmpInt (Pos (Succ zzz4000)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];2816 -> 3289[label="",style="solid", color="black", weight=3]; 130.29/78.13 21909[label="zzz33",fontsize=16,color="green",shape="box"];21910[label="Pos Zero",fontsize=16,color="green",shape="box"];21911[label="zzz4000",fontsize=16,color="green",shape="box"];21912[label="FiniteMap.EmptyFM",fontsize=16,color="green",shape="box"];21913[label="zzz32",fontsize=16,color="green",shape="box"];21914[label="zzz31",fontsize=16,color="green",shape="box"];30794 -> 30437[label="",style="dashed", color="red", weight=0]; 130.29/78.13 30794[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) zzz3073 zzz3074 zzz3075 zzz3076 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3077)) zzz3078 zzz3079 zzz3080 zzz3081 (Pos (Succ zzz3072)) (primCmpNat zzz30820 zzz30830 == LT)))",fontsize=16,color="magenta"];30794 -> 30843[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 30794 -> 30844[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 30795[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) zzz3073 zzz3074 zzz3075 zzz3076 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3077)) zzz3078 zzz3079 zzz3080 zzz3081 (Pos (Succ zzz3072)) (GT == LT)))",fontsize=16,color="black",shape="box"];30795 -> 30845[label="",style="solid", color="black", weight=3]; 130.29/78.13 30796[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) zzz3073 zzz3074 zzz3075 zzz3076 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3077)) zzz3078 zzz3079 zzz3080 zzz3081 (Pos (Succ zzz3072)) (LT == LT)))",fontsize=16,color="black",shape="box"];30796 -> 30846[label="",style="solid", color="black", weight=3]; 130.29/78.13 30797[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) zzz3073 zzz3074 zzz3075 zzz3076 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3077)) zzz3078 zzz3079 zzz3080 zzz3081 (Pos (Succ zzz3072)) (EQ == LT)))",fontsize=16,color="black",shape="box"];30797 -> 30847[label="",style="solid", color="black", weight=3]; 130.29/78.13 28680[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (primCmpInt (Pos (Succ zzz2738)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];28680 -> 28737[label="",style="solid", color="black", weight=3]; 130.29/78.13 28681[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM1 (Neg zzz27430) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) True))",fontsize=16,color="black",shape="box"];28681 -> 28738[label="",style="solid", color="black", weight=3]; 130.29/78.13 2827[label="FiniteMap.splitGT FiniteMap.EmptyFM (Pos (Succ zzz4000))",fontsize=16,color="black",shape="triangle"];2827 -> 3302[label="",style="solid", color="black", weight=3]; 130.29/78.13 22245[label="FiniteMap.splitLT2 (Pos zzz19700) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) (primCmpNat (Succ zzz1975) zzz19700 == LT)",fontsize=16,color="burlywood",shape="box"];65038[label="zzz19700/Succ zzz197000",fontsize=10,color="white",style="solid",shape="box"];22245 -> 65038[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65038 -> 22275[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65039[label="zzz19700/Zero",fontsize=10,color="white",style="solid",shape="box"];22245 -> 65039[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65039 -> 22276[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 22246[label="FiniteMap.splitLT2 (Neg zzz19700) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) (GT == LT)",fontsize=16,color="black",shape="box"];22246 -> 22277[label="",style="solid", color="black", weight=3]; 130.29/78.13 22460[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) zzz1983 zzz1984 zzz1985 zzz1986 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz1987)) zzz1988 zzz1989 zzz1990 zzz1991 (Pos (Succ zzz1982)) (compare (Pos (Succ zzz1982)) (Pos (Succ zzz1987)) == GT)))",fontsize=16,color="black",shape="box"];22460 -> 22502[label="",style="solid", color="black", weight=3]; 130.29/78.13 22461[label="zzz1981",fontsize=16,color="green",shape="box"];22462[label="zzz1979",fontsize=16,color="green",shape="box"];22463[label="zzz1982",fontsize=16,color="green",shape="box"];22464[label="zzz1978",fontsize=16,color="green",shape="box"];22465[label="zzz1985",fontsize=16,color="green",shape="box"];22466[label="zzz1977",fontsize=16,color="green",shape="box"];22467[label="zzz1986",fontsize=16,color="green",shape="box"];22468[label="zzz1980",fontsize=16,color="green",shape="box"];22469[label="zzz1983",fontsize=16,color="green",shape="box"];22470[label="zzz1990",fontsize=16,color="green",shape="box"];22471[label="zzz1984",fontsize=16,color="green",shape="box"];18395[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz1393 zzz1394 zzz1395 zzz1396 (Pos (Succ zzz1387)) True))",fontsize=16,color="black",shape="box"];18395 -> 18567[label="",style="solid", color="black", weight=3]; 130.29/78.13 18396[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Pos (Succ zzz1387))))",fontsize=16,color="black",shape="box"];18396 -> 18568[label="",style="solid", color="black", weight=3]; 130.29/78.13 18397 -> 16425[label="",style="dashed", color="red", weight=0]; 130.29/78.13 18397[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz13960 zzz13961 zzz13962 zzz13963 zzz13964) (Pos (Succ zzz1387))))",fontsize=16,color="magenta"];18397 -> 18569[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18397 -> 18570[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18397 -> 18571[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18397 -> 18572[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18397 -> 18573[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 2843[label="FiniteMap.splitGT1 (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Pos (Succ zzz3000)) == LT)",fontsize=16,color="black",shape="box"];2843 -> 3320[label="",style="solid", color="black", weight=3]; 130.29/78.13 2844 -> 11[label="",style="dashed", color="red", weight=0]; 130.29/78.13 2844[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];10759 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.13 10759[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero)) zzz626",fontsize=16,color="magenta"];10759 -> 10972[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 10759 -> 10973[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 10760 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.13 10760[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero)) zzz625",fontsize=16,color="magenta"];10760 -> 10974[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 10760 -> 10975[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 10761 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.13 10761[label="FiniteMap.mkVBalBranch (Pos Zero) (FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero)) zzz623) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero)) zzz625) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero)) zzz626)",fontsize=16,color="magenta"];10761 -> 10976[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 10761 -> 10977[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 10761 -> 10978[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 10761 -> 10979[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 5519[label="FiniteMap.splitLT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];5519 -> 5562[label="",style="solid", color="black", weight=3]; 130.29/78.13 5520[label="FiniteMap.splitGT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];5520 -> 5563[label="",style="solid", color="black", weight=3]; 130.29/78.13 5521[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos zzz3400) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 (primCmpInt (Pos (Succ zzz3000)) (Pos zzz3400) == LT)",fontsize=16,color="black",shape="box"];5521 -> 5564[label="",style="solid", color="black", weight=3]; 130.29/78.13 5522[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg zzz3400) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 (primCmpInt (Pos (Succ zzz3000)) (Neg zzz3400) == LT)",fontsize=16,color="black",shape="box"];5522 -> 5565[label="",style="solid", color="black", weight=3]; 130.29/78.13 5523[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos zzz3400) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (primCmpInt (Pos Zero) (Pos zzz3400) == LT)",fontsize=16,color="burlywood",shape="box"];65040[label="zzz3400/Succ zzz34000",fontsize=10,color="white",style="solid",shape="box"];5523 -> 65040[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65040 -> 5566[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65041[label="zzz3400/Zero",fontsize=10,color="white",style="solid",shape="box"];5523 -> 65041[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65041 -> 5567[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 5524[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg zzz3400) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (primCmpInt (Pos Zero) (Neg zzz3400) == LT)",fontsize=16,color="burlywood",shape="box"];65042[label="zzz3400/Succ zzz34000",fontsize=10,color="white",style="solid",shape="box"];5524 -> 65042[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65042 -> 5568[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65043[label="zzz3400/Zero",fontsize=10,color="white",style="solid",shape="box"];5524 -> 65043[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65043 -> 5569[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 5525[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos zzz25020) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos zzz25020) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos zzz25020)) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos zzz25020) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];5525 -> 5570[label="",style="solid", color="black", weight=3]; 130.29/78.13 5526[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg zzz25020) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg zzz25020) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg zzz25020)) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg zzz25020) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];5526 -> 5571[label="",style="solid", color="black", weight=3]; 130.29/78.13 2901[label="FiniteMap.splitGT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos Zero) True",fontsize=16,color="black",shape="box"];2901 -> 3350[label="",style="solid", color="black", weight=3]; 130.29/78.13 2902[label="FiniteMap.splitLT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos Zero) False",fontsize=16,color="black",shape="box"];2902 -> 3351[label="",style="solid", color="black", weight=3]; 130.29/78.13 16280[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 False",fontsize=16,color="black",shape="box"];16280 -> 16582[label="",style="solid", color="black", weight=3]; 130.29/78.13 16281[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM0 (Pos Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) otherwise))",fontsize=16,color="black",shape="box"];16281 -> 16583[label="",style="solid", color="black", weight=3]; 130.29/78.13 16282 -> 15403[label="",style="dashed", color="red", weight=0]; 130.29/78.13 16282[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM zzz1205 (Pos Zero)))",fontsize=16,color="magenta"];16282 -> 16584[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 16283[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM0 (Neg Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) otherwise))",fontsize=16,color="black",shape="box"];16283 -> 16585[label="",style="solid", color="black", weight=3]; 130.29/78.13 5527[label="FiniteMap.splitLT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];5527 -> 5572[label="",style="solid", color="black", weight=3]; 130.29/78.13 5528[label="FiniteMap.splitGT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];5528 -> 5573[label="",style="solid", color="black", weight=3]; 130.29/78.13 2911 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.13 2911[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.splitGT FiniteMap.EmptyFM (Neg (Succ zzz4000))) zzz34",fontsize=16,color="magenta"];2911 -> 4182[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 62527[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz633700)",fontsize=16,color="black",shape="box"];62527 -> 62538[label="",style="solid", color="black", weight=3]; 130.29/78.13 62528[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero",fontsize=16,color="black",shape="box"];62528 -> 62539[label="",style="solid", color="black", weight=3]; 130.29/78.13 62529[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos (Succ zzz63380)) zzz6319 == LT)",fontsize=16,color="burlywood",shape="box"];65044[label="zzz6319/Pos zzz63190",fontsize=10,color="white",style="solid",shape="box"];62529 -> 65044[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65044 -> 62540[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65045[label="zzz6319/Neg zzz63190",fontsize=10,color="white",style="solid",shape="box"];62529 -> 65045[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65045 -> 62541[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 62530[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos Zero) zzz6319 == LT)",fontsize=16,color="burlywood",shape="box"];65046[label="zzz6319/Pos zzz63190",fontsize=10,color="white",style="solid",shape="box"];62530 -> 65046[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65046 -> 62542[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65047[label="zzz6319/Neg zzz63190",fontsize=10,color="white",style="solid",shape="box"];62530 -> 65047[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65047 -> 62543[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 62535[label="zzz63370",fontsize=16,color="green",shape="box"];62536[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg (Succ zzz63400)) zzz6319 == LT)",fontsize=16,color="burlywood",shape="box"];65048[label="zzz6319/Pos zzz63190",fontsize=10,color="white",style="solid",shape="box"];62536 -> 65048[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65048 -> 62551[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65049[label="zzz6319/Neg zzz63190",fontsize=10,color="white",style="solid",shape="box"];62536 -> 65049[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65049 -> 62552[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 62537[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg Zero) zzz6319 == LT)",fontsize=16,color="burlywood",shape="box"];65050[label="zzz6319/Pos zzz63190",fontsize=10,color="white",style="solid",shape="box"];62537 -> 65050[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65050 -> 62553[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65051[label="zzz6319/Neg zzz63190",fontsize=10,color="white",style="solid",shape="box"];62537 -> 65051[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65051 -> 62554[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 12382[label="FiniteMap.splitGT2 (Pos zzz742) zzz743 zzz744 zzz745 zzz746 (Neg (Succ zzz747)) (Neg (Succ zzz747) > Pos zzz742)",fontsize=16,color="black",shape="box"];12382 -> 12476[label="",style="solid", color="black", weight=3]; 130.29/78.13 12383[label="FiniteMap.splitLT2 (Pos zzz742) zzz743 zzz744 zzz745 zzz746 (Neg (Succ zzz747)) (Neg (Succ zzz747) < Pos zzz742)",fontsize=16,color="black",shape="box"];12383 -> 12477[label="",style="solid", color="black", weight=3]; 130.29/78.13 28512[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) zzz2761 zzz2762 zzz2763 zzz2764 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2765)) zzz2766 zzz2767 zzz2768 zzz2769 (Neg (Succ zzz2760)) (primCmpNat (Succ zzz27700) (Succ zzz27710) == GT)))",fontsize=16,color="black",shape="box"];28512 -> 28525[label="",style="solid", color="black", weight=3]; 130.29/78.13 28513[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) zzz2761 zzz2762 zzz2763 zzz2764 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2765)) zzz2766 zzz2767 zzz2768 zzz2769 (Neg (Succ zzz2760)) (primCmpNat (Succ zzz27700) Zero == GT)))",fontsize=16,color="black",shape="box"];28513 -> 28526[label="",style="solid", color="black", weight=3]; 130.29/78.13 28514[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) zzz2761 zzz2762 zzz2763 zzz2764 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2765)) zzz2766 zzz2767 zzz2768 zzz2769 (Neg (Succ zzz2760)) (primCmpNat Zero (Succ zzz27710) == GT)))",fontsize=16,color="black",shape="box"];28514 -> 28527[label="",style="solid", color="black", weight=3]; 130.29/78.13 28515[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) zzz2761 zzz2762 zzz2763 zzz2764 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2765)) zzz2766 zzz2767 zzz2768 zzz2769 (Neg (Succ zzz2760)) (primCmpNat Zero Zero == GT)))",fontsize=16,color="black",shape="box"];28515 -> 28528[label="",style="solid", color="black", weight=3]; 130.29/78.13 28482[label="zzz2629",fontsize=16,color="green",shape="box"];28483[label="zzz2631",fontsize=16,color="green",shape="box"];28484[label="zzz2628",fontsize=16,color="green",shape="box"];28485[label="zzz2630",fontsize=16,color="green",shape="box"];28486[label="zzz2632",fontsize=16,color="green",shape="box"];28487[label="zzz2627",fontsize=16,color="green",shape="box"];28488[label="zzz2629",fontsize=16,color="green",shape="box"];28489[label="zzz2631",fontsize=16,color="green",shape="box"];28490[label="zzz2628",fontsize=16,color="green",shape="box"];28491[label="zzz2630",fontsize=16,color="green",shape="box"];28492[label="zzz2632",fontsize=16,color="green",shape="box"];28493[label="zzz2627",fontsize=16,color="green",shape="box"];6358[label="FiniteMap.mkVBalBranch5 (Neg (Succ zzz3000)) zzz31 FiniteMap.EmptyFM zzz426",fontsize=16,color="black",shape="box"];6358 -> 6658[label="",style="solid", color="black", weight=3]; 130.29/78.13 6359[label="FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];6359 -> 6659[label="",style="solid", color="black", weight=3]; 130.29/78.13 6360[label="FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) (FiniteMap.Branch zzz4260 zzz4261 zzz4262 zzz4263 zzz4264)",fontsize=16,color="black",shape="box"];6360 -> 6660[label="",style="solid", color="black", weight=3]; 130.29/78.13 18498[label="FiniteMap.splitGT2 zzz7450 zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (primCmpInt (Neg (Succ zzz747)) zzz7450 == GT)",fontsize=16,color="burlywood",shape="box"];65052[label="zzz7450/Pos zzz74500",fontsize=10,color="white",style="solid",shape="box"];18498 -> 65052[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65052 -> 20940[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65053[label="zzz7450/Neg zzz74500",fontsize=10,color="white",style="solid",shape="box"];18498 -> 65053[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65053 -> 20941[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 14052[label="FiniteMap.splitLT2 zzz7450 zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (primCmpInt (Neg (Succ zzz747)) zzz7450 == LT)",fontsize=16,color="burlywood",shape="box"];65054[label="zzz7450/Pos zzz74500",fontsize=10,color="white",style="solid",shape="box"];14052 -> 65054[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65054 -> 14378[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65055[label="zzz7450/Neg zzz74500",fontsize=10,color="white",style="solid",shape="box"];14052 -> 65055[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65055 -> 14379[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 3023[label="FiniteMap.splitGT1 (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (primCmpInt (Neg (Succ zzz4000)) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];3023 -> 3579[label="",style="solid", color="black", weight=3]; 130.29/78.13 13510[label="FiniteMap.splitGT (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888))",fontsize=16,color="black",shape="box"];13510 -> 13800[label="",style="solid", color="black", weight=3]; 130.29/78.13 13511 -> 13018[label="",style="dashed", color="red", weight=0]; 130.29/78.13 13511[label="FiniteMap.splitLT (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888))",fontsize=16,color="magenta"];13511 -> 13801[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 13511 -> 13802[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 29407[label="zzz1587",fontsize=16,color="green",shape="box"];29408[label="zzz1579",fontsize=16,color="green",shape="box"];29409[label="zzz1577",fontsize=16,color="green",shape="box"];29410[label="zzz1578",fontsize=16,color="green",shape="box"];29411[label="zzz1581",fontsize=16,color="green",shape="box"];29412[label="zzz1583",fontsize=16,color="green",shape="box"];29413[label="zzz1586",fontsize=16,color="green",shape="box"];29414[label="zzz1584",fontsize=16,color="green",shape="box"];29415[label="Succ zzz1581",fontsize=16,color="green",shape="box"];29416[label="zzz1590",fontsize=16,color="green",shape="box"];29417[label="zzz1589",fontsize=16,color="green",shape="box"];29418[label="zzz1582",fontsize=16,color="green",shape="box"];29419[label="Succ zzz1586",fontsize=16,color="green",shape="box"];29420[label="zzz1580",fontsize=16,color="green",shape="box"];29421[label="zzz1585",fontsize=16,color="green",shape="box"];29422[label="zzz1588",fontsize=16,color="green",shape="box"];29406[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) zzz2889 zzz2890 zzz2891 zzz2892 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2893)) zzz2894 zzz2895 zzz2896 zzz2897 (Neg (Succ zzz2888)) (primCmpNat zzz2898 zzz2899 == GT)))",fontsize=16,color="burlywood",shape="triangle"];65056[label="zzz2898/Succ zzz28980",fontsize=10,color="white",style="solid",shape="box"];29406 -> 65056[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65056 -> 29583[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65057[label="zzz2898/Zero",fontsize=10,color="white",style="solid",shape="box"];29406 -> 65057[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65057 -> 29584[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 13002[label="FiniteMap.splitGT1 (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834 (Neg Zero) (LT == LT)",fontsize=16,color="black",shape="box"];13002 -> 13248[label="",style="solid", color="black", weight=3]; 130.29/78.13 13003 -> 11[label="",style="dashed", color="red", weight=0]; 130.29/78.13 13003[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];13004[label="FiniteMap.splitLT2 zzz8330 zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (Neg Zero < zzz8330)",fontsize=16,color="black",shape="box"];13004 -> 13249[label="",style="solid", color="black", weight=3]; 130.29/78.13 13797 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.13 13797[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero)) zzz906",fontsize=16,color="magenta"];13797 -> 14029[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 13797 -> 14030[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 13798 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.13 13798[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero)) zzz907",fontsize=16,color="magenta"];13798 -> 14031[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 13798 -> 14032[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 13799[label="FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero)) zzz904",fontsize=16,color="black",shape="box"];13799 -> 14033[label="",style="solid", color="black", weight=3]; 130.29/78.13 6635[label="FiniteMap.splitLT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];6635 -> 6778[label="",style="solid", color="black", weight=3]; 130.29/78.13 6636[label="FiniteMap.splitGT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];6636 -> 6779[label="",style="solid", color="black", weight=3]; 130.29/78.13 12973[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 zzz9820 zzz9821 zzz9822 zzz9823 zzz9824 (Neg (Succ zzz3000)) zzz31 (primCmpInt (Neg (Succ zzz3000)) zzz9820 == LT)",fontsize=16,color="burlywood",shape="box"];65058[label="zzz9820/Pos zzz98200",fontsize=10,color="white",style="solid",shape="box"];12973 -> 65058[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65058 -> 13005[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65059[label="zzz9820/Neg zzz98200",fontsize=10,color="white",style="solid",shape="box"];12973 -> 65059[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65059 -> 13006[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 12974[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 zzz9820 zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (primCmpInt (Neg Zero) zzz9820 == LT)",fontsize=16,color="burlywood",shape="box"];65060[label="zzz9820/Pos zzz98200",fontsize=10,color="white",style="solid",shape="box"];12974 -> 65060[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65060 -> 13007[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65061[label="zzz9820/Neg zzz98200",fontsize=10,color="white",style="solid",shape="box"];12974 -> 65061[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65061 -> 13008[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 6641[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos zzz35320) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos zzz35320) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos zzz35320)) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos zzz35320) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];6641 -> 6784[label="",style="solid", color="black", weight=3]; 130.29/78.13 6642[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg zzz35320) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg zzz35320) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg zzz35320)) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg zzz35320) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];6642 -> 6785[label="",style="solid", color="black", weight=3]; 130.29/78.13 3083[label="FiniteMap.splitGT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ zzz3000)) == GT)",fontsize=16,color="black",shape="box"];3083 -> 3642[label="",style="solid", color="black", weight=3]; 130.29/78.13 3084[label="FiniteMap.splitLT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ zzz3000)) == LT)",fontsize=16,color="black",shape="box"];3084 -> 3643[label="",style="solid", color="black", weight=3]; 130.29/78.13 20116[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust Nothing)",fontsize=16,color="black",shape="box"];20116 -> 20148[label="",style="solid", color="black", weight=3]; 130.29/78.13 20117[label="zzz16063",fontsize=16,color="green",shape="box"];20118[label="zzz16060",fontsize=16,color="green",shape="box"];20119[label="zzz16061",fontsize=16,color="green",shape="box"];20120[label="zzz16062",fontsize=16,color="green",shape="box"];20121[label="zzz16064",fontsize=16,color="green",shape="box"];20122[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (EQ == GT)))",fontsize=16,color="black",shape="box"];20122 -> 20149[label="",style="solid", color="black", weight=3]; 130.29/78.13 20123[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz160300)) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ zzz160300)) == GT)))",fontsize=16,color="black",shape="box"];20123 -> 20150[label="",style="solid", color="black", weight=3]; 130.29/78.13 20124[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (EQ == GT)))",fontsize=16,color="black",shape="box"];20124 -> 20151[label="",style="solid", color="black", weight=3]; 130.29/78.13 6643[label="FiniteMap.splitLT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];6643 -> 6786[label="",style="solid", color="black", weight=3]; 130.29/78.13 6644[label="FiniteMap.splitGT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];6644 -> 6787[label="",style="solid", color="black", weight=3]; 130.29/78.13 19975[label="FiniteMap.splitGT2 (Pos zzz161200) zzz16121 zzz16122 zzz16123 zzz16124 (Pos (Succ zzz1613)) (primCmpInt (Pos (Succ zzz1613)) (Pos zzz161200) == GT)",fontsize=16,color="black",shape="box"];19975 -> 20097[label="",style="solid", color="black", weight=3]; 130.29/78.13 19976[label="FiniteMap.splitGT2 (Neg zzz161200) zzz16121 zzz16122 zzz16123 zzz16124 (Pos (Succ zzz1613)) (primCmpInt (Pos (Succ zzz1613)) (Neg zzz161200) == GT)",fontsize=16,color="black",shape="box"];19976 -> 20098[label="",style="solid", color="black", weight=3]; 130.29/78.13 23611[label="zzz19743",fontsize=16,color="green",shape="box"];23612[label="zzz19740",fontsize=16,color="green",shape="box"];23613[label="zzz19744",fontsize=16,color="green",shape="box"];23614[label="zzz19742",fontsize=16,color="green",shape="box"];23615[label="zzz19741",fontsize=16,color="green",shape="box"];25155 -> 23586[label="",style="dashed", color="red", weight=0]; 130.29/78.13 25155[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos (Succ zzz2078)) zzz2079 zzz2080 zzz2081 zzz2082) (Pos (Succ zzz2083)) zzz2084 zzz2085 zzz2086 zzz2087 (Maybe.isJust (FiniteMap.lookupFM zzz20914 (Pos (Succ zzz2083))))",fontsize=16,color="magenta"];25155 -> 25210[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 3289[label="FiniteMap.splitGT2 (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos (Succ zzz4000)) (primCmpNat (Succ zzz4000) Zero == GT)",fontsize=16,color="black",shape="box"];3289 -> 3698[label="",style="solid", color="black", weight=3]; 130.29/78.13 30843[label="zzz30820",fontsize=16,color="green",shape="box"];30844[label="zzz30830",fontsize=16,color="green",shape="box"];30845[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) zzz3073 zzz3074 zzz3075 zzz3076 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3077)) zzz3078 zzz3079 zzz3080 zzz3081 (Pos (Succ zzz3072)) False))",fontsize=16,color="black",shape="triangle"];30845 -> 30870[label="",style="solid", color="black", weight=3]; 130.29/78.13 30846[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) zzz3073 zzz3074 zzz3075 zzz3076 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3077)) zzz3078 zzz3079 zzz3080 zzz3081 (Pos (Succ zzz3072)) True))",fontsize=16,color="black",shape="box"];30846 -> 30871[label="",style="solid", color="black", weight=3]; 130.29/78.13 30847 -> 30845[label="",style="dashed", color="red", weight=0]; 130.29/78.13 30847[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) zzz3073 zzz3074 zzz3075 zzz3076 (Maybe.isJust (FiniteMap.lookupFM2 (Pos (Succ zzz3077)) zzz3078 zzz3079 zzz3080 zzz3081 (Pos (Succ zzz3072)) False))",fontsize=16,color="magenta"];28737[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (primCmpNat (Succ zzz2738) Zero == GT)))",fontsize=16,color="black",shape="box"];28737 -> 28922[label="",style="solid", color="black", weight=3]; 130.29/78.13 28738[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM zzz2747 (Pos (Succ zzz2738))))",fontsize=16,color="burlywood",shape="triangle"];65062[label="zzz2747/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];28738 -> 65062[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65062 -> 28923[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65063[label="zzz2747/FiniteMap.Branch zzz27470 zzz27471 zzz27472 zzz27473 zzz27474",fontsize=10,color="white",style="solid",shape="box"];28738 -> 65063[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65063 -> 28924[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 22275[label="FiniteMap.splitLT2 (Pos (Succ zzz197000)) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) (primCmpNat (Succ zzz1975) (Succ zzz197000) == LT)",fontsize=16,color="black",shape="box"];22275 -> 22309[label="",style="solid", color="black", weight=3]; 130.29/78.13 22276[label="FiniteMap.splitLT2 (Pos Zero) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) (primCmpNat (Succ zzz1975) Zero == LT)",fontsize=16,color="black",shape="box"];22276 -> 22310[label="",style="solid", color="black", weight=3]; 130.29/78.13 22277[label="FiniteMap.splitLT2 (Neg zzz19700) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) False",fontsize=16,color="black",shape="box"];22277 -> 22311[label="",style="solid", color="black", weight=3]; 130.29/78.13 22502[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) zzz1983 zzz1984 zzz1985 zzz1986 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz1987)) zzz1988 zzz1989 zzz1990 zzz1991 (Pos (Succ zzz1982)) (primCmpInt (Pos (Succ zzz1982)) (Pos (Succ zzz1987)) == GT)))",fontsize=16,color="black",shape="box"];22502 -> 22520[label="",style="solid", color="black", weight=3]; 130.29/78.13 18567 -> 18275[label="",style="dashed", color="red", weight=0]; 130.29/78.13 18567[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust (FiniteMap.lookupFM zzz1396 (Pos (Succ zzz1387))))",fontsize=16,color="magenta"];18568[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 (Maybe.isJust Nothing)",fontsize=16,color="black",shape="box"];18568 -> 18628[label="",style="solid", color="black", weight=3]; 130.29/78.13 18569[label="zzz13964",fontsize=16,color="green",shape="box"];18570[label="zzz13962",fontsize=16,color="green",shape="box"];18571[label="zzz13960",fontsize=16,color="green",shape="box"];18572[label="zzz13961",fontsize=16,color="green",shape="box"];18573[label="zzz13963",fontsize=16,color="green",shape="box"];3320[label="FiniteMap.splitGT1 (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Pos Zero) (primCmpNat Zero (Succ zzz3000) == LT)",fontsize=16,color="black",shape="box"];3320 -> 3731[label="",style="solid", color="black", weight=3]; 130.29/78.13 10972[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero)",fontsize=16,color="black",shape="triangle"];10972 -> 11156[label="",style="solid", color="black", weight=3]; 130.29/78.13 10973[label="zzz626",fontsize=16,color="green",shape="box"];10974[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero)",fontsize=16,color="black",shape="triangle"];10974 -> 11157[label="",style="solid", color="black", weight=3]; 130.29/78.13 10975[label="zzz625",fontsize=16,color="green",shape="box"];10976 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.13 10976[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero)) zzz625",fontsize=16,color="magenta"];10976 -> 11158[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 10976 -> 11159[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 10977[label="Zero",fontsize=16,color="green",shape="box"];10978 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.13 10978[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero)) zzz626",fontsize=16,color="magenta"];10978 -> 11160[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 10978 -> 11161[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 10979[label="FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero)) zzz623",fontsize=16,color="black",shape="box"];10979 -> 11162[label="",style="solid", color="black", weight=3]; 130.29/78.13 5562[label="FiniteMap.splitLT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (EQ == GT)",fontsize=16,color="black",shape="box"];5562 -> 5607[label="",style="solid", color="black", weight=3]; 130.29/78.13 5563[label="FiniteMap.splitGT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];5563 -> 5608[label="",style="solid", color="black", weight=3]; 130.29/78.13 5564[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos zzz3400) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 (primCmpNat (Succ zzz3000) zzz3400 == LT)",fontsize=16,color="burlywood",shape="box"];65064[label="zzz3400/Succ zzz34000",fontsize=10,color="white",style="solid",shape="box"];5564 -> 65064[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65064 -> 5609[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65065[label="zzz3400/Zero",fontsize=10,color="white",style="solid",shape="box"];5564 -> 65065[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65065 -> 5610[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 5565[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg zzz3400) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 (GT == LT)",fontsize=16,color="black",shape="box"];5565 -> 5611[label="",style="solid", color="black", weight=3]; 130.29/78.13 5566[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz34000)) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (primCmpInt (Pos Zero) (Pos (Succ zzz34000)) == LT)",fontsize=16,color="black",shape="box"];5566 -> 5612[label="",style="solid", color="black", weight=3]; 130.29/78.13 5567[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];5567 -> 5613[label="",style="solid", color="black", weight=3]; 130.29/78.13 5568[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz34000)) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (primCmpInt (Pos Zero) (Neg (Succ zzz34000)) == LT)",fontsize=16,color="black",shape="box"];5568 -> 5614[label="",style="solid", color="black", weight=3]; 130.29/78.13 5569[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];5569 -> 5615[label="",style="solid", color="black", weight=3]; 130.29/78.13 5570[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos zzz25020) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos zzz25020) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz25020)) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos zzz25020) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="burlywood",shape="box"];65066[label="zzz25020/Succ zzz250200",fontsize=10,color="white",style="solid",shape="box"];5570 -> 65066[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65066 -> 5616[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65067[label="zzz25020/Zero",fontsize=10,color="white",style="solid",shape="box"];5570 -> 65067[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65067 -> 5617[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 5571[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg zzz25020) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg zzz25020) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz25020)) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg zzz25020) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="burlywood",shape="box"];65068[label="zzz25020/Succ zzz250200",fontsize=10,color="white",style="solid",shape="box"];5571 -> 65068[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65068 -> 5618[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65069[label="zzz25020/Zero",fontsize=10,color="white",style="solid",shape="box"];5571 -> 65069[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65069 -> 5619[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 3350[label="FiniteMap.splitGT FiniteMap.EmptyFM (Pos Zero)",fontsize=16,color="black",shape="triangle"];3350 -> 3761[label="",style="solid", color="black", weight=3]; 130.29/78.13 3351[label="FiniteMap.splitLT1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos Zero) (Pos Zero > Neg (Succ zzz3000))",fontsize=16,color="black",shape="box"];3351 -> 3762[label="",style="solid", color="black", weight=3]; 130.29/78.13 16582[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 otherwise",fontsize=16,color="black",shape="box"];16582 -> 16826[label="",style="solid", color="black", weight=3]; 130.29/78.13 16583[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM0 (Pos Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) True))",fontsize=16,color="black",shape="box"];16583 -> 16827[label="",style="solid", color="black", weight=3]; 130.29/78.13 16584[label="zzz1205",fontsize=16,color="green",shape="box"];16585[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (FiniteMap.lookupFM0 (Neg Zero) zzz1202 zzz1203 zzz1204 zzz1205 (Pos Zero) True))",fontsize=16,color="black",shape="box"];16585 -> 16828[label="",style="solid", color="black", weight=3]; 130.29/78.13 5572[label="FiniteMap.splitLT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (EQ == GT)",fontsize=16,color="black",shape="box"];5572 -> 5620[label="",style="solid", color="black", weight=3]; 130.29/78.13 5573[label="FiniteMap.splitGT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];5573 -> 5621[label="",style="solid", color="black", weight=3]; 130.29/78.13 4182[label="FiniteMap.splitGT FiniteMap.EmptyFM (Neg (Succ zzz4000))",fontsize=16,color="black",shape="triangle"];4182 -> 4258[label="",style="solid", color="black", weight=3]; 130.29/78.13 62538 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.13 62538[label="primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz633700)) (Succ zzz633700)",fontsize=16,color="magenta"];62538 -> 62555[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 62538 -> 62556[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 62539[label="Zero",fontsize=16,color="green",shape="box"];62540[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos (Succ zzz63380)) (Pos zzz63190) == LT)",fontsize=16,color="black",shape="box"];62540 -> 62557[label="",style="solid", color="black", weight=3]; 130.29/78.13 62541[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos (Succ zzz63380)) (Neg zzz63190) == LT)",fontsize=16,color="black",shape="box"];62541 -> 62558[label="",style="solid", color="black", weight=3]; 130.29/78.13 62542[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos Zero) (Pos zzz63190) == LT)",fontsize=16,color="burlywood",shape="box"];65070[label="zzz63190/Succ zzz631900",fontsize=10,color="white",style="solid",shape="box"];62542 -> 65070[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65070 -> 62559[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65071[label="zzz63190/Zero",fontsize=10,color="white",style="solid",shape="box"];62542 -> 65071[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65071 -> 62560[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 62543[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos Zero) (Neg zzz63190) == LT)",fontsize=16,color="burlywood",shape="box"];65072[label="zzz63190/Succ zzz631900",fontsize=10,color="white",style="solid",shape="box"];62543 -> 65072[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65072 -> 62561[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65073[label="zzz63190/Zero",fontsize=10,color="white",style="solid",shape="box"];62543 -> 65073[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65073 -> 62562[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 62551[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg (Succ zzz63400)) (Pos zzz63190) == LT)",fontsize=16,color="black",shape="box"];62551 -> 62570[label="",style="solid", color="black", weight=3]; 130.29/78.13 62552[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg (Succ zzz63400)) (Neg zzz63190) == LT)",fontsize=16,color="black",shape="box"];62552 -> 62571[label="",style="solid", color="black", weight=3]; 130.29/78.13 62553[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg Zero) (Pos zzz63190) == LT)",fontsize=16,color="burlywood",shape="box"];65074[label="zzz63190/Succ zzz631900",fontsize=10,color="white",style="solid",shape="box"];62553 -> 65074[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65074 -> 62572[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65075[label="zzz63190/Zero",fontsize=10,color="white",style="solid",shape="box"];62553 -> 65075[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65075 -> 62573[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 62554[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg Zero) (Neg zzz63190) == LT)",fontsize=16,color="burlywood",shape="box"];65076[label="zzz63190/Succ zzz631900",fontsize=10,color="white",style="solid",shape="box"];62554 -> 65076[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65076 -> 62574[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65077[label="zzz63190/Zero",fontsize=10,color="white",style="solid",shape="box"];62554 -> 65077[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65077 -> 62575[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 12476[label="FiniteMap.splitGT2 (Pos zzz742) zzz743 zzz744 zzz745 zzz746 (Neg (Succ zzz747)) (compare (Neg (Succ zzz747)) (Pos zzz742) == GT)",fontsize=16,color="black",shape="box"];12476 -> 12573[label="",style="solid", color="black", weight=3]; 130.29/78.13 12477[label="FiniteMap.splitLT2 (Pos zzz742) zzz743 zzz744 zzz745 zzz746 (Neg (Succ zzz747)) (compare (Neg (Succ zzz747)) (Pos zzz742) == LT)",fontsize=16,color="black",shape="box"];12477 -> 12574[label="",style="solid", color="black", weight=3]; 130.29/78.13 28525 -> 28290[label="",style="dashed", color="red", weight=0]; 130.29/78.13 28525[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) zzz2761 zzz2762 zzz2763 zzz2764 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2765)) zzz2766 zzz2767 zzz2768 zzz2769 (Neg (Succ zzz2760)) (primCmpNat zzz27700 zzz27710 == GT)))",fontsize=16,color="magenta"];28525 -> 28538[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28525 -> 28539[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28526[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) zzz2761 zzz2762 zzz2763 zzz2764 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2765)) zzz2766 zzz2767 zzz2768 zzz2769 (Neg (Succ zzz2760)) (GT == GT)))",fontsize=16,color="black",shape="box"];28526 -> 28540[label="",style="solid", color="black", weight=3]; 130.29/78.13 28527[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) zzz2761 zzz2762 zzz2763 zzz2764 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2765)) zzz2766 zzz2767 zzz2768 zzz2769 (Neg (Succ zzz2760)) (LT == GT)))",fontsize=16,color="black",shape="box"];28527 -> 28541[label="",style="solid", color="black", weight=3]; 130.29/78.13 28528[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) zzz2761 zzz2762 zzz2763 zzz2764 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2765)) zzz2766 zzz2767 zzz2768 zzz2769 (Neg (Succ zzz2760)) (EQ == GT)))",fontsize=16,color="black",shape="box"];28528 -> 28542[label="",style="solid", color="black", weight=3]; 130.29/78.13 6658[label="FiniteMap.addToFM zzz426 (Neg (Succ zzz3000)) zzz31",fontsize=16,color="black",shape="triangle"];6658 -> 7396[label="",style="solid", color="black", weight=3]; 130.29/78.13 6659[label="FiniteMap.mkVBalBranch4 (Neg (Succ zzz3000)) zzz31 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];6659 -> 7397[label="",style="solid", color="black", weight=3]; 130.29/78.13 6660[label="FiniteMap.mkVBalBranch3 (Neg (Succ zzz3000)) zzz31 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) (FiniteMap.Branch zzz4260 zzz4261 zzz4262 zzz4263 zzz4264)",fontsize=16,color="black",shape="box"];6660 -> 7398[label="",style="solid", color="black", weight=3]; 130.29/78.13 20940[label="FiniteMap.splitGT2 (Pos zzz74500) zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (primCmpInt (Neg (Succ zzz747)) (Pos zzz74500) == GT)",fontsize=16,color="black",shape="box"];20940 -> 21547[label="",style="solid", color="black", weight=3]; 130.29/78.13 20941[label="FiniteMap.splitGT2 (Neg zzz74500) zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (primCmpInt (Neg (Succ zzz747)) (Neg zzz74500) == GT)",fontsize=16,color="black",shape="box"];20941 -> 21548[label="",style="solid", color="black", weight=3]; 130.29/78.13 14378[label="FiniteMap.splitLT2 (Pos zzz74500) zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (primCmpInt (Neg (Succ zzz747)) (Pos zzz74500) == LT)",fontsize=16,color="black",shape="box"];14378 -> 14452[label="",style="solid", color="black", weight=3]; 130.29/78.13 14379[label="FiniteMap.splitLT2 (Neg zzz74500) zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (primCmpInt (Neg (Succ zzz747)) (Neg zzz74500) == LT)",fontsize=16,color="black",shape="box"];14379 -> 14453[label="",style="solid", color="black", weight=3]; 130.29/78.13 3579[label="FiniteMap.splitGT1 (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (primCmpNat Zero (Succ zzz4000) == LT)",fontsize=16,color="black",shape="box"];3579 -> 3911[label="",style="solid", color="black", weight=3]; 130.29/78.13 13800[label="FiniteMap.splitGT3 (FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887) (Neg (Succ zzz888))",fontsize=16,color="black",shape="box"];13800 -> 14034[label="",style="solid", color="black", weight=3]; 130.29/78.13 13801[label="FiniteMap.Branch (Neg Zero) zzz884 zzz885 zzz886 zzz887",fontsize=16,color="green",shape="box"];13802[label="zzz888",fontsize=16,color="green",shape="box"];29583[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) zzz2889 zzz2890 zzz2891 zzz2892 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2893)) zzz2894 zzz2895 zzz2896 zzz2897 (Neg (Succ zzz2888)) (primCmpNat (Succ zzz28980) zzz2899 == GT)))",fontsize=16,color="burlywood",shape="box"];65078[label="zzz2899/Succ zzz28990",fontsize=10,color="white",style="solid",shape="box"];29583 -> 65078[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65078 -> 29653[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65079[label="zzz2899/Zero",fontsize=10,color="white",style="solid",shape="box"];29583 -> 65079[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65079 -> 29654[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 29584[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) zzz2889 zzz2890 zzz2891 zzz2892 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2893)) zzz2894 zzz2895 zzz2896 zzz2897 (Neg (Succ zzz2888)) (primCmpNat Zero zzz2899 == GT)))",fontsize=16,color="burlywood",shape="box"];65080[label="zzz2899/Succ zzz28990",fontsize=10,color="white",style="solid",shape="box"];29584 -> 65080[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65080 -> 29655[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65081[label="zzz2899/Zero",fontsize=10,color="white",style="solid",shape="box"];29584 -> 65081[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65081 -> 29656[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 13248[label="FiniteMap.splitGT1 (Pos (Succ zzz830)) zzz831 zzz832 zzz833 zzz834 (Neg Zero) True",fontsize=16,color="black",shape="box"];13248 -> 13450[label="",style="solid", color="black", weight=3]; 130.29/78.13 13249[label="FiniteMap.splitLT2 zzz8330 zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (compare (Neg Zero) zzz8330 == LT)",fontsize=16,color="black",shape="triangle"];13249 -> 13451[label="",style="solid", color="black", weight=3]; 130.29/78.13 14029 -> 11969[label="",style="dashed", color="red", weight=0]; 130.29/78.13 14029[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero)",fontsize=16,color="magenta"];14029 -> 14340[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 14029 -> 14341[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 14029 -> 14342[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 14029 -> 14343[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 14029 -> 14344[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 14030[label="zzz906",fontsize=16,color="green",shape="box"];14031 -> 11967[label="",style="dashed", color="red", weight=0]; 130.29/78.13 14031[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz899)) zzz900 zzz901 zzz902 zzz903) (Neg Zero)",fontsize=16,color="magenta"];14031 -> 14345[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 14031 -> 14346[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 14031 -> 14347[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 14031 -> 14348[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 14031 -> 14349[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 14032[label="zzz907",fontsize=16,color="green",shape="box"];14033[label="zzz904",fontsize=16,color="green",shape="box"];6778[label="FiniteMap.splitLT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (EQ == GT)",fontsize=16,color="black",shape="box"];6778 -> 6998[label="",style="solid", color="black", weight=3]; 130.29/78.13 6779[label="FiniteMap.splitGT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];6779 -> 6999[label="",style="solid", color="black", weight=3]; 130.29/78.13 13005[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos zzz98200) zzz9821 zzz9822 zzz9823 zzz9824 (Neg (Succ zzz3000)) zzz31 (primCmpInt (Neg (Succ zzz3000)) (Pos zzz98200) == LT)",fontsize=16,color="black",shape="box"];13005 -> 13250[label="",style="solid", color="black", weight=3]; 130.29/78.13 13006[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg zzz98200) zzz9821 zzz9822 zzz9823 zzz9824 (Neg (Succ zzz3000)) zzz31 (primCmpInt (Neg (Succ zzz3000)) (Neg zzz98200) == LT)",fontsize=16,color="black",shape="box"];13006 -> 13251[label="",style="solid", color="black", weight=3]; 130.29/78.13 13007[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos zzz98200) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (primCmpInt (Neg Zero) (Pos zzz98200) == LT)",fontsize=16,color="burlywood",shape="box"];65082[label="zzz98200/Succ zzz982000",fontsize=10,color="white",style="solid",shape="box"];13007 -> 65082[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65082 -> 13252[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65083[label="zzz98200/Zero",fontsize=10,color="white",style="solid",shape="box"];13007 -> 65083[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65083 -> 13253[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 13008[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg zzz98200) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (primCmpInt (Neg Zero) (Neg zzz98200) == LT)",fontsize=16,color="burlywood",shape="box"];65084[label="zzz98200/Succ zzz982000",fontsize=10,color="white",style="solid",shape="box"];13008 -> 65084[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65084 -> 13254[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65085[label="zzz98200/Zero",fontsize=10,color="white",style="solid",shape="box"];13008 -> 65085[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65085 -> 13255[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 6784[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos zzz35320) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos zzz35320) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz35320)) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos zzz35320) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="burlywood",shape="box"];65086[label="zzz35320/Succ zzz353200",fontsize=10,color="white",style="solid",shape="box"];6784 -> 65086[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65086 -> 7004[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65087[label="zzz35320/Zero",fontsize=10,color="white",style="solid",shape="box"];6784 -> 65087[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65087 -> 7005[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 6785[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg zzz35320) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg zzz35320) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz35320)) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg zzz35320) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="burlywood",shape="box"];65088[label="zzz35320/Succ zzz353200",fontsize=10,color="white",style="solid",shape="box"];6785 -> 65088[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65088 -> 7006[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65089[label="zzz35320/Zero",fontsize=10,color="white",style="solid",shape="box"];6785 -> 65089[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65089 -> 7007[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 3642[label="FiniteMap.splitGT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Neg Zero) (primCmpNat (Succ zzz3000) Zero == GT)",fontsize=16,color="black",shape="box"];3642 -> 3982[label="",style="solid", color="black", weight=3]; 130.29/78.13 3643[label="FiniteMap.splitLT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Neg Zero) (primCmpNat (Succ zzz3000) Zero == LT)",fontsize=16,color="black",shape="box"];3643 -> 3983[label="",style="solid", color="black", weight=3]; 130.29/78.13 20148[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 False",fontsize=16,color="black",shape="box"];20148 -> 20192[label="",style="solid", color="black", weight=3]; 130.29/78.13 20149[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) False))",fontsize=16,color="black",shape="box"];20149 -> 20193[label="",style="solid", color="black", weight=3]; 130.29/78.13 20150[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz160300)) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (primCmpNat (Succ zzz160300) Zero == GT)))",fontsize=16,color="black",shape="box"];20150 -> 20194[label="",style="solid", color="black", weight=3]; 130.29/78.13 20151[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM1 (Neg Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) False))",fontsize=16,color="black",shape="box"];20151 -> 20195[label="",style="solid", color="black", weight=3]; 130.29/78.13 6786[label="FiniteMap.splitLT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (EQ == GT)",fontsize=16,color="black",shape="box"];6786 -> 7008[label="",style="solid", color="black", weight=3]; 130.29/78.13 6787[label="FiniteMap.splitGT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];6787 -> 7009[label="",style="solid", color="black", weight=3]; 130.29/78.13 20097[label="FiniteMap.splitGT2 (Pos zzz161200) zzz16121 zzz16122 zzz16123 zzz16124 (Pos (Succ zzz1613)) (primCmpNat (Succ zzz1613) zzz161200 == GT)",fontsize=16,color="burlywood",shape="box"];65090[label="zzz161200/Succ zzz1612000",fontsize=10,color="white",style="solid",shape="box"];20097 -> 65090[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65090 -> 20366[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65091[label="zzz161200/Zero",fontsize=10,color="white",style="solid",shape="box"];20097 -> 65091[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65091 -> 20367[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 20098[label="FiniteMap.splitGT2 (Neg zzz161200) zzz16121 zzz16122 zzz16123 zzz16124 (Pos (Succ zzz1613)) (GT == GT)",fontsize=16,color="black",shape="box"];20098 -> 20368[label="",style="solid", color="black", weight=3]; 130.29/78.13 25210[label="zzz20914",fontsize=16,color="green",shape="box"];3698[label="FiniteMap.splitGT2 (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos (Succ zzz4000)) (GT == GT)",fontsize=16,color="black",shape="box"];3698 -> 4039[label="",style="solid", color="black", weight=3]; 130.29/78.13 30870[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) zzz3073 zzz3074 zzz3075 zzz3076 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3077)) zzz3078 zzz3079 zzz3080 zzz3081 (Pos (Succ zzz3072)) (Pos (Succ zzz3072) > Pos (Succ zzz3077))))",fontsize=16,color="black",shape="box"];30870 -> 31040[label="",style="solid", color="black", weight=3]; 130.29/78.13 30871 -> 28738[label="",style="dashed", color="red", weight=0]; 130.29/78.13 30871[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) zzz3073 zzz3074 zzz3075 zzz3076 (Maybe.isJust (FiniteMap.lookupFM zzz3080 (Pos (Succ zzz3072))))",fontsize=16,color="magenta"];30871 -> 31041[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 30871 -> 31042[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 30871 -> 31043[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 30871 -> 31044[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 30871 -> 31045[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 30871 -> 31046[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 30871 -> 31047[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 30871 -> 31048[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 30871 -> 31049[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 30871 -> 31050[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 28922[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) (GT == GT)))",fontsize=16,color="black",shape="box"];28922 -> 28997[label="",style="solid", color="black", weight=3]; 130.29/78.13 28923[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM FiniteMap.EmptyFM (Pos (Succ zzz2738))))",fontsize=16,color="black",shape="box"];28923 -> 28998[label="",style="solid", color="black", weight=3]; 130.29/78.13 28924[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM (FiniteMap.Branch zzz27470 zzz27471 zzz27472 zzz27473 zzz27474) (Pos (Succ zzz2738))))",fontsize=16,color="black",shape="box"];28924 -> 28999[label="",style="solid", color="black", weight=3]; 130.29/78.13 22309 -> 31188[label="",style="dashed", color="red", weight=0]; 130.29/78.13 22309[label="FiniteMap.splitLT2 (Pos (Succ zzz197000)) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) (primCmpNat zzz1975 zzz197000 == LT)",fontsize=16,color="magenta"];22309 -> 31189[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22309 -> 31190[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22309 -> 31191[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22309 -> 31192[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22309 -> 31193[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22309 -> 31194[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22309 -> 31195[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22309 -> 31196[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22310[label="FiniteMap.splitLT2 (Pos Zero) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) (GT == LT)",fontsize=16,color="black",shape="box"];22310 -> 22434[label="",style="solid", color="black", weight=3]; 130.29/78.13 22311[label="FiniteMap.splitLT1 (Neg zzz19700) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) (Pos (Succ zzz1975) > Neg zzz19700)",fontsize=16,color="black",shape="box"];22311 -> 22435[label="",style="solid", color="black", weight=3]; 130.29/78.13 22520 -> 31655[label="",style="dashed", color="red", weight=0]; 130.29/78.13 22520[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1977) zzz1978 zzz1979 zzz1980 zzz1981) (Pos (Succ zzz1982)) zzz1983 zzz1984 zzz1985 zzz1986 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz1987)) zzz1988 zzz1989 zzz1990 zzz1991 (Pos (Succ zzz1982)) (primCmpNat (Succ zzz1982) (Succ zzz1987) == GT)))",fontsize=16,color="magenta"];22520 -> 31656[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22520 -> 31657[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22520 -> 31658[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22520 -> 31659[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22520 -> 31660[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22520 -> 31661[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22520 -> 31662[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22520 -> 31663[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22520 -> 31664[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22520 -> 31665[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22520 -> 31666[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22520 -> 31667[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22520 -> 31668[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22520 -> 31669[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22520 -> 31670[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22520 -> 31671[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 22520 -> 31672[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 18628[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 False",fontsize=16,color="black",shape="box"];18628 -> 18702[label="",style="solid", color="black", weight=3]; 130.29/78.13 3731[label="FiniteMap.splitGT1 (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Pos Zero) (LT == LT)",fontsize=16,color="black",shape="box"];3731 -> 4077[label="",style="solid", color="black", weight=3]; 130.29/78.13 11156[label="FiniteMap.splitGT (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero)",fontsize=16,color="black",shape="triangle"];11156 -> 11420[label="",style="solid", color="black", weight=3]; 130.29/78.13 11157[label="FiniteMap.splitLT (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero)",fontsize=16,color="black",shape="box"];11157 -> 11421[label="",style="solid", color="black", weight=3]; 130.29/78.13 11158 -> 10974[label="",style="dashed", color="red", weight=0]; 130.29/78.13 11158[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero)",fontsize=16,color="magenta"];11159[label="zzz625",fontsize=16,color="green",shape="box"];11160 -> 10972[label="",style="dashed", color="red", weight=0]; 130.29/78.13 11160[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero)",fontsize=16,color="magenta"];11161[label="zzz626",fontsize=16,color="green",shape="box"];11162[label="zzz623",fontsize=16,color="green",shape="box"];5607[label="FiniteMap.splitLT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) False",fontsize=16,color="black",shape="box"];5607 -> 5861[label="",style="solid", color="black", weight=3]; 130.29/78.13 5608[label="FiniteMap.splitGT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) False",fontsize=16,color="black",shape="box"];5608 -> 5862[label="",style="solid", color="black", weight=3]; 130.29/78.13 5609[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz34000)) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 (primCmpNat (Succ zzz3000) (Succ zzz34000) == LT)",fontsize=16,color="black",shape="box"];5609 -> 5863[label="",style="solid", color="black", weight=3]; 130.29/78.13 5610[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos Zero) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 (primCmpNat (Succ zzz3000) Zero == LT)",fontsize=16,color="black",shape="box"];5610 -> 5864[label="",style="solid", color="black", weight=3]; 130.29/78.13 5611[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg zzz3400) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 False",fontsize=16,color="black",shape="box"];5611 -> 5865[label="",style="solid", color="black", weight=3]; 130.29/78.13 5612[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz34000)) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (primCmpNat Zero (Succ zzz34000) == LT)",fontsize=16,color="black",shape="box"];5612 -> 5866[label="",style="solid", color="black", weight=3]; 130.29/78.13 5613[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (EQ == LT)",fontsize=16,color="black",shape="box"];5613 -> 5867[label="",style="solid", color="black", weight=3]; 130.29/78.13 5614[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz34000)) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (GT == LT)",fontsize=16,color="black",shape="box"];5614 -> 5868[label="",style="solid", color="black", weight=3]; 130.29/78.13 5615[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (EQ == LT)",fontsize=16,color="black",shape="box"];5615 -> 5869[label="",style="solid", color="black", weight=3]; 130.29/78.13 5616[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];5616 -> 5870[label="",style="solid", color="black", weight=3]; 130.29/78.13 5617[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];5617 -> 5871[label="",style="solid", color="black", weight=3]; 130.29/78.13 5618[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];5618 -> 5872[label="",style="solid", color="black", weight=3]; 130.29/78.13 5619[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];5619 -> 5873[label="",style="solid", color="black", weight=3]; 130.29/78.13 3761[label="FiniteMap.splitGT4 FiniteMap.EmptyFM (Pos Zero)",fontsize=16,color="black",shape="triangle"];3761 -> 4111[label="",style="solid", color="black", weight=3]; 130.29/78.13 3762[label="FiniteMap.splitLT1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos Zero) (compare (Pos Zero) (Neg (Succ zzz3000)) == GT)",fontsize=16,color="black",shape="box"];3762 -> 4112[label="",style="solid", color="black", weight=3]; 130.29/78.13 16826[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 True",fontsize=16,color="black",shape="box"];16826 -> 17237[label="",style="solid", color="black", weight=3]; 130.29/78.13 16827[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (Just zzz1202))",fontsize=16,color="black",shape="triangle"];16827 -> 17238[label="",style="solid", color="black", weight=3]; 130.29/78.13 16828 -> 16827[label="",style="dashed", color="red", weight=0]; 130.29/78.13 16828[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 (Maybe.isJust (Just zzz1202))",fontsize=16,color="magenta"];5620[label="FiniteMap.splitLT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) False",fontsize=16,color="black",shape="box"];5620 -> 5874[label="",style="solid", color="black", weight=3]; 130.29/78.13 5621[label="FiniteMap.splitGT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) False",fontsize=16,color="black",shape="box"];5621 -> 5875[label="",style="solid", color="black", weight=3]; 130.29/78.13 62555[label="Succ zzz633700",fontsize=16,color="green",shape="box"];62556 -> 43384[label="",style="dashed", color="red", weight=0]; 130.29/78.13 62556[label="primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz633700)",fontsize=16,color="magenta"];62556 -> 62576[label="",style="dashed", color="magenta", weight=3]; 130.29/78.13 42929[label="primPlusNat zzz5092000 zzz54200",fontsize=16,color="burlywood",shape="triangle"];65092[label="zzz5092000/Succ zzz50920000",fontsize=10,color="white",style="solid",shape="box"];42929 -> 65092[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65092 -> 43355[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 65093[label="zzz5092000/Zero",fontsize=10,color="white",style="solid",shape="box"];42929 -> 65093[label="",style="solid", color="burlywood", weight=9]; 130.29/78.13 65093 -> 43356[label="",style="solid", color="burlywood", weight=3]; 130.29/78.13 62557[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat (Succ zzz63380) zzz63190 == LT)",fontsize=16,color="burlywood",shape="triangle"];65094[label="zzz63190/Succ zzz631900",fontsize=10,color="white",style="solid",shape="box"];62557 -> 65094[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65094 -> 62577[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 65095[label="zzz63190/Zero",fontsize=10,color="white",style="solid",shape="box"];62557 -> 65095[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65095 -> 62578[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 62558[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (GT == LT)",fontsize=16,color="black",shape="triangle"];62558 -> 62579[label="",style="solid", color="black", weight=3]; 130.29/78.14 62559[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos Zero) (Pos (Succ zzz631900)) == LT)",fontsize=16,color="black",shape="box"];62559 -> 62580[label="",style="solid", color="black", weight=3]; 130.29/78.14 62560[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];62560 -> 62581[label="",style="solid", color="black", weight=3]; 130.29/78.14 62561[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos Zero) (Neg (Succ zzz631900)) == LT)",fontsize=16,color="black",shape="box"];62561 -> 62582[label="",style="solid", color="black", weight=3]; 130.29/78.14 62562[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];62562 -> 62583[label="",style="solid", color="black", weight=3]; 130.29/78.14 62570[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (LT == LT)",fontsize=16,color="black",shape="triangle"];62570 -> 62585[label="",style="solid", color="black", weight=3]; 130.29/78.14 62571[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat zzz63190 (Succ zzz63400) == LT)",fontsize=16,color="burlywood",shape="triangle"];65096[label="zzz63190/Succ zzz631900",fontsize=10,color="white",style="solid",shape="box"];62571 -> 65096[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65096 -> 62586[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 65097[label="zzz63190/Zero",fontsize=10,color="white",style="solid",shape="box"];62571 -> 65097[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65097 -> 62587[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 62572[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg Zero) (Pos (Succ zzz631900)) == LT)",fontsize=16,color="black",shape="box"];62572 -> 62588[label="",style="solid", color="black", weight=3]; 130.29/78.14 62573[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];62573 -> 62589[label="",style="solid", color="black", weight=3]; 130.29/78.14 62574[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg Zero) (Neg (Succ zzz631900)) == LT)",fontsize=16,color="black",shape="box"];62574 -> 62590[label="",style="solid", color="black", weight=3]; 130.29/78.14 62575[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];62575 -> 62591[label="",style="solid", color="black", weight=3]; 130.29/78.14 12573[label="FiniteMap.splitGT2 (Pos zzz742) zzz743 zzz744 zzz745 zzz746 (Neg (Succ zzz747)) (primCmpInt (Neg (Succ zzz747)) (Pos zzz742) == GT)",fontsize=16,color="black",shape="box"];12573 -> 12656[label="",style="solid", color="black", weight=3]; 130.29/78.14 12574[label="FiniteMap.splitLT2 (Pos zzz742) zzz743 zzz744 zzz745 zzz746 (Neg (Succ zzz747)) (primCmpInt (Neg (Succ zzz747)) (Pos zzz742) == LT)",fontsize=16,color="black",shape="box"];12574 -> 12657[label="",style="solid", color="black", weight=3]; 130.29/78.14 28538[label="zzz27710",fontsize=16,color="green",shape="box"];28539[label="zzz27700",fontsize=16,color="green",shape="box"];28540[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) zzz2761 zzz2762 zzz2763 zzz2764 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2765)) zzz2766 zzz2767 zzz2768 zzz2769 (Neg (Succ zzz2760)) True))",fontsize=16,color="black",shape="box"];28540 -> 28563[label="",style="solid", color="black", weight=3]; 130.29/78.14 28541[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) zzz2761 zzz2762 zzz2763 zzz2764 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2765)) zzz2766 zzz2767 zzz2768 zzz2769 (Neg (Succ zzz2760)) False))",fontsize=16,color="black",shape="triangle"];28541 -> 28564[label="",style="solid", color="black", weight=3]; 130.29/78.14 28542 -> 28541[label="",style="dashed", color="red", weight=0]; 130.29/78.14 28542[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) zzz2761 zzz2762 zzz2763 zzz2764 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2765)) zzz2766 zzz2767 zzz2768 zzz2769 (Neg (Succ zzz2760)) False))",fontsize=16,color="magenta"];7396 -> 12360[label="",style="dashed", color="red", weight=0]; 130.29/78.14 7396[label="FiniteMap.addToFM_C FiniteMap.addToFM0 zzz426 (Neg (Succ zzz3000)) zzz31",fontsize=16,color="magenta"];7396 -> 12363[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 7396 -> 12364[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 7397 -> 6658[label="",style="dashed", color="red", weight=0]; 130.29/78.14 7397[label="FiniteMap.addToFM (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) (Neg (Succ zzz3000)) zzz31",fontsize=16,color="magenta"];7397 -> 7766[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 7398[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 < FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264)",fontsize=16,color="black",shape="box"];7398 -> 7767[label="",style="solid", color="black", weight=3]; 130.29/78.14 21547 -> 12656[label="",style="dashed", color="red", weight=0]; 130.29/78.14 21547[label="FiniteMap.splitGT2 (Pos zzz74500) zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (LT == GT)",fontsize=16,color="magenta"];21547 -> 21799[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 21547 -> 21800[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 21547 -> 21801[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 21547 -> 21802[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 21547 -> 21803[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 21548[label="FiniteMap.splitGT2 (Neg zzz74500) zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (primCmpNat zzz74500 (Succ zzz747) == GT)",fontsize=16,color="burlywood",shape="box"];65098[label="zzz74500/Succ zzz745000",fontsize=10,color="white",style="solid",shape="box"];21548 -> 65098[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65098 -> 21804[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 65099[label="zzz74500/Zero",fontsize=10,color="white",style="solid",shape="box"];21548 -> 65099[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65099 -> 21805[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 14452 -> 12657[label="",style="dashed", color="red", weight=0]; 130.29/78.14 14452[label="FiniteMap.splitLT2 (Pos zzz74500) zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (LT == LT)",fontsize=16,color="magenta"];14452 -> 14565[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 14452 -> 14566[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 14452 -> 14567[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 14452 -> 14568[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 14452 -> 14569[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 14453[label="FiniteMap.splitLT2 (Neg zzz74500) zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (primCmpNat zzz74500 (Succ zzz747) == LT)",fontsize=16,color="burlywood",shape="box"];65100[label="zzz74500/Succ zzz745000",fontsize=10,color="white",style="solid",shape="box"];14453 -> 65100[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65100 -> 14570[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 65101[label="zzz74500/Zero",fontsize=10,color="white",style="solid",shape="box"];14453 -> 65101[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65101 -> 14571[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 3911[label="FiniteMap.splitGT1 (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) (LT == LT)",fontsize=16,color="black",shape="box"];3911 -> 4495[label="",style="solid", color="black", weight=3]; 130.29/78.14 14034[label="FiniteMap.splitGT2 (Neg Zero) zzz884 zzz885 zzz886 zzz887 (Neg (Succ zzz888)) (Neg (Succ zzz888) > Neg Zero)",fontsize=16,color="black",shape="box"];14034 -> 14350[label="",style="solid", color="black", weight=3]; 130.29/78.14 29653[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) zzz2889 zzz2890 zzz2891 zzz2892 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2893)) zzz2894 zzz2895 zzz2896 zzz2897 (Neg (Succ zzz2888)) (primCmpNat (Succ zzz28980) (Succ zzz28990) == GT)))",fontsize=16,color="black",shape="box"];29653 -> 29685[label="",style="solid", color="black", weight=3]; 130.29/78.14 29654[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) zzz2889 zzz2890 zzz2891 zzz2892 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2893)) zzz2894 zzz2895 zzz2896 zzz2897 (Neg (Succ zzz2888)) (primCmpNat (Succ zzz28980) Zero == GT)))",fontsize=16,color="black",shape="box"];29654 -> 29686[label="",style="solid", color="black", weight=3]; 130.29/78.14 29655[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) zzz2889 zzz2890 zzz2891 zzz2892 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2893)) zzz2894 zzz2895 zzz2896 zzz2897 (Neg (Succ zzz2888)) (primCmpNat Zero (Succ zzz28990) == GT)))",fontsize=16,color="black",shape="box"];29655 -> 29687[label="",style="solid", color="black", weight=3]; 130.29/78.14 29656[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) zzz2889 zzz2890 zzz2891 zzz2892 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2893)) zzz2894 zzz2895 zzz2896 zzz2897 (Neg (Succ zzz2888)) (primCmpNat Zero Zero == GT)))",fontsize=16,color="black",shape="box"];29656 -> 29688[label="",style="solid", color="black", weight=3]; 130.29/78.14 13450 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.14 13450[label="FiniteMap.mkVBalBranch (Pos (Succ zzz830)) zzz831 (FiniteMap.splitGT zzz833 (Neg Zero)) zzz834",fontsize=16,color="magenta"];13450 -> 13521[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 13450 -> 13522[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 13450 -> 13523[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 13450 -> 13524[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 13451[label="FiniteMap.splitLT2 zzz8330 zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (primCmpInt (Neg Zero) zzz8330 == LT)",fontsize=16,color="burlywood",shape="box"];65102[label="zzz8330/Pos zzz83300",fontsize=10,color="white",style="solid",shape="box"];13451 -> 65102[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65102 -> 13525[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 65103[label="zzz8330/Neg zzz83300",fontsize=10,color="white",style="solid",shape="box"];13451 -> 65103[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65103 -> 13526[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 14340[label="zzz900",fontsize=16,color="green",shape="box"];14341[label="zzz899",fontsize=16,color="green",shape="box"];14342[label="zzz901",fontsize=16,color="green",shape="box"];14343[label="zzz903",fontsize=16,color="green",shape="box"];14344[label="zzz902",fontsize=16,color="green",shape="box"];14345[label="zzz900",fontsize=16,color="green",shape="box"];14346[label="zzz899",fontsize=16,color="green",shape="box"];14347[label="zzz901",fontsize=16,color="green",shape="box"];14348[label="zzz903",fontsize=16,color="green",shape="box"];14349[label="zzz902",fontsize=16,color="green",shape="box"];6998[label="FiniteMap.splitLT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) False",fontsize=16,color="black",shape="box"];6998 -> 7082[label="",style="solid", color="black", weight=3]; 130.29/78.14 6999[label="FiniteMap.splitGT1 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) False",fontsize=16,color="black",shape="box"];6999 -> 7083[label="",style="solid", color="black", weight=3]; 130.29/78.14 13250[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos zzz98200) zzz9821 zzz9822 zzz9823 zzz9824 (Neg (Succ zzz3000)) zzz31 (LT == LT)",fontsize=16,color="black",shape="box"];13250 -> 13452[label="",style="solid", color="black", weight=3]; 130.29/78.14 13251[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg zzz98200) zzz9821 zzz9822 zzz9823 zzz9824 (Neg (Succ zzz3000)) zzz31 (primCmpNat zzz98200 (Succ zzz3000) == LT)",fontsize=16,color="burlywood",shape="box"];65104[label="zzz98200/Succ zzz982000",fontsize=10,color="white",style="solid",shape="box"];13251 -> 65104[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65104 -> 13453[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 65105[label="zzz98200/Zero",fontsize=10,color="white",style="solid",shape="box"];13251 -> 65105[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65105 -> 13454[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 13252[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz982000)) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (primCmpInt (Neg Zero) (Pos (Succ zzz982000)) == LT)",fontsize=16,color="black",shape="box"];13252 -> 13455[label="",style="solid", color="black", weight=3]; 130.29/78.14 13253[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];13253 -> 13456[label="",style="solid", color="black", weight=3]; 130.29/78.14 13254[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz982000)) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (primCmpInt (Neg Zero) (Neg (Succ zzz982000)) == LT)",fontsize=16,color="black",shape="box"];13254 -> 13457[label="",style="solid", color="black", weight=3]; 130.29/78.14 13255[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];13255 -> 13458[label="",style="solid", color="black", weight=3]; 130.29/78.14 7004[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];7004 -> 7088[label="",style="solid", color="black", weight=3]; 130.29/78.14 7005[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];7005 -> 7089[label="",style="solid", color="black", weight=3]; 130.29/78.14 7006[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];7006 -> 7090[label="",style="solid", color="black", weight=3]; 130.29/78.14 7007[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];7007 -> 7091[label="",style="solid", color="black", weight=3]; 130.29/78.14 3982[label="FiniteMap.splitGT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Neg Zero) (GT == GT)",fontsize=16,color="black",shape="box"];3982 -> 4578[label="",style="solid", color="black", weight=3]; 130.29/78.14 3983[label="FiniteMap.splitLT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Neg Zero) (GT == LT)",fontsize=16,color="black",shape="box"];3983 -> 4579[label="",style="solid", color="black", weight=3]; 130.29/78.14 20192[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 otherwise",fontsize=16,color="black",shape="box"];20192 -> 20259[label="",style="solid", color="black", weight=3]; 130.29/78.14 20193[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM0 (Pos Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) otherwise))",fontsize=16,color="black",shape="box"];20193 -> 20260[label="",style="solid", color="black", weight=3]; 130.29/78.14 20194[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz160300)) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) (GT == GT)))",fontsize=16,color="black",shape="box"];20194 -> 20261[label="",style="solid", color="black", weight=3]; 130.29/78.14 20195[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM0 (Neg Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) otherwise))",fontsize=16,color="black",shape="box"];20195 -> 20262[label="",style="solid", color="black", weight=3]; 130.29/78.14 7008[label="FiniteMap.splitLT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) False",fontsize=16,color="black",shape="box"];7008 -> 7092[label="",style="solid", color="black", weight=3]; 130.29/78.14 7009[label="FiniteMap.splitGT1 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) False",fontsize=16,color="black",shape="box"];7009 -> 7093[label="",style="solid", color="black", weight=3]; 130.29/78.14 20366[label="FiniteMap.splitGT2 (Pos (Succ zzz1612000)) zzz16121 zzz16122 zzz16123 zzz16124 (Pos (Succ zzz1613)) (primCmpNat (Succ zzz1613) (Succ zzz1612000) == GT)",fontsize=16,color="black",shape="box"];20366 -> 20566[label="",style="solid", color="black", weight=3]; 130.29/78.14 20367[label="FiniteMap.splitGT2 (Pos Zero) zzz16121 zzz16122 zzz16123 zzz16124 (Pos (Succ zzz1613)) (primCmpNat (Succ zzz1613) Zero == GT)",fontsize=16,color="black",shape="box"];20367 -> 20567[label="",style="solid", color="black", weight=3]; 130.29/78.14 20368[label="FiniteMap.splitGT2 (Neg zzz161200) zzz16121 zzz16122 zzz16123 zzz16124 (Pos (Succ zzz1613)) True",fontsize=16,color="black",shape="box"];20368 -> 20568[label="",style="solid", color="black", weight=3]; 130.29/78.14 4039[label="FiniteMap.splitGT2 (Pos Zero) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos (Succ zzz4000)) True",fontsize=16,color="black",shape="box"];4039 -> 4721[label="",style="solid", color="black", weight=3]; 130.29/78.14 31040[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) zzz3073 zzz3074 zzz3075 zzz3076 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3077)) zzz3078 zzz3079 zzz3080 zzz3081 (Pos (Succ zzz3072)) (compare (Pos (Succ zzz3072)) (Pos (Succ zzz3077)) == GT)))",fontsize=16,color="black",shape="box"];31040 -> 31074[label="",style="solid", color="black", weight=3]; 130.29/78.14 31041[label="zzz3076",fontsize=16,color="green",shape="box"];31042[label="zzz3071",fontsize=16,color="green",shape="box"];31043[label="zzz3073",fontsize=16,color="green",shape="box"];31044[label="zzz3070",fontsize=16,color="green",shape="box"];31045[label="zzz3074",fontsize=16,color="green",shape="box"];31046[label="zzz3080",fontsize=16,color="green",shape="box"];31047[label="zzz3068",fontsize=16,color="green",shape="box"];31048[label="zzz3069",fontsize=16,color="green",shape="box"];31049[label="zzz3072",fontsize=16,color="green",shape="box"];31050[label="zzz3075",fontsize=16,color="green",shape="box"];28997[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM1 (Pos Zero) zzz2744 zzz2745 zzz2746 zzz2747 (Pos (Succ zzz2738)) True))",fontsize=16,color="black",shape="box"];28997 -> 29211[label="",style="solid", color="black", weight=3]; 130.29/78.14 28998[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Pos (Succ zzz2738))))",fontsize=16,color="black",shape="box"];28998 -> 29212[label="",style="solid", color="black", weight=3]; 130.29/78.14 28999[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM3 (FiniteMap.Branch zzz27470 zzz27471 zzz27472 zzz27473 zzz27474) (Pos (Succ zzz2738))))",fontsize=16,color="black",shape="box"];28999 -> 29213[label="",style="solid", color="black", weight=3]; 130.29/78.14 31189[label="zzz1972",fontsize=16,color="green",shape="box"];31190[label="zzz1974",fontsize=16,color="green",shape="box"];31191[label="zzz1975",fontsize=16,color="green",shape="box"];31192[label="zzz1975",fontsize=16,color="green",shape="box"];31193[label="zzz1971",fontsize=16,color="green",shape="box"];31194[label="zzz1973",fontsize=16,color="green",shape="box"];31195[label="zzz197000",fontsize=16,color="green",shape="box"];31196[label="zzz197000",fontsize=16,color="green",shape="box"];31188[label="FiniteMap.splitLT2 (Pos (Succ zzz3133)) zzz3134 zzz3135 zzz3136 zzz3137 (Pos (Succ zzz3138)) (primCmpNat zzz3139 zzz3140 == LT)",fontsize=16,color="burlywood",shape="triangle"];65106[label="zzz3139/Succ zzz31390",fontsize=10,color="white",style="solid",shape="box"];31188 -> 65106[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65106 -> 31269[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 65107[label="zzz3139/Zero",fontsize=10,color="white",style="solid",shape="box"];31188 -> 65107[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65107 -> 31270[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 22434[label="FiniteMap.splitLT2 (Pos Zero) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) False",fontsize=16,color="black",shape="box"];22434 -> 22476[label="",style="solid", color="black", weight=3]; 130.29/78.14 22435[label="FiniteMap.splitLT1 (Neg zzz19700) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) (compare (Pos (Succ zzz1975)) (Neg zzz19700) == GT)",fontsize=16,color="black",shape="box"];22435 -> 22477[label="",style="solid", color="black", weight=3]; 130.29/78.14 31656[label="zzz1979",fontsize=16,color="green",shape="box"];31657[label="zzz1988",fontsize=16,color="green",shape="box"];31658[label="zzz1984",fontsize=16,color="green",shape="box"];31659[label="zzz1977",fontsize=16,color="green",shape="box"];31660[label="zzz1983",fontsize=16,color="green",shape="box"];31661[label="Succ zzz1982",fontsize=16,color="green",shape="box"];31662[label="zzz1980",fontsize=16,color="green",shape="box"];31663[label="zzz1985",fontsize=16,color="green",shape="box"];31664[label="zzz1990",fontsize=16,color="green",shape="box"];31665[label="zzz1987",fontsize=16,color="green",shape="box"];31666[label="zzz1978",fontsize=16,color="green",shape="box"];31667[label="zzz1989",fontsize=16,color="green",shape="box"];31668[label="Succ zzz1987",fontsize=16,color="green",shape="box"];31669[label="zzz1981",fontsize=16,color="green",shape="box"];31670[label="zzz1986",fontsize=16,color="green",shape="box"];31671[label="zzz1982",fontsize=16,color="green",shape="box"];31672[label="zzz1991",fontsize=16,color="green",shape="box"];31655[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) zzz3169 zzz3170 zzz3171 zzz3172 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3173)) zzz3174 zzz3175 zzz3176 zzz3177 (Pos (Succ zzz3168)) (primCmpNat zzz3178 zzz3179 == GT)))",fontsize=16,color="burlywood",shape="triangle"];65108[label="zzz3178/Succ zzz31780",fontsize=10,color="white",style="solid",shape="box"];31655 -> 65108[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65108 -> 31843[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 65109[label="zzz3178/Zero",fontsize=10,color="white",style="solid",shape="box"];31655 -> 65109[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65109 -> 31844[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 18702[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 otherwise",fontsize=16,color="black",shape="box"];18702 -> 18782[label="",style="solid", color="black", weight=3]; 130.29/78.14 4077[label="FiniteMap.splitGT1 (Pos (Succ zzz3000)) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Pos Zero) True",fontsize=16,color="black",shape="box"];4077 -> 4762[label="",style="solid", color="black", weight=3]; 130.29/78.14 11420[label="FiniteMap.splitGT3 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero)",fontsize=16,color="black",shape="box"];11420 -> 11688[label="",style="solid", color="black", weight=3]; 130.29/78.14 11421[label="FiniteMap.splitLT3 (FiniteMap.Branch (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622) (Pos Zero)",fontsize=16,color="black",shape="box"];11421 -> 11689[label="",style="solid", color="black", weight=3]; 130.29/78.14 5861[label="FiniteMap.splitLT0 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) otherwise",fontsize=16,color="black",shape="box"];5861 -> 6039[label="",style="solid", color="black", weight=3]; 130.29/78.14 5862[label="FiniteMap.splitGT0 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) otherwise",fontsize=16,color="black",shape="box"];5862 -> 6040[label="",style="solid", color="black", weight=3]; 130.29/78.14 5863 -> 31858[label="",style="dashed", color="red", weight=0]; 130.29/78.14 5863[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz34000)) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 (primCmpNat zzz3000 zzz34000 == LT)",fontsize=16,color="magenta"];5863 -> 31859[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 5863 -> 31860[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 5863 -> 31861[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 5863 -> 31862[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 5863 -> 31863[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 5863 -> 31864[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 5863 -> 31865[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 5863 -> 31866[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 5863 -> 31867[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 5864[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos Zero) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 (GT == LT)",fontsize=16,color="black",shape="box"];5864 -> 6043[label="",style="solid", color="black", weight=3]; 130.29/78.14 5865[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg zzz3400) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 (Pos (Succ zzz3000) > Neg zzz3400)",fontsize=16,color="black",shape="box"];5865 -> 6044[label="",style="solid", color="black", weight=3]; 130.29/78.14 5866[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz34000)) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (LT == LT)",fontsize=16,color="black",shape="box"];5866 -> 6045[label="",style="solid", color="black", weight=3]; 130.29/78.14 5867[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 False",fontsize=16,color="black",shape="box"];5867 -> 6046[label="",style="solid", color="black", weight=3]; 130.29/78.14 5868[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz34000)) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 False",fontsize=16,color="black",shape="box"];5868 -> 6047[label="",style="solid", color="black", weight=3]; 130.29/78.14 5869[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 False",fontsize=16,color="black",shape="box"];5869 -> 6048[label="",style="solid", color="black", weight=3]; 130.29/78.14 5870[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz250200)) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];5870 -> 6049[label="",style="solid", color="black", weight=3]; 130.29/78.14 5871[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];5871 -> 6050[label="",style="solid", color="black", weight=3]; 130.29/78.14 5872[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz250200)) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];5872 -> 6051[label="",style="solid", color="black", weight=3]; 130.29/78.14 5873[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];5873 -> 6052[label="",style="solid", color="black", weight=3]; 130.29/78.14 4111 -> 11[label="",style="dashed", color="red", weight=0]; 130.29/78.14 4111[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];4112[label="FiniteMap.splitLT1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ zzz3000)) == GT)",fontsize=16,color="black",shape="box"];4112 -> 4782[label="",style="solid", color="black", weight=3]; 130.29/78.14 17237 -> 288[label="",style="dashed", color="red", weight=0]; 130.29/78.14 17237[label="FiniteMap.glueVBal (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero)) zzz1199) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero)) zzz1200)",fontsize=16,color="magenta"];17237 -> 17571[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 17237 -> 17572[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 17238[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero) zzz1197 zzz1198 zzz1199 zzz1200 True",fontsize=16,color="black",shape="box"];17238 -> 17573[label="",style="solid", color="black", weight=3]; 130.29/78.14 5874[label="FiniteMap.splitLT0 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) otherwise",fontsize=16,color="black",shape="box"];5874 -> 6053[label="",style="solid", color="black", weight=3]; 130.29/78.14 5875[label="FiniteMap.splitGT0 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) otherwise",fontsize=16,color="black",shape="box"];5875 -> 6054[label="",style="solid", color="black", weight=3]; 130.29/78.14 62576[label="zzz633700",fontsize=16,color="green",shape="box"];43384[label="primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz4739)",fontsize=16,color="black",shape="triangle"];43384 -> 43412[label="",style="solid", color="black", weight=3]; 130.29/78.14 43355[label="primPlusNat (Succ zzz50920000) zzz54200",fontsize=16,color="burlywood",shape="box"];65110[label="zzz54200/Succ zzz542000",fontsize=10,color="white",style="solid",shape="box"];43355 -> 65110[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65110 -> 43479[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 65111[label="zzz54200/Zero",fontsize=10,color="white",style="solid",shape="box"];43355 -> 65111[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65111 -> 43480[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 43356[label="primPlusNat Zero zzz54200",fontsize=16,color="burlywood",shape="box"];65112[label="zzz54200/Succ zzz542000",fontsize=10,color="white",style="solid",shape="box"];43356 -> 65112[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65112 -> 43481[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 65113[label="zzz54200/Zero",fontsize=10,color="white",style="solid",shape="box"];43356 -> 65113[label="",style="solid", color="burlywood", weight=9]; 130.29/78.14 65113 -> 43482[label="",style="solid", color="burlywood", weight=3]; 130.29/78.14 62577[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat (Succ zzz63380) (Succ zzz631900) == LT)",fontsize=16,color="black",shape="box"];62577 -> 62592[label="",style="solid", color="black", weight=3]; 130.29/78.14 62578[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat (Succ zzz63380) Zero == LT)",fontsize=16,color="black",shape="box"];62578 -> 62593[label="",style="solid", color="black", weight=3]; 130.29/78.14 62579[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 False",fontsize=16,color="black",shape="triangle"];62579 -> 62594[label="",style="solid", color="black", weight=3]; 130.29/78.14 62580 -> 62571[label="",style="dashed", color="red", weight=0]; 130.29/78.14 62580[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat Zero (Succ zzz631900) == LT)",fontsize=16,color="magenta"];62580 -> 62595[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 62580 -> 62596[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 62581[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (EQ == LT)",fontsize=16,color="black",shape="triangle"];62581 -> 62597[label="",style="solid", color="black", weight=3]; 130.29/78.14 62582 -> 62558[label="",style="dashed", color="red", weight=0]; 130.29/78.14 62582[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (GT == LT)",fontsize=16,color="magenta"];62583 -> 62581[label="",style="dashed", color="red", weight=0]; 130.29/78.14 62583[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (EQ == LT)",fontsize=16,color="magenta"];62585[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 True",fontsize=16,color="black",shape="box"];62585 -> 62600[label="",style="solid", color="black", weight=3]; 130.29/78.14 62586[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat (Succ zzz631900) (Succ zzz63400) == LT)",fontsize=16,color="black",shape="box"];62586 -> 62601[label="",style="solid", color="black", weight=3]; 130.29/78.14 62587[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat Zero (Succ zzz63400) == LT)",fontsize=16,color="black",shape="box"];62587 -> 62602[label="",style="solid", color="black", weight=3]; 130.29/78.14 62588 -> 62570[label="",style="dashed", color="red", weight=0]; 130.29/78.14 62588[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (LT == LT)",fontsize=16,color="magenta"];62589 -> 62581[label="",style="dashed", color="red", weight=0]; 130.29/78.14 62589[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (EQ == LT)",fontsize=16,color="magenta"];62590 -> 62557[label="",style="dashed", color="red", weight=0]; 130.29/78.14 62590[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat (Succ zzz631900) Zero == LT)",fontsize=16,color="magenta"];62590 -> 62603[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 62590 -> 62604[label="",style="dashed", color="magenta", weight=3]; 130.29/78.14 62591 -> 62581[label="",style="dashed", color="red", weight=0]; 130.29/78.15 62591[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (EQ == LT)",fontsize=16,color="magenta"];12656[label="FiniteMap.splitGT2 (Pos zzz742) zzz743 zzz744 zzz745 zzz746 (Neg (Succ zzz747)) (LT == GT)",fontsize=16,color="black",shape="triangle"];12656 -> 12940[label="",style="solid", color="black", weight=3]; 130.29/78.15 12657[label="FiniteMap.splitLT2 (Pos zzz742) zzz743 zzz744 zzz745 zzz746 (Neg (Succ zzz747)) (LT == LT)",fontsize=16,color="black",shape="triangle"];12657 -> 12941[label="",style="solid", color="black", weight=3]; 130.29/78.15 28563 -> 10612[label="",style="dashed", color="red", weight=0]; 130.29/78.15 28563[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) zzz2761 zzz2762 zzz2763 zzz2764 (Maybe.isJust (FiniteMap.lookupFM zzz2769 (Neg (Succ zzz2760))))",fontsize=16,color="magenta"];28563 -> 28577[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 28563 -> 28578[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 28563 -> 28579[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 28563 -> 28580[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 28563 -> 28581[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 28563 -> 28582[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 28563 -> 28583[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 28563 -> 28584[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 28563 -> 28585[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 28563 -> 28586[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 28563 -> 28587[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 28564[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) zzz2761 zzz2762 zzz2763 zzz2764 (Maybe.isJust (FiniteMap.lookupFM0 (Neg (Succ zzz2765)) zzz2766 zzz2767 zzz2768 zzz2769 (Neg (Succ zzz2760)) otherwise))",fontsize=16,color="black",shape="box"];28564 -> 28588[label="",style="solid", color="black", weight=3]; 130.29/78.15 12363[label="zzz426",fontsize=16,color="green",shape="box"];12364[label="Succ zzz3000",fontsize=16,color="green",shape="box"];7766[label="FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334",fontsize=16,color="green",shape="box"];7767[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];7767 -> 7991[label="",style="solid", color="black", weight=3]; 130.29/78.15 21799[label="zzz7452",fontsize=16,color="green",shape="box"];21800[label="zzz7453",fontsize=16,color="green",shape="box"];21801[label="zzz7454",fontsize=16,color="green",shape="box"];21802[label="zzz74500",fontsize=16,color="green",shape="box"];21803[label="zzz7451",fontsize=16,color="green",shape="box"];21804[label="FiniteMap.splitGT2 (Neg (Succ zzz745000)) zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (primCmpNat (Succ zzz745000) (Succ zzz747) == GT)",fontsize=16,color="black",shape="box"];21804 -> 21841[label="",style="solid", color="black", weight=3]; 130.29/78.15 21805[label="FiniteMap.splitGT2 (Neg Zero) zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (primCmpNat Zero (Succ zzz747) == GT)",fontsize=16,color="black",shape="box"];21805 -> 21842[label="",style="solid", color="black", weight=3]; 130.29/78.15 14565[label="zzz7452",fontsize=16,color="green",shape="box"];14566[label="zzz7453",fontsize=16,color="green",shape="box"];14567[label="zzz7454",fontsize=16,color="green",shape="box"];14568[label="zzz74500",fontsize=16,color="green",shape="box"];14569[label="zzz7451",fontsize=16,color="green",shape="box"];14570[label="FiniteMap.splitLT2 (Neg (Succ zzz745000)) zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (primCmpNat (Succ zzz745000) (Succ zzz747) == LT)",fontsize=16,color="black",shape="box"];14570 -> 14938[label="",style="solid", color="black", weight=3]; 130.29/78.15 14571[label="FiniteMap.splitLT2 (Neg Zero) zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (primCmpNat Zero (Succ zzz747) == LT)",fontsize=16,color="black",shape="box"];14571 -> 14939[label="",style="solid", color="black", weight=3]; 130.29/78.15 4495[label="FiniteMap.splitGT1 (Neg Zero) zzz31 zzz32 FiniteMap.EmptyFM zzz34 (Neg (Succ zzz4000)) True",fontsize=16,color="black",shape="box"];4495 -> 5101[label="",style="solid", color="black", weight=3]; 130.29/78.15 14350[label="FiniteMap.splitGT2 (Neg Zero) zzz884 zzz885 zzz886 zzz887 (Neg (Succ zzz888)) (compare (Neg (Succ zzz888)) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];14350 -> 14437[label="",style="solid", color="black", weight=3]; 130.29/78.15 29685 -> 29406[label="",style="dashed", color="red", weight=0]; 130.29/78.15 29685[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) zzz2889 zzz2890 zzz2891 zzz2892 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2893)) zzz2894 zzz2895 zzz2896 zzz2897 (Neg (Succ zzz2888)) (primCmpNat zzz28980 zzz28990 == GT)))",fontsize=16,color="magenta"];29685 -> 29724[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 29685 -> 29725[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 29686[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) zzz2889 zzz2890 zzz2891 zzz2892 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2893)) zzz2894 zzz2895 zzz2896 zzz2897 (Neg (Succ zzz2888)) (GT == GT)))",fontsize=16,color="black",shape="box"];29686 -> 29726[label="",style="solid", color="black", weight=3]; 130.29/78.15 29687[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) zzz2889 zzz2890 zzz2891 zzz2892 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2893)) zzz2894 zzz2895 zzz2896 zzz2897 (Neg (Succ zzz2888)) (LT == GT)))",fontsize=16,color="black",shape="box"];29687 -> 29727[label="",style="solid", color="black", weight=3]; 130.29/78.15 29688[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) zzz2889 zzz2890 zzz2891 zzz2892 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2893)) zzz2894 zzz2895 zzz2896 zzz2897 (Neg (Succ zzz2888)) (EQ == GT)))",fontsize=16,color="black",shape="box"];29688 -> 29728[label="",style="solid", color="black", weight=3]; 130.29/78.15 13521[label="FiniteMap.splitGT zzz833 (Neg Zero)",fontsize=16,color="burlywood",shape="triangle"];65114[label="zzz833/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];13521 -> 65114[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65114 -> 13814[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65115[label="zzz833/FiniteMap.Branch zzz8330 zzz8331 zzz8332 zzz8333 zzz8334",fontsize=10,color="white",style="solid",shape="box"];13521 -> 65115[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65115 -> 13815[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 13522[label="Succ zzz830",fontsize=16,color="green",shape="box"];13523[label="zzz834",fontsize=16,color="green",shape="box"];13524[label="zzz831",fontsize=16,color="green",shape="box"];13525[label="FiniteMap.splitLT2 (Pos zzz83300) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (primCmpInt (Neg Zero) (Pos zzz83300) == LT)",fontsize=16,color="burlywood",shape="box"];65116[label="zzz83300/Succ zzz833000",fontsize=10,color="white",style="solid",shape="box"];13525 -> 65116[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65116 -> 13816[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65117[label="zzz83300/Zero",fontsize=10,color="white",style="solid",shape="box"];13525 -> 65117[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65117 -> 13817[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 13526[label="FiniteMap.splitLT2 (Neg zzz83300) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (primCmpInt (Neg Zero) (Neg zzz83300) == LT)",fontsize=16,color="burlywood",shape="box"];65118[label="zzz83300/Succ zzz833000",fontsize=10,color="white",style="solid",shape="box"];13526 -> 65118[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65118 -> 13818[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65119[label="zzz83300/Zero",fontsize=10,color="white",style="solid",shape="box"];13526 -> 65119[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65119 -> 13819[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 7082[label="FiniteMap.splitLT0 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) otherwise",fontsize=16,color="black",shape="box"];7082 -> 7290[label="",style="solid", color="black", weight=3]; 130.29/78.15 7083[label="FiniteMap.splitGT0 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) otherwise",fontsize=16,color="black",shape="box"];7083 -> 7291[label="",style="solid", color="black", weight=3]; 130.29/78.15 13452[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos zzz98200) zzz9821 zzz9822 zzz9823 zzz9824 (Neg (Succ zzz3000)) zzz31 True",fontsize=16,color="black",shape="box"];13452 -> 13527[label="",style="solid", color="black", weight=3]; 130.29/78.15 13453[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz982000)) zzz9821 zzz9822 zzz9823 zzz9824 (Neg (Succ zzz3000)) zzz31 (primCmpNat (Succ zzz982000) (Succ zzz3000) == LT)",fontsize=16,color="black",shape="box"];13453 -> 13528[label="",style="solid", color="black", weight=3]; 130.29/78.15 13454[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg (Succ zzz3000)) zzz31 (primCmpNat Zero (Succ zzz3000) == LT)",fontsize=16,color="black",shape="box"];13454 -> 13529[label="",style="solid", color="black", weight=3]; 130.29/78.15 13455[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz982000)) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (LT == LT)",fontsize=16,color="black",shape="box"];13455 -> 13530[label="",style="solid", color="black", weight=3]; 130.29/78.15 13456[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (EQ == LT)",fontsize=16,color="black",shape="box"];13456 -> 13531[label="",style="solid", color="black", weight=3]; 130.29/78.15 13457[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz982000)) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (primCmpNat (Succ zzz982000) Zero == LT)",fontsize=16,color="black",shape="box"];13457 -> 13532[label="",style="solid", color="black", weight=3]; 130.29/78.15 13458[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (EQ == LT)",fontsize=16,color="black",shape="box"];13458 -> 13533[label="",style="solid", color="black", weight=3]; 130.29/78.15 7088[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz353200)) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];7088 -> 7295[label="",style="solid", color="black", weight=3]; 130.29/78.15 7089[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];7089 -> 7296[label="",style="solid", color="black", weight=3]; 130.29/78.15 7090[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz353200)) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];7090 -> 7297[label="",style="solid", color="black", weight=3]; 130.29/78.15 7091[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];7091 -> 7298[label="",style="solid", color="black", weight=3]; 130.29/78.15 4578[label="FiniteMap.splitGT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Neg Zero) True",fontsize=16,color="black",shape="box"];4578 -> 5191[label="",style="solid", color="black", weight=3]; 130.29/78.15 4579[label="FiniteMap.splitLT2 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Neg Zero) False",fontsize=16,color="black",shape="box"];4579 -> 5192[label="",style="solid", color="black", weight=3]; 130.29/78.15 20259[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 True",fontsize=16,color="black",shape="box"];20259 -> 20309[label="",style="solid", color="black", weight=3]; 130.29/78.15 20260[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM0 (Pos Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) True))",fontsize=16,color="black",shape="box"];20260 -> 20310[label="",style="solid", color="black", weight=3]; 130.29/78.15 20261[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz160300)) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) True))",fontsize=16,color="black",shape="box"];20261 -> 20311[label="",style="solid", color="black", weight=3]; 130.29/78.15 20262[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM0 (Neg Zero) zzz1604 zzz1605 zzz1606 zzz1607 (Neg Zero) True))",fontsize=16,color="black",shape="box"];20262 -> 20312[label="",style="solid", color="black", weight=3]; 130.29/78.15 7092[label="FiniteMap.splitLT0 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) otherwise",fontsize=16,color="black",shape="box"];7092 -> 7299[label="",style="solid", color="black", weight=3]; 130.29/78.15 7093[label="FiniteMap.splitGT0 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) otherwise",fontsize=16,color="black",shape="box"];7093 -> 7300[label="",style="solid", color="black", weight=3]; 130.29/78.15 20566 -> 33577[label="",style="dashed", color="red", weight=0]; 130.29/78.15 20566[label="FiniteMap.splitGT2 (Pos (Succ zzz1612000)) zzz16121 zzz16122 zzz16123 zzz16124 (Pos (Succ zzz1613)) (primCmpNat zzz1613 zzz1612000 == GT)",fontsize=16,color="magenta"];20566 -> 33578[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20566 -> 33579[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20566 -> 33580[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20566 -> 33581[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20566 -> 33582[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20566 -> 33583[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20566 -> 33584[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20566 -> 33585[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20567[label="FiniteMap.splitGT2 (Pos Zero) zzz16121 zzz16122 zzz16123 zzz16124 (Pos (Succ zzz1613)) (GT == GT)",fontsize=16,color="black",shape="triangle"];20567 -> 20779[label="",style="solid", color="black", weight=3]; 130.29/78.15 20568 -> 19598[label="",style="dashed", color="red", weight=0]; 130.29/78.15 20568[label="FiniteMap.splitGT zzz16124 (Pos (Succ zzz1613))",fontsize=16,color="magenta"];20568 -> 20780[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 4721 -> 2827[label="",style="dashed", color="red", weight=0]; 130.29/78.15 4721[label="FiniteMap.splitGT FiniteMap.EmptyFM (Pos (Succ zzz4000))",fontsize=16,color="magenta"];31074[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) zzz3073 zzz3074 zzz3075 zzz3076 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3077)) zzz3078 zzz3079 zzz3080 zzz3081 (Pos (Succ zzz3072)) (primCmpInt (Pos (Succ zzz3072)) (Pos (Succ zzz3077)) == GT)))",fontsize=16,color="black",shape="box"];31074 -> 31185[label="",style="solid", color="black", weight=3]; 130.29/78.15 29211 -> 28738[label="",style="dashed", color="red", weight=0]; 130.29/78.15 29211[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM zzz2747 (Pos (Succ zzz2738))))",fontsize=16,color="magenta"];29212[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust Nothing)",fontsize=16,color="black",shape="box"];29212 -> 29258[label="",style="solid", color="black", weight=3]; 130.29/78.15 29213 -> 27965[label="",style="dashed", color="red", weight=0]; 130.29/78.15 29213[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 (Maybe.isJust (FiniteMap.lookupFM2 zzz27470 zzz27471 zzz27472 zzz27473 zzz27474 (Pos (Succ zzz2738)) (Pos (Succ zzz2738) < zzz27470)))",fontsize=16,color="magenta"];29213 -> 29259[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 29213 -> 29260[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 29213 -> 29261[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 29213 -> 29262[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 29213 -> 29263[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31269[label="FiniteMap.splitLT2 (Pos (Succ zzz3133)) zzz3134 zzz3135 zzz3136 zzz3137 (Pos (Succ zzz3138)) (primCmpNat (Succ zzz31390) zzz3140 == LT)",fontsize=16,color="burlywood",shape="box"];65120[label="zzz3140/Succ zzz31400",fontsize=10,color="white",style="solid",shape="box"];31269 -> 65120[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65120 -> 31320[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65121[label="zzz3140/Zero",fontsize=10,color="white",style="solid",shape="box"];31269 -> 65121[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65121 -> 31321[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 31270[label="FiniteMap.splitLT2 (Pos (Succ zzz3133)) zzz3134 zzz3135 zzz3136 zzz3137 (Pos (Succ zzz3138)) (primCmpNat Zero zzz3140 == LT)",fontsize=16,color="burlywood",shape="box"];65122[label="zzz3140/Succ zzz31400",fontsize=10,color="white",style="solid",shape="box"];31270 -> 65122[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65122 -> 31322[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65123[label="zzz3140/Zero",fontsize=10,color="white",style="solid",shape="box"];31270 -> 65123[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65123 -> 31323[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 22476[label="FiniteMap.splitLT1 (Pos Zero) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) (Pos (Succ zzz1975) > Pos Zero)",fontsize=16,color="black",shape="box"];22476 -> 22507[label="",style="solid", color="black", weight=3]; 130.29/78.15 22477[label="FiniteMap.splitLT1 (Neg zzz19700) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) (primCmpInt (Pos (Succ zzz1975)) (Neg zzz19700) == GT)",fontsize=16,color="black",shape="box"];22477 -> 22508[label="",style="solid", color="black", weight=3]; 130.29/78.15 31843[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) zzz3169 zzz3170 zzz3171 zzz3172 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3173)) zzz3174 zzz3175 zzz3176 zzz3177 (Pos (Succ zzz3168)) (primCmpNat (Succ zzz31780) zzz3179 == GT)))",fontsize=16,color="burlywood",shape="box"];65124[label="zzz3179/Succ zzz31790",fontsize=10,color="white",style="solid",shape="box"];31843 -> 65124[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65124 -> 31949[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65125[label="zzz3179/Zero",fontsize=10,color="white",style="solid",shape="box"];31843 -> 65125[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65125 -> 31950[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 31844[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) zzz3169 zzz3170 zzz3171 zzz3172 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3173)) zzz3174 zzz3175 zzz3176 zzz3177 (Pos (Succ zzz3168)) (primCmpNat Zero zzz3179 == GT)))",fontsize=16,color="burlywood",shape="box"];65126[label="zzz3179/Succ zzz31790",fontsize=10,color="white",style="solid",shape="box"];31844 -> 65126[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65126 -> 31951[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65127[label="zzz3179/Zero",fontsize=10,color="white",style="solid",shape="box"];31844 -> 65127[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65127 -> 31952[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 18782[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387)) zzz1388 zzz1389 zzz1390 zzz1391 True",fontsize=16,color="black",shape="box"];18782 -> 18882[label="",style="solid", color="black", weight=3]; 130.29/78.15 4762 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.15 4762[label="FiniteMap.mkVBalBranch (Pos (Succ zzz3000)) zzz31 (FiniteMap.splitGT FiniteMap.EmptyFM (Pos Zero)) zzz34",fontsize=16,color="magenta"];4762 -> 5252[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 4762 -> 5253[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 11688[label="FiniteMap.splitGT2 (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622 (Pos Zero) (Pos Zero > Pos (Succ zzz618))",fontsize=16,color="black",shape="box"];11688 -> 11828[label="",style="solid", color="black", weight=3]; 130.29/78.15 11689[label="FiniteMap.splitLT2 (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622 (Pos Zero) (Pos Zero < Pos (Succ zzz618))",fontsize=16,color="black",shape="box"];11689 -> 11829[label="",style="solid", color="black", weight=3]; 130.29/78.15 6039[label="FiniteMap.splitLT0 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) True",fontsize=16,color="black",shape="box"];6039 -> 6097[label="",style="solid", color="black", weight=3]; 130.29/78.15 6040[label="FiniteMap.splitGT0 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) True",fontsize=16,color="black",shape="box"];6040 -> 6098[label="",style="solid", color="black", weight=3]; 130.29/78.15 31859[label="zzz3000",fontsize=16,color="green",shape="box"];31860[label="zzz34000",fontsize=16,color="green",shape="box"];31861[label="zzz342",fontsize=16,color="green",shape="box"];31862[label="zzz341",fontsize=16,color="green",shape="box"];31863[label="zzz344",fontsize=16,color="green",shape="box"];31864[label="zzz31",fontsize=16,color="green",shape="box"];31865[label="zzz3000",fontsize=16,color="green",shape="box"];31866[label="zzz343",fontsize=16,color="green",shape="box"];31867[label="zzz34000",fontsize=16,color="green",shape="box"];31858[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz3181)) zzz3182 zzz3183 zzz3184 zzz3185 (Pos (Succ zzz3186)) zzz3187 (primCmpNat zzz3188 zzz3189 == LT)",fontsize=16,color="burlywood",shape="triangle"];65128[label="zzz3188/Succ zzz31880",fontsize=10,color="white",style="solid",shape="box"];31858 -> 65128[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65128 -> 31953[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65129[label="zzz3188/Zero",fontsize=10,color="white",style="solid",shape="box"];31858 -> 65129[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65129 -> 31954[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 6043[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos Zero) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 False",fontsize=16,color="black",shape="box"];6043 -> 6103[label="",style="solid", color="black", weight=3]; 130.29/78.15 6044[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg zzz3400) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 (compare (Pos (Succ zzz3000)) (Neg zzz3400) == GT)",fontsize=16,color="black",shape="box"];6044 -> 6104[label="",style="solid", color="black", weight=3]; 130.29/78.15 6045[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz34000)) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 True",fontsize=16,color="black",shape="box"];6045 -> 6105[label="",style="solid", color="black", weight=3]; 130.29/78.15 6046[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (Pos Zero > Pos Zero)",fontsize=16,color="black",shape="box"];6046 -> 6106[label="",style="solid", color="black", weight=3]; 130.29/78.15 6047[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz34000)) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (Pos Zero > Neg (Succ zzz34000))",fontsize=16,color="black",shape="box"];6047 -> 6107[label="",style="solid", color="black", weight=3]; 130.29/78.15 6048[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (Pos Zero > Neg Zero)",fontsize=16,color="black",shape="box"];6048 -> 6108[label="",style="solid", color="black", weight=3]; 130.29/78.15 6049[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (primPlusNat (primMulNat (Succ (Succ (Succ Zero))) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];6049 -> 6109[label="",style="solid", color="black", weight=3]; 130.29/78.15 6050[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) == LT)",fontsize=16,color="black",shape="box"];6050 -> 6110[label="",style="solid", color="black", weight=3]; 130.29/78.15 6051[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primMulNat (Succ (Succ (Succ Zero))) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];6051 -> 6111[label="",style="solid", color="black", weight=3]; 130.29/78.15 6052[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) == LT)",fontsize=16,color="black",shape="box"];6052 -> 6112[label="",style="solid", color="black", weight=3]; 130.29/78.15 4782[label="FiniteMap.splitLT1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos Zero) (GT == GT)",fontsize=16,color="black",shape="box"];4782 -> 5271[label="",style="solid", color="black", weight=3]; 130.29/78.15 17571 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.15 17571[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero)) zzz1200",fontsize=16,color="magenta"];17571 -> 17695[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 17571 -> 17696[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 17572 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.15 17572[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero)) zzz1199",fontsize=16,color="magenta"];17572 -> 17697[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 17572 -> 17698[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 17573 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.15 17573[label="FiniteMap.mkVBalBranch (Pos Zero) (FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero)) zzz1197) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero)) zzz1199) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero)) zzz1200)",fontsize=16,color="magenta"];17573 -> 17699[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 17573 -> 17700[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 17573 -> 17701[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 17573 -> 17702[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 6053[label="FiniteMap.splitLT0 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) True",fontsize=16,color="black",shape="box"];6053 -> 6113[label="",style="solid", color="black", weight=3]; 130.29/78.15 6054[label="FiniteMap.splitGT0 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Pos Zero) True",fontsize=16,color="black",shape="box"];6054 -> 6114[label="",style="solid", color="black", weight=3]; 130.29/78.15 43412 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.15 43412[label="primPlusNat (primMulNat (Succ (Succ (Succ Zero))) (Succ zzz4739)) (Succ zzz4739)",fontsize=16,color="magenta"];43412 -> 43494[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 43412 -> 43495[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 43479[label="primPlusNat (Succ zzz50920000) (Succ zzz542000)",fontsize=16,color="black",shape="box"];43479 -> 43496[label="",style="solid", color="black", weight=3]; 130.29/78.15 43480[label="primPlusNat (Succ zzz50920000) Zero",fontsize=16,color="black",shape="box"];43480 -> 43497[label="",style="solid", color="black", weight=3]; 130.29/78.15 43481[label="primPlusNat Zero (Succ zzz542000)",fontsize=16,color="black",shape="box"];43481 -> 43498[label="",style="solid", color="black", weight=3]; 130.29/78.15 43482[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];43482 -> 43499[label="",style="solid", color="black", weight=3]; 130.29/78.15 62592[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat zzz63380 zzz631900 == LT)",fontsize=16,color="burlywood",shape="triangle"];65130[label="zzz63380/Succ zzz633800",fontsize=10,color="white",style="solid",shape="box"];62592 -> 65130[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65130 -> 62605[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65131[label="zzz63380/Zero",fontsize=10,color="white",style="solid",shape="box"];62592 -> 65131[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65131 -> 62606[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 62593 -> 62558[label="",style="dashed", color="red", weight=0]; 130.29/78.15 62593[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (GT == LT)",fontsize=16,color="magenta"];62594 -> 62607[label="",style="dashed", color="red", weight=0]; 130.29/78.15 62594[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (FiniteMap.sIZE_RATIO * FiniteMap.glueVBal3Size_r zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 < FiniteMap.glueVBal3Size_l zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464)",fontsize=16,color="magenta"];62594 -> 62608[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 62595[label="zzz631900",fontsize=16,color="green",shape="box"];62596[label="Zero",fontsize=16,color="green",shape="box"];62597 -> 62579[label="",style="dashed", color="red", weight=0]; 130.29/78.15 62597[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 False",fontsize=16,color="magenta"];62600 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.15 62600[label="FiniteMap.mkBalBranch zzz474030 zzz474031 (FiniteMap.glueVBal (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) zzz474033) zzz474034",fontsize=16,color="magenta"];62600 -> 63084[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 62601 -> 62592[label="",style="dashed", color="red", weight=0]; 130.29/78.15 62601[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat zzz631900 zzz63400 == LT)",fontsize=16,color="magenta"];62601 -> 62610[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 62601 -> 62611[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 62602 -> 62570[label="",style="dashed", color="red", weight=0]; 130.29/78.15 62602[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (LT == LT)",fontsize=16,color="magenta"];62603[label="zzz631900",fontsize=16,color="green",shape="box"];62604[label="Zero",fontsize=16,color="green",shape="box"];12940[label="FiniteMap.splitGT2 (Pos zzz742) zzz743 zzz744 zzz745 zzz746 (Neg (Succ zzz747)) False",fontsize=16,color="black",shape="box"];12940 -> 13017[label="",style="solid", color="black", weight=3]; 130.29/78.15 12941[label="FiniteMap.splitLT2 (Pos zzz742) zzz743 zzz744 zzz745 zzz746 (Neg (Succ zzz747)) True",fontsize=16,color="black",shape="box"];12941 -> 13018[label="",style="solid", color="black", weight=3]; 130.29/78.15 28577[label="zzz2757",fontsize=16,color="green",shape="box"];28578[label="zzz2762",fontsize=16,color="green",shape="box"];28579[label="zzz2758",fontsize=16,color="green",shape="box"];28580[label="zzz2764",fontsize=16,color="green",shape="box"];28581[label="zzz2761",fontsize=16,color="green",shape="box"];28582[label="zzz2759",fontsize=16,color="green",shape="box"];28583[label="zzz2763",fontsize=16,color="green",shape="box"];28584[label="zzz2755",fontsize=16,color="green",shape="box"];28585[label="zzz2756",fontsize=16,color="green",shape="box"];28586[label="zzz2760",fontsize=16,color="green",shape="box"];28587[label="zzz2769",fontsize=16,color="green",shape="box"];28588[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) zzz2761 zzz2762 zzz2763 zzz2764 (Maybe.isJust (FiniteMap.lookupFM0 (Neg (Succ zzz2765)) zzz2766 zzz2767 zzz2768 zzz2769 (Neg (Succ zzz2760)) True))",fontsize=16,color="black",shape="box"];28588 -> 28601[label="",style="solid", color="black", weight=3]; 130.29/78.15 7991[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];7991 -> 8580[label="",style="solid", color="black", weight=3]; 130.29/78.15 21841 -> 34162[label="",style="dashed", color="red", weight=0]; 130.29/78.15 21841[label="FiniteMap.splitGT2 (Neg (Succ zzz745000)) zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (primCmpNat zzz745000 zzz747 == GT)",fontsize=16,color="magenta"];21841 -> 34163[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 21841 -> 34164[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 21841 -> 34165[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 21841 -> 34166[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 21841 -> 34167[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 21841 -> 34168[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 21841 -> 34169[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 21841 -> 34170[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 21842 -> 14823[label="",style="dashed", color="red", weight=0]; 130.29/78.15 21842[label="FiniteMap.splitGT2 (Neg Zero) zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (LT == GT)",fontsize=16,color="magenta"];21842 -> 21967[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 21842 -> 21968[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 21842 -> 21969[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 21842 -> 21970[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 21842 -> 21971[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14938 -> 34273[label="",style="dashed", color="red", weight=0]; 130.29/78.15 14938[label="FiniteMap.splitLT2 (Neg (Succ zzz745000)) zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (primCmpNat zzz745000 zzz747 == LT)",fontsize=16,color="magenta"];14938 -> 34274[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14938 -> 34275[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14938 -> 34276[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14938 -> 34277[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14938 -> 34278[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14938 -> 34279[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14938 -> 34280[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14938 -> 34281[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14939[label="FiniteMap.splitLT2 (Neg Zero) zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) (LT == LT)",fontsize=16,color="black",shape="box"];14939 -> 15229[label="",style="solid", color="black", weight=3]; 130.29/78.15 5101 -> 5407[label="",style="dashed", color="red", weight=0]; 130.29/78.15 5101[label="FiniteMap.mkVBalBranch (Neg Zero) zzz31 (FiniteMap.splitGT FiniteMap.EmptyFM (Neg (Succ zzz4000))) zzz34",fontsize=16,color="magenta"];5101 -> 5432[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14437[label="FiniteMap.splitGT2 (Neg Zero) zzz884 zzz885 zzz886 zzz887 (Neg (Succ zzz888)) (primCmpInt (Neg (Succ zzz888)) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];14437 -> 14550[label="",style="solid", color="black", weight=3]; 130.29/78.15 29724[label="zzz28990",fontsize=16,color="green",shape="box"];29725[label="zzz28980",fontsize=16,color="green",shape="box"];29726[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) zzz2889 zzz2890 zzz2891 zzz2892 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2893)) zzz2894 zzz2895 zzz2896 zzz2897 (Neg (Succ zzz2888)) True))",fontsize=16,color="black",shape="box"];29726 -> 29835[label="",style="solid", color="black", weight=3]; 130.29/78.15 29727[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) zzz2889 zzz2890 zzz2891 zzz2892 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2893)) zzz2894 zzz2895 zzz2896 zzz2897 (Neg (Succ zzz2888)) False))",fontsize=16,color="black",shape="triangle"];29727 -> 29836[label="",style="solid", color="black", weight=3]; 130.29/78.15 29728 -> 29727[label="",style="dashed", color="red", weight=0]; 130.29/78.15 29728[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) zzz2889 zzz2890 zzz2891 zzz2892 (Maybe.isJust (FiniteMap.lookupFM1 (Neg (Succ zzz2893)) zzz2894 zzz2895 zzz2896 zzz2897 (Neg (Succ zzz2888)) False))",fontsize=16,color="magenta"];13814[label="FiniteMap.splitGT FiniteMap.EmptyFM (Neg Zero)",fontsize=16,color="black",shape="box"];13814 -> 14046[label="",style="solid", color="black", weight=3]; 130.29/78.15 13815[label="FiniteMap.splitGT (FiniteMap.Branch zzz8330 zzz8331 zzz8332 zzz8333 zzz8334) (Neg Zero)",fontsize=16,color="black",shape="box"];13815 -> 14047[label="",style="solid", color="black", weight=3]; 130.29/78.15 13816[label="FiniteMap.splitLT2 (Pos (Succ zzz833000)) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (primCmpInt (Neg Zero) (Pos (Succ zzz833000)) == LT)",fontsize=16,color="black",shape="box"];13816 -> 14048[label="",style="solid", color="black", weight=3]; 130.29/78.15 13817[label="FiniteMap.splitLT2 (Pos Zero) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];13817 -> 14049[label="",style="solid", color="black", weight=3]; 130.29/78.15 13818[label="FiniteMap.splitLT2 (Neg (Succ zzz833000)) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ zzz833000)) == LT)",fontsize=16,color="black",shape="box"];13818 -> 14050[label="",style="solid", color="black", weight=3]; 130.29/78.15 13819[label="FiniteMap.splitLT2 (Neg Zero) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];13819 -> 14051[label="",style="solid", color="black", weight=3]; 130.29/78.15 7290[label="FiniteMap.splitLT0 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) True",fontsize=16,color="black",shape="box"];7290 -> 7552[label="",style="solid", color="black", weight=3]; 130.29/78.15 7291[label="FiniteMap.splitGT0 (Pos Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) True",fontsize=16,color="black",shape="box"];7291 -> 7553[label="",style="solid", color="black", weight=3]; 130.29/78.15 13527 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.15 13527[label="FiniteMap.mkBalBranch (Pos zzz98200) zzz9821 (FiniteMap.addToFM_C FiniteMap.addToFM0 zzz9823 (Neg (Succ zzz3000)) zzz31) zzz9824",fontsize=16,color="magenta"];13527 -> 63085[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 13527 -> 63086[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 13527 -> 63087[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 13527 -> 63088[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 13528 -> 33397[label="",style="dashed", color="red", weight=0]; 130.29/78.15 13528[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz982000)) zzz9821 zzz9822 zzz9823 zzz9824 (Neg (Succ zzz3000)) zzz31 (primCmpNat zzz982000 zzz3000 == LT)",fontsize=16,color="magenta"];13528 -> 33398[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 13528 -> 33399[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 13528 -> 33400[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 13528 -> 33401[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 13528 -> 33402[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 13528 -> 33403[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 13528 -> 33404[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 13528 -> 33405[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 13528 -> 33406[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 13529[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg (Succ zzz3000)) zzz31 (LT == LT)",fontsize=16,color="black",shape="box"];13529 -> 13826[label="",style="solid", color="black", weight=3]; 130.29/78.15 13530[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz982000)) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 True",fontsize=16,color="black",shape="box"];13530 -> 13827[label="",style="solid", color="black", weight=3]; 130.29/78.15 13531[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 False",fontsize=16,color="black",shape="box"];13531 -> 13828[label="",style="solid", color="black", weight=3]; 130.29/78.15 13532[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz982000)) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (GT == LT)",fontsize=16,color="black",shape="box"];13532 -> 13829[label="",style="solid", color="black", weight=3]; 130.29/78.15 13533[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 False",fontsize=16,color="black",shape="box"];13533 -> 13830[label="",style="solid", color="black", weight=3]; 130.29/78.15 7295[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (primPlusNat (primMulNat (Succ (Succ (Succ Zero))) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];7295 -> 7557[label="",style="solid", color="black", weight=3]; 130.29/78.15 7296[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) == LT)",fontsize=16,color="black",shape="box"];7296 -> 7558[label="",style="solid", color="black", weight=3]; 130.29/78.15 7297[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primMulNat (Succ (Succ (Succ Zero))) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];7297 -> 7559[label="",style="solid", color="black", weight=3]; 130.29/78.15 7298[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) == LT)",fontsize=16,color="black",shape="box"];7298 -> 7560[label="",style="solid", color="black", weight=3]; 130.29/78.15 5191 -> 4192[label="",style="dashed", color="red", weight=0]; 130.29/78.15 5191[label="FiniteMap.splitGT FiniteMap.EmptyFM (Neg Zero)",fontsize=16,color="magenta"];5192[label="FiniteMap.splitLT1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Neg Zero) (Neg Zero > Neg (Succ zzz3000))",fontsize=16,color="black",shape="box"];5192 -> 5680[label="",style="solid", color="black", weight=3]; 130.29/78.15 20309 -> 288[label="",style="dashed", color="red", weight=0]; 130.29/78.15 20309[label="FiniteMap.glueVBal (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero)) zzz1601) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero)) zzz1602)",fontsize=16,color="magenta"];20309 -> 20335[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20309 -> 20336[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20310[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (Just zzz1604))",fontsize=16,color="black",shape="triangle"];20310 -> 20337[label="",style="solid", color="black", weight=3]; 130.29/78.15 20311 -> 19884[label="",style="dashed", color="red", weight=0]; 130.29/78.15 20311[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (FiniteMap.lookupFM zzz1607 (Neg Zero)))",fontsize=16,color="magenta"];20311 -> 20338[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20312 -> 20310[label="",style="dashed", color="red", weight=0]; 130.29/78.15 20312[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 (Maybe.isJust (Just zzz1604))",fontsize=16,color="magenta"];7299[label="FiniteMap.splitLT0 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) True",fontsize=16,color="black",shape="box"];7299 -> 7561[label="",style="solid", color="black", weight=3]; 130.29/78.15 7300[label="FiniteMap.splitGT0 (Neg Zero) zzz31 zzz32 zzz33 zzz34 (Neg Zero) True",fontsize=16,color="black",shape="box"];7300 -> 7562[label="",style="solid", color="black", weight=3]; 130.29/78.15 33578[label="zzz16121",fontsize=16,color="green",shape="box"];33579[label="zzz16123",fontsize=16,color="green",shape="box"];33580[label="zzz16124",fontsize=16,color="green",shape="box"];33581[label="zzz1613",fontsize=16,color="green",shape="box"];33582[label="zzz1612000",fontsize=16,color="green",shape="box"];33583[label="zzz1613",fontsize=16,color="green",shape="box"];33584[label="zzz1612000",fontsize=16,color="green",shape="box"];33585[label="zzz16122",fontsize=16,color="green",shape="box"];33577[label="FiniteMap.splitGT2 (Pos (Succ zzz3396)) zzz3397 zzz3398 zzz3399 zzz3400 (Pos (Succ zzz3401)) (primCmpNat zzz3402 zzz3403 == GT)",fontsize=16,color="burlywood",shape="triangle"];65132[label="zzz3402/Succ zzz34020",fontsize=10,color="white",style="solid",shape="box"];33577 -> 65132[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65132 -> 33666[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65133[label="zzz3402/Zero",fontsize=10,color="white",style="solid",shape="box"];33577 -> 65133[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65133 -> 33667[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 20779[label="FiniteMap.splitGT2 (Pos Zero) zzz16121 zzz16122 zzz16123 zzz16124 (Pos (Succ zzz1613)) True",fontsize=16,color="black",shape="triangle"];20779 -> 21062[label="",style="solid", color="black", weight=3]; 130.29/78.15 20780[label="zzz16124",fontsize=16,color="green",shape="box"];31185 -> 34521[label="",style="dashed", color="red", weight=0]; 130.29/78.15 31185[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3068 zzz3069 zzz3070 zzz3071) (Pos (Succ zzz3072)) zzz3073 zzz3074 zzz3075 zzz3076 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3077)) zzz3078 zzz3079 zzz3080 zzz3081 (Pos (Succ zzz3072)) (primCmpNat (Succ zzz3072) (Succ zzz3077) == GT)))",fontsize=16,color="magenta"];31185 -> 34522[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31185 -> 34523[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31185 -> 34524[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31185 -> 34525[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31185 -> 34526[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31185 -> 34527[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31185 -> 34528[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31185 -> 34529[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31185 -> 34530[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31185 -> 34531[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31185 -> 34532[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31185 -> 34533[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31185 -> 34534[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31185 -> 34535[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31185 -> 34536[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31185 -> 34537[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 29258[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 False",fontsize=16,color="black",shape="box"];29258 -> 29294[label="",style="solid", color="black", weight=3]; 130.29/78.15 29259[label="zzz27471",fontsize=16,color="green",shape="box"];29260[label="zzz27474",fontsize=16,color="green",shape="box"];29261[label="zzz27472",fontsize=16,color="green",shape="box"];29262[label="zzz27473",fontsize=16,color="green",shape="box"];29263[label="zzz27470",fontsize=16,color="green",shape="box"];31320[label="FiniteMap.splitLT2 (Pos (Succ zzz3133)) zzz3134 zzz3135 zzz3136 zzz3137 (Pos (Succ zzz3138)) (primCmpNat (Succ zzz31390) (Succ zzz31400) == LT)",fontsize=16,color="black",shape="box"];31320 -> 31413[label="",style="solid", color="black", weight=3]; 130.29/78.15 31321[label="FiniteMap.splitLT2 (Pos (Succ zzz3133)) zzz3134 zzz3135 zzz3136 zzz3137 (Pos (Succ zzz3138)) (primCmpNat (Succ zzz31390) Zero == LT)",fontsize=16,color="black",shape="box"];31321 -> 31414[label="",style="solid", color="black", weight=3]; 130.29/78.15 31322[label="FiniteMap.splitLT2 (Pos (Succ zzz3133)) zzz3134 zzz3135 zzz3136 zzz3137 (Pos (Succ zzz3138)) (primCmpNat Zero (Succ zzz31400) == LT)",fontsize=16,color="black",shape="box"];31322 -> 31415[label="",style="solid", color="black", weight=3]; 130.29/78.15 31323[label="FiniteMap.splitLT2 (Pos (Succ zzz3133)) zzz3134 zzz3135 zzz3136 zzz3137 (Pos (Succ zzz3138)) (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];31323 -> 31416[label="",style="solid", color="black", weight=3]; 130.29/78.15 22507[label="FiniteMap.splitLT1 (Pos Zero) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) (compare (Pos (Succ zzz1975)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];22507 -> 22526[label="",style="solid", color="black", weight=3]; 130.29/78.15 22508[label="FiniteMap.splitLT1 (Neg zzz19700) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) (GT == GT)",fontsize=16,color="black",shape="box"];22508 -> 22527[label="",style="solid", color="black", weight=3]; 130.29/78.15 31949[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) zzz3169 zzz3170 zzz3171 zzz3172 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3173)) zzz3174 zzz3175 zzz3176 zzz3177 (Pos (Succ zzz3168)) (primCmpNat (Succ zzz31780) (Succ zzz31790) == GT)))",fontsize=16,color="black",shape="box"];31949 -> 32022[label="",style="solid", color="black", weight=3]; 130.29/78.15 31950[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) zzz3169 zzz3170 zzz3171 zzz3172 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3173)) zzz3174 zzz3175 zzz3176 zzz3177 (Pos (Succ zzz3168)) (primCmpNat (Succ zzz31780) Zero == GT)))",fontsize=16,color="black",shape="box"];31950 -> 32023[label="",style="solid", color="black", weight=3]; 130.29/78.15 31951[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) zzz3169 zzz3170 zzz3171 zzz3172 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3173)) zzz3174 zzz3175 zzz3176 zzz3177 (Pos (Succ zzz3168)) (primCmpNat Zero (Succ zzz31790) == GT)))",fontsize=16,color="black",shape="box"];31951 -> 32024[label="",style="solid", color="black", weight=3]; 130.29/78.15 31952[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) zzz3169 zzz3170 zzz3171 zzz3172 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3173)) zzz3174 zzz3175 zzz3176 zzz3177 (Pos (Succ zzz3168)) (primCmpNat Zero Zero == GT)))",fontsize=16,color="black",shape="box"];31952 -> 32025[label="",style="solid", color="black", weight=3]; 130.29/78.15 18882 -> 288[label="",style="dashed", color="red", weight=0]; 130.29/78.15 18882[label="FiniteMap.glueVBal (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387))) zzz1390) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387))) zzz1391)",fontsize=16,color="magenta"];18882 -> 18968[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 18882 -> 18969[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 5252 -> 3350[label="",style="dashed", color="red", weight=0]; 130.29/78.15 5252[label="FiniteMap.splitGT FiniteMap.EmptyFM (Pos Zero)",fontsize=16,color="magenta"];5253[label="Succ zzz3000",fontsize=16,color="green",shape="box"];11828[label="FiniteMap.splitGT2 (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622 (Pos Zero) (compare (Pos Zero) (Pos (Succ zzz618)) == GT)",fontsize=16,color="black",shape="box"];11828 -> 11992[label="",style="solid", color="black", weight=3]; 130.29/78.15 11829[label="FiniteMap.splitLT2 (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622 (Pos Zero) (compare (Pos Zero) (Pos (Succ zzz618)) == LT)",fontsize=16,color="black",shape="box"];11829 -> 11993[label="",style="solid", color="black", weight=3]; 130.29/78.15 6097[label="zzz33",fontsize=16,color="green",shape="box"];6098[label="zzz34",fontsize=16,color="green",shape="box"];31953[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz3181)) zzz3182 zzz3183 zzz3184 zzz3185 (Pos (Succ zzz3186)) zzz3187 (primCmpNat (Succ zzz31880) zzz3189 == LT)",fontsize=16,color="burlywood",shape="box"];65134[label="zzz3189/Succ zzz31890",fontsize=10,color="white",style="solid",shape="box"];31953 -> 65134[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65134 -> 32026[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65135[label="zzz3189/Zero",fontsize=10,color="white",style="solid",shape="box"];31953 -> 65135[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65135 -> 32027[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 31954[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz3181)) zzz3182 zzz3183 zzz3184 zzz3185 (Pos (Succ zzz3186)) zzz3187 (primCmpNat Zero zzz3189 == LT)",fontsize=16,color="burlywood",shape="box"];65136[label="zzz3189/Succ zzz31890",fontsize=10,color="white",style="solid",shape="box"];31954 -> 65136[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65136 -> 32028[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65137[label="zzz3189/Zero",fontsize=10,color="white",style="solid",shape="box"];31954 -> 65137[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65137 -> 32029[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 6103[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 (Pos (Succ zzz3000) > Pos Zero)",fontsize=16,color="black",shape="box"];6103 -> 6303[label="",style="solid", color="black", weight=3]; 130.29/78.15 6104[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg zzz3400) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 (primCmpInt (Pos (Succ zzz3000)) (Neg zzz3400) == GT)",fontsize=16,color="black",shape="box"];6104 -> 6304[label="",style="solid", color="black", weight=3]; 130.29/78.15 6105 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.15 6105[label="FiniteMap.mkBalBranch (Pos (Succ zzz34000)) zzz341 (FiniteMap.addToFM_C FiniteMap.addToFM0 zzz343 (Pos Zero) zzz31) zzz344",fontsize=16,color="magenta"];6105 -> 63089[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 6105 -> 63090[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 6105 -> 63091[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 6105 -> 63092[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 6106[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (compare (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];6106 -> 6347[label="",style="solid", color="black", weight=3]; 130.29/78.15 6107[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz34000)) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (compare (Pos Zero) (Neg (Succ zzz34000)) == GT)",fontsize=16,color="black",shape="box"];6107 -> 6348[label="",style="solid", color="black", weight=3]; 130.29/78.15 6108[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (compare (Pos Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];6108 -> 6349[label="",style="solid", color="black", weight=3]; 130.29/78.15 6109[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ (Succ Zero)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];6109 -> 6350[label="",style="solid", color="black", weight=3]; 130.29/78.15 6110[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos Zero) zzz342 == LT)",fontsize=16,color="burlywood",shape="box"];65138[label="zzz342/Pos zzz3420",fontsize=10,color="white",style="solid",shape="box"];6110 -> 65138[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65138 -> 6351[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65139[label="zzz342/Neg zzz3420",fontsize=10,color="white",style="solid",shape="box"];6110 -> 65139[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65139 -> 6352[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 6111[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ (Succ Zero)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];6111 -> 6353[label="",style="solid", color="black", weight=3]; 130.29/78.15 6112[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg Zero) zzz342 == LT)",fontsize=16,color="burlywood",shape="box"];65140[label="zzz342/Pos zzz3420",fontsize=10,color="white",style="solid",shape="box"];6112 -> 65140[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65140 -> 6354[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65141[label="zzz342/Neg zzz3420",fontsize=10,color="white",style="solid",shape="box"];6112 -> 65141[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65141 -> 6355[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 5271[label="FiniteMap.splitLT1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Pos Zero) True",fontsize=16,color="black",shape="box"];5271 -> 5770[label="",style="solid", color="black", weight=3]; 130.29/78.15 17695[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero)",fontsize=16,color="black",shape="triangle"];17695 -> 17808[label="",style="solid", color="black", weight=3]; 130.29/78.15 17696[label="zzz1200",fontsize=16,color="green",shape="box"];17697[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero)",fontsize=16,color="black",shape="triangle"];17697 -> 17809[label="",style="solid", color="black", weight=3]; 130.29/78.15 17698[label="zzz1199",fontsize=16,color="green",shape="box"];17699 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.15 17699[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero)) zzz1199",fontsize=16,color="magenta"];17699 -> 17810[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 17699 -> 17811[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 17700[label="Zero",fontsize=16,color="green",shape="box"];17701 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.15 17701[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero)) zzz1200",fontsize=16,color="magenta"];17701 -> 17812[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 17701 -> 17813[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 17702[label="FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero)) zzz1197",fontsize=16,color="black",shape="box"];17702 -> 17814[label="",style="solid", color="black", weight=3]; 130.29/78.15 6113[label="zzz33",fontsize=16,color="green",shape="box"];6114[label="zzz34",fontsize=16,color="green",shape="box"];43494[label="Succ zzz4739",fontsize=16,color="green",shape="box"];43495[label="primMulNat (Succ (Succ (Succ Zero))) (Succ zzz4739)",fontsize=16,color="black",shape="box"];43495 -> 43511[label="",style="solid", color="black", weight=3]; 130.29/78.15 43496[label="Succ (Succ (primPlusNat zzz50920000 zzz542000))",fontsize=16,color="green",shape="box"];43496 -> 43512[label="",style="dashed", color="green", weight=3]; 130.29/78.15 43497[label="Succ zzz50920000",fontsize=16,color="green",shape="box"];43498[label="Succ zzz542000",fontsize=16,color="green",shape="box"];43499[label="Zero",fontsize=16,color="green",shape="box"];62605[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat (Succ zzz633800) zzz631900 == LT)",fontsize=16,color="burlywood",shape="box"];65142[label="zzz631900/Succ zzz6319000",fontsize=10,color="white",style="solid",shape="box"];62605 -> 65142[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65142 -> 62612[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65143[label="zzz631900/Zero",fontsize=10,color="white",style="solid",shape="box"];62605 -> 65143[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65143 -> 62613[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 62606[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat Zero zzz631900 == LT)",fontsize=16,color="burlywood",shape="box"];65144[label="zzz631900/Succ zzz6319000",fontsize=10,color="white",style="solid",shape="box"];62606 -> 65144[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65144 -> 62614[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65145[label="zzz631900/Zero",fontsize=10,color="white",style="solid",shape="box"];62606 -> 65145[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65145 -> 62615[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 62608 -> 62470[label="",style="dashed", color="red", weight=0]; 130.29/78.15 62608[label="FiniteMap.glueVBal3Size_l zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464",fontsize=16,color="magenta"];62607[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (FiniteMap.sIZE_RATIO * FiniteMap.glueVBal3Size_r zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 < zzz6343)",fontsize=16,color="black",shape="triangle"];62607 -> 62616[label="",style="solid", color="black", weight=3]; 130.29/78.15 63084[label="FiniteMap.glueVBal (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) zzz474033",fontsize=16,color="burlywood",shape="box"];65146[label="zzz474033/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];63084 -> 65146[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65146 -> 63358[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65147[label="zzz474033/FiniteMap.Branch zzz4740330 zzz4740331 zzz4740332 zzz4740333 zzz4740334",fontsize=10,color="white",style="solid",shape="box"];63084 -> 65147[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65147 -> 63359[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 63083[label="FiniteMap.mkBalBranch zzz474030 zzz474031 zzz6373 zzz474034",fontsize=16,color="black",shape="triangle"];63083 -> 63360[label="",style="solid", color="black", weight=3]; 130.29/78.15 62610[label="zzz63400",fontsize=16,color="green",shape="box"];62611[label="zzz631900",fontsize=16,color="green",shape="box"];13017[label="FiniteMap.splitGT1 (Pos zzz742) zzz743 zzz744 zzz745 zzz746 (Neg (Succ zzz747)) (Neg (Succ zzz747) < Pos zzz742)",fontsize=16,color="black",shape="box"];13017 -> 13268[label="",style="solid", color="black", weight=3]; 130.29/78.15 28601[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) zzz2761 zzz2762 zzz2763 zzz2764 (Maybe.isJust (Just zzz2766))",fontsize=16,color="black",shape="box"];28601 -> 28682[label="",style="solid", color="black", weight=3]; 130.29/78.15 8580[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264)) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];8580 -> 8817[label="",style="solid", color="black", weight=3]; 130.29/78.15 34163[label="zzz747",fontsize=16,color="green",shape="box"];34164[label="zzz7454",fontsize=16,color="green",shape="box"];34165[label="zzz7451",fontsize=16,color="green",shape="box"];34166[label="zzz745000",fontsize=16,color="green",shape="box"];34167[label="zzz7452",fontsize=16,color="green",shape="box"];34168[label="zzz7453",fontsize=16,color="green",shape="box"];34169[label="zzz745000",fontsize=16,color="green",shape="box"];34170[label="zzz747",fontsize=16,color="green",shape="box"];34162[label="FiniteMap.splitGT2 (Neg (Succ zzz3494)) zzz3495 zzz3496 zzz3497 zzz3498 (Neg (Succ zzz3499)) (primCmpNat zzz3500 zzz3501 == GT)",fontsize=16,color="burlywood",shape="triangle"];65148[label="zzz3500/Succ zzz35000",fontsize=10,color="white",style="solid",shape="box"];34162 -> 65148[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65148 -> 34259[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65149[label="zzz3500/Zero",fontsize=10,color="white",style="solid",shape="box"];34162 -> 65149[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65149 -> 34260[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 21967[label="zzz7452",fontsize=16,color="green",shape="box"];21968[label="zzz7451",fontsize=16,color="green",shape="box"];21969[label="zzz7453",fontsize=16,color="green",shape="box"];21970[label="zzz747",fontsize=16,color="green",shape="box"];21971[label="zzz7454",fontsize=16,color="green",shape="box"];14823[label="FiniteMap.splitGT2 (Neg Zero) zzz884 zzz885 zzz886 zzz887 (Neg (Succ zzz888)) (LT == GT)",fontsize=16,color="black",shape="triangle"];14823 -> 14881[label="",style="solid", color="black", weight=3]; 130.29/78.15 34274[label="zzz747",fontsize=16,color="green",shape="box"];34275[label="zzz7453",fontsize=16,color="green",shape="box"];34276[label="zzz7454",fontsize=16,color="green",shape="box"];34277[label="zzz747",fontsize=16,color="green",shape="box"];34278[label="zzz745000",fontsize=16,color="green",shape="box"];34279[label="zzz7451",fontsize=16,color="green",shape="box"];34280[label="zzz745000",fontsize=16,color="green",shape="box"];34281[label="zzz7452",fontsize=16,color="green",shape="box"];34273[label="FiniteMap.splitLT2 (Neg (Succ zzz3503)) zzz3504 zzz3505 zzz3506 zzz3507 (Neg (Succ zzz3508)) (primCmpNat zzz3509 zzz3510 == LT)",fontsize=16,color="burlywood",shape="triangle"];65150[label="zzz3509/Succ zzz35090",fontsize=10,color="white",style="solid",shape="box"];34273 -> 65150[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65150 -> 34362[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65151[label="zzz3509/Zero",fontsize=10,color="white",style="solid",shape="box"];34273 -> 65151[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65151 -> 34363[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 15229[label="FiniteMap.splitLT2 (Neg Zero) zzz7451 zzz7452 zzz7453 zzz7454 (Neg (Succ zzz747)) True",fontsize=16,color="black",shape="box"];15229 -> 15464[label="",style="solid", color="black", weight=3]; 130.29/78.15 5432 -> 4182[label="",style="dashed", color="red", weight=0]; 130.29/78.15 5432[label="FiniteMap.splitGT FiniteMap.EmptyFM (Neg (Succ zzz4000))",fontsize=16,color="magenta"];14550[label="FiniteMap.splitGT2 (Neg Zero) zzz884 zzz885 zzz886 zzz887 (Neg (Succ zzz888)) (primCmpNat Zero (Succ zzz888) == GT)",fontsize=16,color="black",shape="box"];14550 -> 14823[label="",style="solid", color="black", weight=3]; 130.29/78.15 29835 -> 12274[label="",style="dashed", color="red", weight=0]; 130.29/78.15 29835[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) zzz2889 zzz2890 zzz2891 zzz2892 (Maybe.isJust (FiniteMap.lookupFM zzz2897 (Neg (Succ zzz2888))))",fontsize=16,color="magenta"];29835 -> 29853[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 29835 -> 29854[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 29835 -> 29855[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 29835 -> 29856[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 29835 -> 29857[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 29835 -> 29858[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 29835 -> 29859[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 29835 -> 29860[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 29835 -> 29861[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 29835 -> 29862[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 29836[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) zzz2889 zzz2890 zzz2891 zzz2892 (Maybe.isJust (FiniteMap.lookupFM0 (Neg (Succ zzz2893)) zzz2894 zzz2895 zzz2896 zzz2897 (Neg (Succ zzz2888)) otherwise))",fontsize=16,color="black",shape="box"];29836 -> 29863[label="",style="solid", color="black", weight=3]; 130.29/78.15 14046 -> 4545[label="",style="dashed", color="red", weight=0]; 130.29/78.15 14046[label="FiniteMap.splitGT4 FiniteMap.EmptyFM (Neg Zero)",fontsize=16,color="magenta"];14047[label="FiniteMap.splitGT3 (FiniteMap.Branch zzz8330 zzz8331 zzz8332 zzz8333 zzz8334) (Neg Zero)",fontsize=16,color="black",shape="box"];14047 -> 14363[label="",style="solid", color="black", weight=3]; 130.29/78.15 14048 -> 12473[label="",style="dashed", color="red", weight=0]; 130.29/78.15 14048[label="FiniteMap.splitLT2 (Pos (Succ zzz833000)) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (LT == LT)",fontsize=16,color="magenta"];14048 -> 14364[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14048 -> 14365[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14048 -> 14366[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14048 -> 14367[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14048 -> 14368[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14049 -> 6083[label="",style="dashed", color="red", weight=0]; 130.29/78.15 14049[label="FiniteMap.splitLT2 (Pos Zero) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (EQ == LT)",fontsize=16,color="magenta"];14049 -> 14369[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14049 -> 14370[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14049 -> 14371[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14049 -> 14372[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14050[label="FiniteMap.splitLT2 (Neg (Succ zzz833000)) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (primCmpNat (Succ zzz833000) Zero == LT)",fontsize=16,color="black",shape="box"];14050 -> 14373[label="",style="solid", color="black", weight=3]; 130.29/78.15 14051 -> 6088[label="",style="dashed", color="red", weight=0]; 130.29/78.15 14051[label="FiniteMap.splitLT2 (Neg Zero) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (EQ == LT)",fontsize=16,color="magenta"];14051 -> 14374[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14051 -> 14375[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14051 -> 14376[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14051 -> 14377[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 7552[label="zzz33",fontsize=16,color="green",shape="box"];7553[label="zzz34",fontsize=16,color="green",shape="box"];63085[label="Pos zzz98200",fontsize=16,color="green",shape="box"];63086[label="zzz9824",fontsize=16,color="green",shape="box"];63087 -> 12360[label="",style="dashed", color="red", weight=0]; 130.29/78.15 63087[label="FiniteMap.addToFM_C FiniteMap.addToFM0 zzz9823 (Neg (Succ zzz3000)) zzz31",fontsize=16,color="magenta"];63087 -> 63361[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 63087 -> 63362[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 63088[label="zzz9821",fontsize=16,color="green",shape="box"];33398[label="zzz3000",fontsize=16,color="green",shape="box"];33399[label="zzz31",fontsize=16,color="green",shape="box"];33400[label="zzz9823",fontsize=16,color="green",shape="box"];33401[label="zzz3000",fontsize=16,color="green",shape="box"];33402[label="zzz9822",fontsize=16,color="green",shape="box"];33403[label="zzz982000",fontsize=16,color="green",shape="box"];33404[label="zzz982000",fontsize=16,color="green",shape="box"];33405[label="zzz9821",fontsize=16,color="green",shape="box"];33406[label="zzz9824",fontsize=16,color="green",shape="box"];33397[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz3386)) zzz3387 zzz3388 zzz3389 zzz3390 (Neg (Succ zzz3391)) zzz3392 (primCmpNat zzz3393 zzz3394 == LT)",fontsize=16,color="burlywood",shape="triangle"];65152[label="zzz3393/Succ zzz33930",fontsize=10,color="white",style="solid",shape="box"];33397 -> 65152[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65152 -> 33488[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65153[label="zzz3393/Zero",fontsize=10,color="white",style="solid",shape="box"];33397 -> 65153[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65153 -> 33489[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 13826[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg (Succ zzz3000)) zzz31 True",fontsize=16,color="black",shape="box"];13826 -> 14059[label="",style="solid", color="black", weight=3]; 130.29/78.15 13827 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.15 13827[label="FiniteMap.mkBalBranch (Pos (Succ zzz982000)) zzz9821 (FiniteMap.addToFM_C FiniteMap.addToFM0 zzz9823 (Neg Zero) zzz31) zzz9824",fontsize=16,color="magenta"];13827 -> 63097[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 13827 -> 63098[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 13827 -> 63099[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 13827 -> 63100[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 13828[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (Neg Zero > Pos Zero)",fontsize=16,color="black",shape="box"];13828 -> 14064[label="",style="solid", color="black", weight=3]; 130.29/78.15 13829[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz982000)) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 False",fontsize=16,color="black",shape="box"];13829 -> 14065[label="",style="solid", color="black", weight=3]; 130.29/78.15 13830[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (Neg Zero > Neg Zero)",fontsize=16,color="black",shape="box"];13830 -> 14066[label="",style="solid", color="black", weight=3]; 130.29/78.15 7557[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ (Succ Zero)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];7557 -> 7778[label="",style="solid", color="black", weight=3]; 130.29/78.15 7558[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos Zero) zzz342 == LT)",fontsize=16,color="burlywood",shape="box"];65154[label="zzz342/Pos zzz3420",fontsize=10,color="white",style="solid",shape="box"];7558 -> 65154[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65154 -> 7779[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65155[label="zzz342/Neg zzz3420",fontsize=10,color="white",style="solid",shape="box"];7558 -> 65155[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65155 -> 7780[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 7559[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ (Succ Zero)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];7559 -> 7781[label="",style="solid", color="black", weight=3]; 130.29/78.15 7560[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg Zero) zzz342 == LT)",fontsize=16,color="burlywood",shape="box"];65156[label="zzz342/Pos zzz3420",fontsize=10,color="white",style="solid",shape="box"];7560 -> 65156[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65156 -> 7782[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65157[label="zzz342/Neg zzz3420",fontsize=10,color="white",style="solid",shape="box"];7560 -> 65157[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65157 -> 7783[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 4192[label="FiniteMap.splitGT FiniteMap.EmptyFM (Neg Zero)",fontsize=16,color="black",shape="triangle"];4192 -> 4545[label="",style="solid", color="black", weight=3]; 130.29/78.15 5680[label="FiniteMap.splitLT1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Neg Zero) (compare (Neg Zero) (Neg (Succ zzz3000)) == GT)",fontsize=16,color="black",shape="box"];5680 -> 6150[label="",style="solid", color="black", weight=3]; 130.29/78.15 20335 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.15 20335[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero)) zzz1602",fontsize=16,color="magenta"];20335 -> 20409[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20335 -> 20410[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20336 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.15 20336[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero)) zzz1601",fontsize=16,color="magenta"];20336 -> 20411[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20336 -> 20412[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20337[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero) zzz1599 zzz1600 zzz1601 zzz1602 True",fontsize=16,color="black",shape="box"];20337 -> 20413[label="",style="solid", color="black", weight=3]; 130.29/78.15 20338[label="zzz1607",fontsize=16,color="green",shape="box"];7561[label="zzz33",fontsize=16,color="green",shape="box"];7562[label="zzz34",fontsize=16,color="green",shape="box"];33666[label="FiniteMap.splitGT2 (Pos (Succ zzz3396)) zzz3397 zzz3398 zzz3399 zzz3400 (Pos (Succ zzz3401)) (primCmpNat (Succ zzz34020) zzz3403 == GT)",fontsize=16,color="burlywood",shape="box"];65158[label="zzz3403/Succ zzz34030",fontsize=10,color="white",style="solid",shape="box"];33666 -> 65158[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65158 -> 33691[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65159[label="zzz3403/Zero",fontsize=10,color="white",style="solid",shape="box"];33666 -> 65159[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65159 -> 33692[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 33667[label="FiniteMap.splitGT2 (Pos (Succ zzz3396)) zzz3397 zzz3398 zzz3399 zzz3400 (Pos (Succ zzz3401)) (primCmpNat Zero zzz3403 == GT)",fontsize=16,color="burlywood",shape="box"];65160[label="zzz3403/Succ zzz34030",fontsize=10,color="white",style="solid",shape="box"];33667 -> 65160[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65160 -> 33693[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65161[label="zzz3403/Zero",fontsize=10,color="white",style="solid",shape="box"];33667 -> 65161[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65161 -> 33694[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 21062 -> 19598[label="",style="dashed", color="red", weight=0]; 130.29/78.15 21062[label="FiniteMap.splitGT zzz16124 (Pos (Succ zzz1613))",fontsize=16,color="magenta"];21062 -> 21285[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 34522[label="zzz3077",fontsize=16,color="green",shape="box"];34523[label="zzz3078",fontsize=16,color="green",shape="box"];34524[label="zzz3072",fontsize=16,color="green",shape="box"];34525[label="zzz3074",fontsize=16,color="green",shape="box"];34526[label="zzz3079",fontsize=16,color="green",shape="box"];34527[label="zzz3080",fontsize=16,color="green",shape="box"];34528[label="Succ zzz3077",fontsize=16,color="green",shape="box"];34529[label="zzz3075",fontsize=16,color="green",shape="box"];34530[label="zzz3070",fontsize=16,color="green",shape="box"];34531[label="Succ zzz3072",fontsize=16,color="green",shape="box"];34532[label="zzz3068",fontsize=16,color="green",shape="box"];34533[label="zzz3081",fontsize=16,color="green",shape="box"];34534[label="zzz3069",fontsize=16,color="green",shape="box"];34535[label="zzz3073",fontsize=16,color="green",shape="box"];34536[label="zzz3076",fontsize=16,color="green",shape="box"];34537[label="zzz3071",fontsize=16,color="green",shape="box"];34521[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) zzz3530 zzz3531 zzz3532 zzz3533 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3534)) zzz3535 zzz3536 zzz3537 zzz3538 (Pos (Succ zzz3529)) (primCmpNat zzz3539 zzz3540 == GT)))",fontsize=16,color="burlywood",shape="triangle"];65162[label="zzz3539/Succ zzz35390",fontsize=10,color="white",style="solid",shape="box"];34521 -> 65162[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65162 -> 34698[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65163[label="zzz3539/Zero",fontsize=10,color="white",style="solid",shape="box"];34521 -> 65163[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65163 -> 34699[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 29294[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 otherwise",fontsize=16,color="black",shape="box"];29294 -> 29322[label="",style="solid", color="black", weight=3]; 130.29/78.15 31413 -> 31188[label="",style="dashed", color="red", weight=0]; 130.29/78.15 31413[label="FiniteMap.splitLT2 (Pos (Succ zzz3133)) zzz3134 zzz3135 zzz3136 zzz3137 (Pos (Succ zzz3138)) (primCmpNat zzz31390 zzz31400 == LT)",fontsize=16,color="magenta"];31413 -> 31845[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31413 -> 31846[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31414[label="FiniteMap.splitLT2 (Pos (Succ zzz3133)) zzz3134 zzz3135 zzz3136 zzz3137 (Pos (Succ zzz3138)) (GT == LT)",fontsize=16,color="black",shape="box"];31414 -> 31847[label="",style="solid", color="black", weight=3]; 130.29/78.15 31415[label="FiniteMap.splitLT2 (Pos (Succ zzz3133)) zzz3134 zzz3135 zzz3136 zzz3137 (Pos (Succ zzz3138)) (LT == LT)",fontsize=16,color="black",shape="box"];31415 -> 31848[label="",style="solid", color="black", weight=3]; 130.29/78.15 31416[label="FiniteMap.splitLT2 (Pos (Succ zzz3133)) zzz3134 zzz3135 zzz3136 zzz3137 (Pos (Succ zzz3138)) (EQ == LT)",fontsize=16,color="black",shape="box"];31416 -> 31849[label="",style="solid", color="black", weight=3]; 130.29/78.15 22526[label="FiniteMap.splitLT1 (Pos Zero) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) (primCmpInt (Pos (Succ zzz1975)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];22526 -> 22617[label="",style="solid", color="black", weight=3]; 130.29/78.15 22527[label="FiniteMap.splitLT1 (Neg zzz19700) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) True",fontsize=16,color="black",shape="box"];22527 -> 22618[label="",style="solid", color="black", weight=3]; 130.29/78.15 32022 -> 31655[label="",style="dashed", color="red", weight=0]; 130.29/78.15 32022[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) zzz3169 zzz3170 zzz3171 zzz3172 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3173)) zzz3174 zzz3175 zzz3176 zzz3177 (Pos (Succ zzz3168)) (primCmpNat zzz31780 zzz31790 == GT)))",fontsize=16,color="magenta"];32022 -> 32057[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 32022 -> 32058[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 32023[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) zzz3169 zzz3170 zzz3171 zzz3172 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3173)) zzz3174 zzz3175 zzz3176 zzz3177 (Pos (Succ zzz3168)) (GT == GT)))",fontsize=16,color="black",shape="box"];32023 -> 32059[label="",style="solid", color="black", weight=3]; 130.29/78.15 32024[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) zzz3169 zzz3170 zzz3171 zzz3172 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3173)) zzz3174 zzz3175 zzz3176 zzz3177 (Pos (Succ zzz3168)) (LT == GT)))",fontsize=16,color="black",shape="box"];32024 -> 32060[label="",style="solid", color="black", weight=3]; 130.29/78.15 32025[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) zzz3169 zzz3170 zzz3171 zzz3172 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3173)) zzz3174 zzz3175 zzz3176 zzz3177 (Pos (Succ zzz3168)) (EQ == GT)))",fontsize=16,color="black",shape="box"];32025 -> 32061[label="",style="solid", color="black", weight=3]; 130.29/78.15 18968 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.15 18968[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387))) zzz1391",fontsize=16,color="magenta"];18968 -> 19223[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 18968 -> 19224[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 18969 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.15 18969[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387))) zzz1390",fontsize=16,color="magenta"];18969 -> 19225[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 18969 -> 19226[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 11992[label="FiniteMap.splitGT2 (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622 (Pos Zero) (primCmpInt (Pos Zero) (Pos (Succ zzz618)) == GT)",fontsize=16,color="black",shape="box"];11992 -> 12107[label="",style="solid", color="black", weight=3]; 130.29/78.15 11993[label="FiniteMap.splitLT2 (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622 (Pos Zero) (primCmpInt (Pos Zero) (Pos (Succ zzz618)) == LT)",fontsize=16,color="black",shape="box"];11993 -> 12108[label="",style="solid", color="black", weight=3]; 130.29/78.15 32026[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz3181)) zzz3182 zzz3183 zzz3184 zzz3185 (Pos (Succ zzz3186)) zzz3187 (primCmpNat (Succ zzz31880) (Succ zzz31890) == LT)",fontsize=16,color="black",shape="box"];32026 -> 32062[label="",style="solid", color="black", weight=3]; 130.29/78.15 32027[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz3181)) zzz3182 zzz3183 zzz3184 zzz3185 (Pos (Succ zzz3186)) zzz3187 (primCmpNat (Succ zzz31880) Zero == LT)",fontsize=16,color="black",shape="box"];32027 -> 32063[label="",style="solid", color="black", weight=3]; 130.29/78.15 32028[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz3181)) zzz3182 zzz3183 zzz3184 zzz3185 (Pos (Succ zzz3186)) zzz3187 (primCmpNat Zero (Succ zzz31890) == LT)",fontsize=16,color="black",shape="box"];32028 -> 32064[label="",style="solid", color="black", weight=3]; 130.29/78.15 32029[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz3181)) zzz3182 zzz3183 zzz3184 zzz3185 (Pos (Succ zzz3186)) zzz3187 (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];32029 -> 32065[label="",style="solid", color="black", weight=3]; 130.29/78.15 6303[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 (compare (Pos (Succ zzz3000)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];6303 -> 6366[label="",style="solid", color="black", weight=3]; 130.29/78.15 6304[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg zzz3400) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 (GT == GT)",fontsize=16,color="black",shape="box"];6304 -> 6367[label="",style="solid", color="black", weight=3]; 130.29/78.15 63089[label="Pos (Succ zzz34000)",fontsize=16,color="green",shape="box"];63090[label="zzz344",fontsize=16,color="green",shape="box"];63091 -> 4379[label="",style="dashed", color="red", weight=0]; 130.29/78.15 63091[label="FiniteMap.addToFM_C FiniteMap.addToFM0 zzz343 (Pos Zero) zzz31",fontsize=16,color="magenta"];63091 -> 63363[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 63091 -> 63364[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 63092[label="zzz341",fontsize=16,color="green",shape="box"];6347[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (primCmpInt (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];6347 -> 6559[label="",style="solid", color="black", weight=3]; 130.29/78.15 6348[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz34000)) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (primCmpInt (Pos Zero) (Neg (Succ zzz34000)) == GT)",fontsize=16,color="black",shape="box"];6348 -> 6560[label="",style="solid", color="black", weight=3]; 130.29/78.15 6349[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (primCmpInt (Pos Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];6349 -> 6561[label="",style="solid", color="black", weight=3]; 130.29/78.15 6350[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ Zero) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];6350 -> 6562[label="",style="solid", color="black", weight=3]; 130.29/78.15 6351[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (primCmpInt (Pos Zero) (Pos zzz3420) == LT)",fontsize=16,color="burlywood",shape="box"];65164[label="zzz3420/Succ zzz34200",fontsize=10,color="white",style="solid",shape="box"];6351 -> 65164[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65164 -> 6563[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65165[label="zzz3420/Zero",fontsize=10,color="white",style="solid",shape="box"];6351 -> 65165[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65165 -> 6564[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 6352[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (Pos Zero) (Neg zzz3420) == LT)",fontsize=16,color="burlywood",shape="box"];65166[label="zzz3420/Succ zzz34200",fontsize=10,color="white",style="solid",shape="box"];6352 -> 65166[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65166 -> 6565[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65167[label="zzz3420/Zero",fontsize=10,color="white",style="solid",shape="box"];6352 -> 65167[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65167 -> 6566[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 6353[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ Zero) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];6353 -> 6567[label="",style="solid", color="black", weight=3]; 130.29/78.15 6354[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (primCmpInt (Neg Zero) (Pos zzz3420) == LT)",fontsize=16,color="burlywood",shape="box"];65168[label="zzz3420/Succ zzz34200",fontsize=10,color="white",style="solid",shape="box"];6354 -> 65168[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65168 -> 6568[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65169[label="zzz3420/Zero",fontsize=10,color="white",style="solid",shape="box"];6354 -> 65169[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65169 -> 6569[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 6355[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (Neg Zero) (Neg zzz3420) == LT)",fontsize=16,color="burlywood",shape="box"];65170[label="zzz3420/Succ zzz34200",fontsize=10,color="white",style="solid",shape="box"];6355 -> 65170[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65170 -> 6570[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65171[label="zzz3420/Zero",fontsize=10,color="white",style="solid",shape="box"];6355 -> 65171[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65171 -> 6571[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 5770 -> 6244[label="",style="dashed", color="red", weight=0]; 130.29/78.15 5770[label="FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 zzz33 (FiniteMap.splitLT FiniteMap.EmptyFM (Pos Zero))",fontsize=16,color="magenta"];5770 -> 6257[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 17808[label="FiniteMap.splitGT (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero)",fontsize=16,color="black",shape="box"];17808 -> 17873[label="",style="solid", color="black", weight=3]; 130.29/78.15 17809 -> 12322[label="",style="dashed", color="red", weight=0]; 130.29/78.15 17809[label="FiniteMap.splitLT (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero)",fontsize=16,color="magenta"];17809 -> 17874[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 17810 -> 17697[label="",style="dashed", color="red", weight=0]; 130.29/78.15 17810[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero)",fontsize=16,color="magenta"];17811[label="zzz1199",fontsize=16,color="green",shape="box"];17812 -> 17695[label="",style="dashed", color="red", weight=0]; 130.29/78.15 17812[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero)",fontsize=16,color="magenta"];17813[label="zzz1200",fontsize=16,color="green",shape="box"];17814[label="zzz1197",fontsize=16,color="green",shape="box"];43511 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.15 43511[label="primPlusNat (primMulNat (Succ (Succ Zero)) (Succ zzz4739)) (Succ zzz4739)",fontsize=16,color="magenta"];43511 -> 43534[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 43511 -> 43535[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 43512 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.15 43512[label="primPlusNat zzz50920000 zzz542000",fontsize=16,color="magenta"];43512 -> 43536[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 43512 -> 43537[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 62612[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat (Succ zzz633800) (Succ zzz6319000) == LT)",fontsize=16,color="black",shape="box"];62612 -> 62623[label="",style="solid", color="black", weight=3]; 130.29/78.15 62613[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat (Succ zzz633800) Zero == LT)",fontsize=16,color="black",shape="box"];62613 -> 62624[label="",style="solid", color="black", weight=3]; 130.29/78.15 62614[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat Zero (Succ zzz6319000) == LT)",fontsize=16,color="black",shape="box"];62614 -> 62625[label="",style="solid", color="black", weight=3]; 130.29/78.15 62615[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];62615 -> 62626[label="",style="solid", color="black", weight=3]; 130.29/78.15 62616[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (compare (FiniteMap.sIZE_RATIO * FiniteMap.glueVBal3Size_r zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) zzz6343 == LT)",fontsize=16,color="black",shape="box"];62616 -> 62627[label="",style="solid", color="black", weight=3]; 130.29/78.15 63358[label="FiniteMap.glueVBal (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];63358 -> 63573[label="",style="solid", color="black", weight=3]; 130.29/78.15 63359[label="FiniteMap.glueVBal (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz4740330 zzz4740331 zzz4740332 zzz4740333 zzz4740334)",fontsize=16,color="black",shape="box"];63359 -> 63574[label="",style="solid", color="black", weight=3]; 130.29/78.15 63360[label="FiniteMap.mkBalBranch6 zzz474030 zzz474031 zzz6373 zzz474034",fontsize=16,color="black",shape="box"];63360 -> 63575[label="",style="solid", color="black", weight=3]; 130.29/78.15 13268[label="FiniteMap.splitGT1 (Pos zzz742) zzz743 zzz744 zzz745 zzz746 (Neg (Succ zzz747)) (compare (Neg (Succ zzz747)) (Pos zzz742) == LT)",fontsize=16,color="black",shape="box"];13268 -> 13470[label="",style="solid", color="black", weight=3]; 130.29/78.15 28682[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760)) zzz2761 zzz2762 zzz2763 zzz2764 True",fontsize=16,color="black",shape="box"];28682 -> 28739[label="",style="solid", color="black", weight=3]; 130.29/78.15 8817[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264)) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];8817 -> 9324[label="",style="solid", color="black", weight=3]; 130.29/78.15 34259[label="FiniteMap.splitGT2 (Neg (Succ zzz3494)) zzz3495 zzz3496 zzz3497 zzz3498 (Neg (Succ zzz3499)) (primCmpNat (Succ zzz35000) zzz3501 == GT)",fontsize=16,color="burlywood",shape="box"];65172[label="zzz3501/Succ zzz35010",fontsize=10,color="white",style="solid",shape="box"];34259 -> 65172[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65172 -> 34364[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65173[label="zzz3501/Zero",fontsize=10,color="white",style="solid",shape="box"];34259 -> 65173[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65173 -> 34365[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 34260[label="FiniteMap.splitGT2 (Neg (Succ zzz3494)) zzz3495 zzz3496 zzz3497 zzz3498 (Neg (Succ zzz3499)) (primCmpNat Zero zzz3501 == GT)",fontsize=16,color="burlywood",shape="box"];65174[label="zzz3501/Succ zzz35010",fontsize=10,color="white",style="solid",shape="box"];34260 -> 65174[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65174 -> 34366[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65175[label="zzz3501/Zero",fontsize=10,color="white",style="solid",shape="box"];34260 -> 65175[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65175 -> 34367[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 14881[label="FiniteMap.splitGT2 (Neg Zero) zzz884 zzz885 zzz886 zzz887 (Neg (Succ zzz888)) False",fontsize=16,color="black",shape="box"];14881 -> 14928[label="",style="solid", color="black", weight=3]; 130.29/78.15 34362[label="FiniteMap.splitLT2 (Neg (Succ zzz3503)) zzz3504 zzz3505 zzz3506 zzz3507 (Neg (Succ zzz3508)) (primCmpNat (Succ zzz35090) zzz3510 == LT)",fontsize=16,color="burlywood",shape="box"];65176[label="zzz3510/Succ zzz35100",fontsize=10,color="white",style="solid",shape="box"];34362 -> 65176[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65176 -> 34462[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65177[label="zzz3510/Zero",fontsize=10,color="white",style="solid",shape="box"];34362 -> 65177[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65177 -> 34463[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 34363[label="FiniteMap.splitLT2 (Neg (Succ zzz3503)) zzz3504 zzz3505 zzz3506 zzz3507 (Neg (Succ zzz3508)) (primCmpNat Zero zzz3510 == LT)",fontsize=16,color="burlywood",shape="box"];65178[label="zzz3510/Succ zzz35100",fontsize=10,color="white",style="solid",shape="box"];34363 -> 65178[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65178 -> 34464[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65179[label="zzz3510/Zero",fontsize=10,color="white",style="solid",shape="box"];34363 -> 65179[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65179 -> 34465[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 15464 -> 13018[label="",style="dashed", color="red", weight=0]; 130.29/78.15 15464[label="FiniteMap.splitLT zzz7453 (Neg (Succ zzz747))",fontsize=16,color="magenta"];15464 -> 15738[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 29853[label="zzz2885",fontsize=16,color="green",shape="box"];29854[label="zzz2884",fontsize=16,color="green",shape="box"];29855[label="zzz2897",fontsize=16,color="green",shape="box"];29856[label="zzz2892",fontsize=16,color="green",shape="box"];29857[label="zzz2890",fontsize=16,color="green",shape="box"];29858[label="zzz2891",fontsize=16,color="green",shape="box"];29859[label="zzz2886",fontsize=16,color="green",shape="box"];29860[label="zzz2889",fontsize=16,color="green",shape="box"];29861[label="zzz2888",fontsize=16,color="green",shape="box"];29862[label="zzz2887",fontsize=16,color="green",shape="box"];29863[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) zzz2889 zzz2890 zzz2891 zzz2892 (Maybe.isJust (FiniteMap.lookupFM0 (Neg (Succ zzz2893)) zzz2894 zzz2895 zzz2896 zzz2897 (Neg (Succ zzz2888)) True))",fontsize=16,color="black",shape="box"];29863 -> 29921[label="",style="solid", color="black", weight=3]; 130.29/78.15 4545[label="FiniteMap.splitGT4 FiniteMap.EmptyFM (Neg Zero)",fontsize=16,color="black",shape="triangle"];4545 -> 5155[label="",style="solid", color="black", weight=3]; 130.29/78.15 14363[label="FiniteMap.splitGT2 zzz8330 zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (Neg Zero > zzz8330)",fontsize=16,color="black",shape="box"];14363 -> 14450[label="",style="solid", color="black", weight=3]; 130.29/78.15 14364[label="zzz8331",fontsize=16,color="green",shape="box"];14365[label="zzz833000",fontsize=16,color="green",shape="box"];14366[label="zzz8332",fontsize=16,color="green",shape="box"];14367[label="zzz8334",fontsize=16,color="green",shape="box"];14368[label="zzz8333",fontsize=16,color="green",shape="box"];14369[label="zzz8332",fontsize=16,color="green",shape="box"];14370[label="zzz8334",fontsize=16,color="green",shape="box"];14371[label="zzz8333",fontsize=16,color="green",shape="box"];14372[label="zzz8331",fontsize=16,color="green",shape="box"];14373[label="FiniteMap.splitLT2 (Neg (Succ zzz833000)) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (GT == LT)",fontsize=16,color="black",shape="triangle"];14373 -> 14451[label="",style="solid", color="black", weight=3]; 130.29/78.15 14374[label="zzz8332",fontsize=16,color="green",shape="box"];14375[label="zzz8334",fontsize=16,color="green",shape="box"];14376[label="zzz8333",fontsize=16,color="green",shape="box"];14377[label="zzz8331",fontsize=16,color="green",shape="box"];63361[label="zzz9823",fontsize=16,color="green",shape="box"];63362[label="Succ zzz3000",fontsize=16,color="green",shape="box"];33488[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz3386)) zzz3387 zzz3388 zzz3389 zzz3390 (Neg (Succ zzz3391)) zzz3392 (primCmpNat (Succ zzz33930) zzz3394 == LT)",fontsize=16,color="burlywood",shape="box"];65180[label="zzz3394/Succ zzz33940",fontsize=10,color="white",style="solid",shape="box"];33488 -> 65180[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65180 -> 33668[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65181[label="zzz3394/Zero",fontsize=10,color="white",style="solid",shape="box"];33488 -> 65181[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65181 -> 33669[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 33489[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz3386)) zzz3387 zzz3388 zzz3389 zzz3390 (Neg (Succ zzz3391)) zzz3392 (primCmpNat Zero zzz3394 == LT)",fontsize=16,color="burlywood",shape="box"];65182[label="zzz3394/Succ zzz33940",fontsize=10,color="white",style="solid",shape="box"];33489 -> 65182[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65182 -> 33670[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65183[label="zzz3394/Zero",fontsize=10,color="white",style="solid",shape="box"];33489 -> 65183[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65183 -> 33671[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 14059 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.15 14059[label="FiniteMap.mkBalBranch (Neg Zero) zzz9821 (FiniteMap.addToFM_C FiniteMap.addToFM0 zzz9823 (Neg (Succ zzz3000)) zzz31) zzz9824",fontsize=16,color="magenta"];14059 -> 63101[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14059 -> 63102[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14059 -> 63103[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 14059 -> 63104[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 63097[label="Pos (Succ zzz982000)",fontsize=16,color="green",shape="box"];63098[label="zzz9824",fontsize=16,color="green",shape="box"];63099 -> 12360[label="",style="dashed", color="red", weight=0]; 130.29/78.15 63099[label="FiniteMap.addToFM_C FiniteMap.addToFM0 zzz9823 (Neg Zero) zzz31",fontsize=16,color="magenta"];63099 -> 63365[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 63099 -> 63366[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 63100[label="zzz9821",fontsize=16,color="green",shape="box"];14064[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (compare (Neg Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];14064 -> 14390[label="",style="solid", color="black", weight=3]; 130.29/78.15 14065[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz982000)) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (Neg Zero > Neg (Succ zzz982000))",fontsize=16,color="black",shape="box"];14065 -> 14391[label="",style="solid", color="black", weight=3]; 130.29/78.15 14066[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (compare (Neg Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];14066 -> 14392[label="",style="solid", color="black", weight=3]; 130.29/78.15 7778[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ Zero) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];7778 -> 8004[label="",style="solid", color="black", weight=3]; 130.29/78.15 7779[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (primCmpInt (Pos Zero) (Pos zzz3420) == LT)",fontsize=16,color="burlywood",shape="box"];65184[label="zzz3420/Succ zzz34200",fontsize=10,color="white",style="solid",shape="box"];7779 -> 65184[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65184 -> 8005[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65185[label="zzz3420/Zero",fontsize=10,color="white",style="solid",shape="box"];7779 -> 65185[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65185 -> 8006[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 7780[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (Pos Zero) (Neg zzz3420) == LT)",fontsize=16,color="burlywood",shape="box"];65186[label="zzz3420/Succ zzz34200",fontsize=10,color="white",style="solid",shape="box"];7780 -> 65186[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65186 -> 8007[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65187[label="zzz3420/Zero",fontsize=10,color="white",style="solid",shape="box"];7780 -> 65187[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65187 -> 8008[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 7781[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ Zero) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];7781 -> 8009[label="",style="solid", color="black", weight=3]; 130.29/78.15 7782[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (primCmpInt (Neg Zero) (Pos zzz3420) == LT)",fontsize=16,color="burlywood",shape="box"];65188[label="zzz3420/Succ zzz34200",fontsize=10,color="white",style="solid",shape="box"];7782 -> 65188[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65188 -> 8010[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65189[label="zzz3420/Zero",fontsize=10,color="white",style="solid",shape="box"];7782 -> 65189[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65189 -> 8011[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 7783[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (Neg Zero) (Neg zzz3420) == LT)",fontsize=16,color="burlywood",shape="box"];65190[label="zzz3420/Succ zzz34200",fontsize=10,color="white",style="solid",shape="box"];7783 -> 65190[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65190 -> 8012[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65191[label="zzz3420/Zero",fontsize=10,color="white",style="solid",shape="box"];7783 -> 65191[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65191 -> 8013[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 6150[label="FiniteMap.splitLT1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ zzz3000)) == GT)",fontsize=16,color="black",shape="box"];6150 -> 6856[label="",style="solid", color="black", weight=3]; 130.29/78.15 20409[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero)",fontsize=16,color="black",shape="triangle"];20409 -> 20481[label="",style="solid", color="black", weight=3]; 130.29/78.15 20410[label="zzz1602",fontsize=16,color="green",shape="box"];20411[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero)",fontsize=16,color="black",shape="triangle"];20411 -> 20482[label="",style="solid", color="black", weight=3]; 130.29/78.15 20412[label="zzz1601",fontsize=16,color="green",shape="box"];20413 -> 5407[label="",style="dashed", color="red", weight=0]; 130.29/78.15 20413[label="FiniteMap.mkVBalBranch (Neg Zero) (FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero)) zzz1599) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero)) zzz1601) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero)) zzz1602)",fontsize=16,color="magenta"];20413 -> 20483[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20413 -> 20484[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20413 -> 20485[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 33691[label="FiniteMap.splitGT2 (Pos (Succ zzz3396)) zzz3397 zzz3398 zzz3399 zzz3400 (Pos (Succ zzz3401)) (primCmpNat (Succ zzz34020) (Succ zzz34030) == GT)",fontsize=16,color="black",shape="box"];33691 -> 33710[label="",style="solid", color="black", weight=3]; 130.29/78.15 33692[label="FiniteMap.splitGT2 (Pos (Succ zzz3396)) zzz3397 zzz3398 zzz3399 zzz3400 (Pos (Succ zzz3401)) (primCmpNat (Succ zzz34020) Zero == GT)",fontsize=16,color="black",shape="box"];33692 -> 33711[label="",style="solid", color="black", weight=3]; 130.29/78.15 33693[label="FiniteMap.splitGT2 (Pos (Succ zzz3396)) zzz3397 zzz3398 zzz3399 zzz3400 (Pos (Succ zzz3401)) (primCmpNat Zero (Succ zzz34030) == GT)",fontsize=16,color="black",shape="box"];33693 -> 33712[label="",style="solid", color="black", weight=3]; 130.29/78.15 33694[label="FiniteMap.splitGT2 (Pos (Succ zzz3396)) zzz3397 zzz3398 zzz3399 zzz3400 (Pos (Succ zzz3401)) (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];33694 -> 33713[label="",style="solid", color="black", weight=3]; 130.29/78.15 21285[label="zzz16124",fontsize=16,color="green",shape="box"];34698[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) zzz3530 zzz3531 zzz3532 zzz3533 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3534)) zzz3535 zzz3536 zzz3537 zzz3538 (Pos (Succ zzz3529)) (primCmpNat (Succ zzz35390) zzz3540 == GT)))",fontsize=16,color="burlywood",shape="box"];65192[label="zzz3540/Succ zzz35400",fontsize=10,color="white",style="solid",shape="box"];34698 -> 65192[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65192 -> 34770[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65193[label="zzz3540/Zero",fontsize=10,color="white",style="solid",shape="box"];34698 -> 65193[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65193 -> 34771[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 34699[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) zzz3530 zzz3531 zzz3532 zzz3533 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3534)) zzz3535 zzz3536 zzz3537 zzz3538 (Pos (Succ zzz3529)) (primCmpNat Zero zzz3540 == GT)))",fontsize=16,color="burlywood",shape="box"];65194[label="zzz3540/Succ zzz35400",fontsize=10,color="white",style="solid",shape="box"];34699 -> 65194[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65194 -> 34772[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65195[label="zzz3540/Zero",fontsize=10,color="white",style="solid",shape="box"];34699 -> 65195[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65195 -> 34773[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 29322[label="FiniteMap.intersectFM_C2IntersectFM_C0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738)) zzz2739 zzz2740 zzz2741 zzz2742 True",fontsize=16,color="black",shape="box"];29322 -> 29598[label="",style="solid", color="black", weight=3]; 130.29/78.15 31845[label="zzz31390",fontsize=16,color="green",shape="box"];31846[label="zzz31400",fontsize=16,color="green",shape="box"];31847[label="FiniteMap.splitLT2 (Pos (Succ zzz3133)) zzz3134 zzz3135 zzz3136 zzz3137 (Pos (Succ zzz3138)) False",fontsize=16,color="black",shape="triangle"];31847 -> 31955[label="",style="solid", color="black", weight=3]; 130.29/78.15 31848[label="FiniteMap.splitLT2 (Pos (Succ zzz3133)) zzz3134 zzz3135 zzz3136 zzz3137 (Pos (Succ zzz3138)) True",fontsize=16,color="black",shape="box"];31848 -> 31956[label="",style="solid", color="black", weight=3]; 130.29/78.15 31849 -> 31847[label="",style="dashed", color="red", weight=0]; 130.29/78.15 31849[label="FiniteMap.splitLT2 (Pos (Succ zzz3133)) zzz3134 zzz3135 zzz3136 zzz3137 (Pos (Succ zzz3138)) False",fontsize=16,color="magenta"];22617[label="FiniteMap.splitLT1 (Pos Zero) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) (primCmpNat (Succ zzz1975) Zero == GT)",fontsize=16,color="black",shape="box"];22617 -> 22667[label="",style="solid", color="black", weight=3]; 130.29/78.15 22618[label="FiniteMap.mkVBalBranch (Neg zzz19700) zzz1971 zzz1973 (FiniteMap.splitLT zzz1974 (Pos (Succ zzz1975)))",fontsize=16,color="burlywood",shape="box"];65196[label="zzz1973/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];22618 -> 65196[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65196 -> 22668[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65197[label="zzz1973/FiniteMap.Branch zzz19730 zzz19731 zzz19732 zzz19733 zzz19734",fontsize=10,color="white",style="solid",shape="box"];22618 -> 65197[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65197 -> 22669[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 32057[label="zzz31780",fontsize=16,color="green",shape="box"];32058[label="zzz31790",fontsize=16,color="green",shape="box"];32059[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) zzz3169 zzz3170 zzz3171 zzz3172 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3173)) zzz3174 zzz3175 zzz3176 zzz3177 (Pos (Succ zzz3168)) True))",fontsize=16,color="black",shape="box"];32059 -> 32217[label="",style="solid", color="black", weight=3]; 130.29/78.15 32060[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) zzz3169 zzz3170 zzz3171 zzz3172 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3173)) zzz3174 zzz3175 zzz3176 zzz3177 (Pos (Succ zzz3168)) False))",fontsize=16,color="black",shape="triangle"];32060 -> 32218[label="",style="solid", color="black", weight=3]; 130.29/78.15 32061 -> 32060[label="",style="dashed", color="red", weight=0]; 130.29/78.15 32061[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) zzz3169 zzz3170 zzz3171 zzz3172 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3173)) zzz3174 zzz3175 zzz3176 zzz3177 (Pos (Succ zzz3168)) False))",fontsize=16,color="magenta"];19223[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387))",fontsize=16,color="black",shape="triangle"];19223 -> 19449[label="",style="solid", color="black", weight=3]; 130.29/78.15 19224[label="zzz1391",fontsize=16,color="green",shape="box"];19225[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387))",fontsize=16,color="black",shape="triangle"];19225 -> 19450[label="",style="solid", color="black", weight=3]; 130.29/78.15 19226[label="zzz1390",fontsize=16,color="green",shape="box"];12107[label="FiniteMap.splitGT2 (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622 (Pos Zero) (primCmpNat Zero (Succ zzz618) == GT)",fontsize=16,color="black",shape="triangle"];12107 -> 12173[label="",style="solid", color="black", weight=3]; 130.29/78.15 12108[label="FiniteMap.splitLT2 (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622 (Pos Zero) (primCmpNat Zero (Succ zzz618) == LT)",fontsize=16,color="black",shape="triangle"];12108 -> 12174[label="",style="solid", color="black", weight=3]; 130.29/78.15 32062 -> 31858[label="",style="dashed", color="red", weight=0]; 130.29/78.15 32062[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz3181)) zzz3182 zzz3183 zzz3184 zzz3185 (Pos (Succ zzz3186)) zzz3187 (primCmpNat zzz31880 zzz31890 == LT)",fontsize=16,color="magenta"];32062 -> 32219[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 32062 -> 32220[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 32063[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz3181)) zzz3182 zzz3183 zzz3184 zzz3185 (Pos (Succ zzz3186)) zzz3187 (GT == LT)",fontsize=16,color="black",shape="box"];32063 -> 32221[label="",style="solid", color="black", weight=3]; 130.29/78.15 32064[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz3181)) zzz3182 zzz3183 zzz3184 zzz3185 (Pos (Succ zzz3186)) zzz3187 (LT == LT)",fontsize=16,color="black",shape="box"];32064 -> 32222[label="",style="solid", color="black", weight=3]; 130.29/78.15 32065[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz3181)) zzz3182 zzz3183 zzz3184 zzz3185 (Pos (Succ zzz3186)) zzz3187 (EQ == LT)",fontsize=16,color="black",shape="box"];32065 -> 32223[label="",style="solid", color="black", weight=3]; 130.29/78.15 6366[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 (primCmpInt (Pos (Succ zzz3000)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];6366 -> 7158[label="",style="solid", color="black", weight=3]; 130.29/78.15 6367[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg zzz3400) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 True",fontsize=16,color="black",shape="box"];6367 -> 7159[label="",style="solid", color="black", weight=3]; 130.29/78.15 63363[label="Zero",fontsize=16,color="green",shape="box"];63364[label="zzz343",fontsize=16,color="green",shape="box"];6559[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (EQ == GT)",fontsize=16,color="black",shape="box"];6559 -> 7161[label="",style="solid", color="black", weight=3]; 130.29/78.15 6560[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz34000)) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (GT == GT)",fontsize=16,color="black",shape="box"];6560 -> 7162[label="",style="solid", color="black", weight=3]; 130.29/78.15 6561[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 (EQ == GT)",fontsize=16,color="black",shape="box"];6561 -> 7163[label="",style="solid", color="black", weight=3]; 130.29/78.15 6562[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat Zero (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];6562 -> 7164[label="",style="solid", color="black", weight=3]; 130.29/78.15 6563[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Pos Zero) (Pos (Succ zzz34200)) == LT)",fontsize=16,color="black",shape="box"];6563 -> 7165[label="",style="solid", color="black", weight=3]; 130.29/78.15 6564[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];6564 -> 7166[label="",style="solid", color="black", weight=3]; 130.29/78.15 6565[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Pos Zero) (Neg (Succ zzz34200)) == LT)",fontsize=16,color="black",shape="box"];6565 -> 7167[label="",style="solid", color="black", weight=3]; 130.29/78.15 6566[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];6566 -> 7168[label="",style="solid", color="black", weight=3]; 130.29/78.15 6567[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat Zero (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];6567 -> 7169[label="",style="solid", color="black", weight=3]; 130.29/78.15 6568[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg Zero) (Pos (Succ zzz34200)) == LT)",fontsize=16,color="black",shape="box"];6568 -> 7170[label="",style="solid", color="black", weight=3]; 130.29/78.15 6569[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];6569 -> 7171[label="",style="solid", color="black", weight=3]; 130.29/78.15 6570[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg Zero) (Neg (Succ zzz34200)) == LT)",fontsize=16,color="black",shape="box"];6570 -> 7172[label="",style="solid", color="black", weight=3]; 130.29/78.15 6571[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];6571 -> 7173[label="",style="solid", color="black", weight=3]; 130.29/78.15 6257 -> 2057[label="",style="dashed", color="red", weight=0]; 130.29/78.15 6257[label="FiniteMap.splitLT FiniteMap.EmptyFM (Pos Zero)",fontsize=16,color="magenta"];17873[label="FiniteMap.splitGT3 (FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196) (Pos Zero)",fontsize=16,color="black",shape="box"];17873 -> 18140[label="",style="solid", color="black", weight=3]; 130.29/78.15 17874[label="FiniteMap.Branch (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196",fontsize=16,color="green",shape="box"];12322[label="FiniteMap.splitLT zzz621 (Pos Zero)",fontsize=16,color="burlywood",shape="triangle"];65198[label="zzz621/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];12322 -> 65198[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65198 -> 12733[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65199[label="zzz621/FiniteMap.Branch zzz6210 zzz6211 zzz6212 zzz6213 zzz6214",fontsize=10,color="white",style="solid",shape="box"];12322 -> 65199[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65199 -> 12734[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 43534[label="Succ zzz4739",fontsize=16,color="green",shape="box"];43535[label="primMulNat (Succ (Succ Zero)) (Succ zzz4739)",fontsize=16,color="black",shape="box"];43535 -> 44331[label="",style="solid", color="black", weight=3]; 130.29/78.15 43536[label="zzz542000",fontsize=16,color="green",shape="box"];43537[label="zzz50920000",fontsize=16,color="green",shape="box"];62623 -> 62592[label="",style="dashed", color="red", weight=0]; 130.29/78.15 62623[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat zzz633800 zzz6319000 == LT)",fontsize=16,color="magenta"];62623 -> 62631[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 62623 -> 62632[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 62624 -> 62558[label="",style="dashed", color="red", weight=0]; 130.29/78.15 62624[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (GT == LT)",fontsize=16,color="magenta"];62625 -> 62570[label="",style="dashed", color="red", weight=0]; 130.29/78.15 62625[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (LT == LT)",fontsize=16,color="magenta"];62626 -> 62581[label="",style="dashed", color="red", weight=0]; 130.29/78.15 62626[label="FiniteMap.glueVBal3GlueVBal2 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (EQ == LT)",fontsize=16,color="magenta"];62627[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.glueVBal3Size_r zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) zzz6343 == LT)",fontsize=16,color="black",shape="box"];62627 -> 62633[label="",style="solid", color="black", weight=3]; 130.29/78.15 63573[label="FiniteMap.glueVBal4 (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];63573 -> 63594[label="",style="solid", color="black", weight=3]; 130.29/78.15 63574[label="FiniteMap.glueVBal3 (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz4740330 zzz4740331 zzz4740332 zzz4740333 zzz4740334)",fontsize=16,color="black",shape="triangle"];63574 -> 63595[label="",style="solid", color="black", weight=3]; 130.29/78.15 63575[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (FiniteMap.mkBalBranch6Size_l zzz474034 zzz474030 zzz474031 zzz6373 + FiniteMap.mkBalBranch6Size_r zzz474034 zzz474030 zzz474031 zzz6373 < Pos (Succ (Succ Zero)))",fontsize=16,color="black",shape="box"];63575 -> 63596[label="",style="solid", color="black", weight=3]; 130.29/78.15 13470[label="FiniteMap.splitGT1 (Pos zzz742) zzz743 zzz744 zzz745 zzz746 (Neg (Succ zzz747)) (primCmpInt (Neg (Succ zzz747)) (Pos zzz742) == LT)",fontsize=16,color="black",shape="box"];13470 -> 13542[label="",style="solid", color="black", weight=3]; 130.29/78.15 28739 -> 6244[label="",style="dashed", color="red", weight=0]; 130.29/78.15 28739[label="FiniteMap.mkVBalBranch (Neg (Succ zzz2760)) (FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760))) zzz2761) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760))) zzz2763) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760))) zzz2764)",fontsize=16,color="magenta"];28739 -> 28925[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 28739 -> 28926[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 28739 -> 28927[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 28739 -> 28928[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 9324[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];9324 -> 10990[label="",style="solid", color="black", weight=3]; 130.29/78.15 34364[label="FiniteMap.splitGT2 (Neg (Succ zzz3494)) zzz3495 zzz3496 zzz3497 zzz3498 (Neg (Succ zzz3499)) (primCmpNat (Succ zzz35000) (Succ zzz35010) == GT)",fontsize=16,color="black",shape="box"];34364 -> 34466[label="",style="solid", color="black", weight=3]; 130.29/78.15 34365[label="FiniteMap.splitGT2 (Neg (Succ zzz3494)) zzz3495 zzz3496 zzz3497 zzz3498 (Neg (Succ zzz3499)) (primCmpNat (Succ zzz35000) Zero == GT)",fontsize=16,color="black",shape="box"];34365 -> 34467[label="",style="solid", color="black", weight=3]; 130.29/78.15 34366[label="FiniteMap.splitGT2 (Neg (Succ zzz3494)) zzz3495 zzz3496 zzz3497 zzz3498 (Neg (Succ zzz3499)) (primCmpNat Zero (Succ zzz35010) == GT)",fontsize=16,color="black",shape="box"];34366 -> 34468[label="",style="solid", color="black", weight=3]; 130.29/78.15 34367[label="FiniteMap.splitGT2 (Neg (Succ zzz3494)) zzz3495 zzz3496 zzz3497 zzz3498 (Neg (Succ zzz3499)) (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];34367 -> 34469[label="",style="solid", color="black", weight=3]; 130.29/78.15 14928[label="FiniteMap.splitGT1 (Neg Zero) zzz884 zzz885 zzz886 zzz887 (Neg (Succ zzz888)) (Neg (Succ zzz888) < Neg Zero)",fontsize=16,color="black",shape="box"];14928 -> 15050[label="",style="solid", color="black", weight=3]; 130.29/78.15 34462[label="FiniteMap.splitLT2 (Neg (Succ zzz3503)) zzz3504 zzz3505 zzz3506 zzz3507 (Neg (Succ zzz3508)) (primCmpNat (Succ zzz35090) (Succ zzz35100) == LT)",fontsize=16,color="black",shape="box"];34462 -> 34700[label="",style="solid", color="black", weight=3]; 130.29/78.15 34463[label="FiniteMap.splitLT2 (Neg (Succ zzz3503)) zzz3504 zzz3505 zzz3506 zzz3507 (Neg (Succ zzz3508)) (primCmpNat (Succ zzz35090) Zero == LT)",fontsize=16,color="black",shape="box"];34463 -> 34701[label="",style="solid", color="black", weight=3]; 130.29/78.15 34464[label="FiniteMap.splitLT2 (Neg (Succ zzz3503)) zzz3504 zzz3505 zzz3506 zzz3507 (Neg (Succ zzz3508)) (primCmpNat Zero (Succ zzz35100) == LT)",fontsize=16,color="black",shape="box"];34464 -> 34702[label="",style="solid", color="black", weight=3]; 130.29/78.15 34465[label="FiniteMap.splitLT2 (Neg (Succ zzz3503)) zzz3504 zzz3505 zzz3506 zzz3507 (Neg (Succ zzz3508)) (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];34465 -> 34703[label="",style="solid", color="black", weight=3]; 130.29/78.15 15738[label="zzz7453",fontsize=16,color="green",shape="box"];29921[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) zzz2889 zzz2890 zzz2891 zzz2892 (Maybe.isJust (Just zzz2894))",fontsize=16,color="black",shape="box"];29921 -> 29965[label="",style="solid", color="black", weight=3]; 130.29/78.15 5155 -> 11[label="",style="dashed", color="red", weight=0]; 130.29/78.15 5155[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];14450[label="FiniteMap.splitGT2 zzz8330 zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (compare (Neg Zero) zzz8330 == GT)",fontsize=16,color="black",shape="box"];14450 -> 14563[label="",style="solid", color="black", weight=3]; 130.29/78.15 14451[label="FiniteMap.splitLT2 (Neg (Succ zzz833000)) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) False",fontsize=16,color="black",shape="box"];14451 -> 14564[label="",style="solid", color="black", weight=3]; 130.29/78.15 33668[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz3386)) zzz3387 zzz3388 zzz3389 zzz3390 (Neg (Succ zzz3391)) zzz3392 (primCmpNat (Succ zzz33930) (Succ zzz33940) == LT)",fontsize=16,color="black",shape="box"];33668 -> 33695[label="",style="solid", color="black", weight=3]; 130.29/78.15 33669[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz3386)) zzz3387 zzz3388 zzz3389 zzz3390 (Neg (Succ zzz3391)) zzz3392 (primCmpNat (Succ zzz33930) Zero == LT)",fontsize=16,color="black",shape="box"];33669 -> 33696[label="",style="solid", color="black", weight=3]; 130.29/78.15 33670[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz3386)) zzz3387 zzz3388 zzz3389 zzz3390 (Neg (Succ zzz3391)) zzz3392 (primCmpNat Zero (Succ zzz33940) == LT)",fontsize=16,color="black",shape="box"];33670 -> 33697[label="",style="solid", color="black", weight=3]; 130.29/78.15 33671[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz3386)) zzz3387 zzz3388 zzz3389 zzz3390 (Neg (Succ zzz3391)) zzz3392 (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];33671 -> 33698[label="",style="solid", color="black", weight=3]; 130.29/78.15 63101[label="Neg Zero",fontsize=16,color="green",shape="box"];63102[label="zzz9824",fontsize=16,color="green",shape="box"];63103 -> 12360[label="",style="dashed", color="red", weight=0]; 130.29/78.15 63103[label="FiniteMap.addToFM_C FiniteMap.addToFM0 zzz9823 (Neg (Succ zzz3000)) zzz31",fontsize=16,color="magenta"];63103 -> 63367[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 63103 -> 63368[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 63104[label="zzz9821",fontsize=16,color="green",shape="box"];63365[label="zzz9823",fontsize=16,color="green",shape="box"];63366[label="Zero",fontsize=16,color="green",shape="box"];14390[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (primCmpInt (Neg Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];14390 -> 14461[label="",style="solid", color="black", weight=3]; 130.29/78.15 14391[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz982000)) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (compare (Neg Zero) (Neg (Succ zzz982000)) == GT)",fontsize=16,color="black",shape="box"];14391 -> 14462[label="",style="solid", color="black", weight=3]; 130.29/78.15 14392[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (primCmpInt (Neg Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];14392 -> 14463[label="",style="solid", color="black", weight=3]; 130.29/78.15 8004[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat Zero (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];8004 -> 8835[label="",style="solid", color="black", weight=3]; 130.29/78.15 8005[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Pos Zero) (Pos (Succ zzz34200)) == LT)",fontsize=16,color="black",shape="box"];8005 -> 8836[label="",style="solid", color="black", weight=3]; 130.29/78.15 8006[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];8006 -> 8837[label="",style="solid", color="black", weight=3]; 130.29/78.15 8007[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Pos Zero) (Neg (Succ zzz34200)) == LT)",fontsize=16,color="black",shape="box"];8007 -> 8838[label="",style="solid", color="black", weight=3]; 130.29/78.15 8008[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];8008 -> 8839[label="",style="solid", color="black", weight=3]; 130.29/78.15 8009[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat Zero (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];8009 -> 8840[label="",style="solid", color="black", weight=3]; 130.29/78.15 8010[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg Zero) (Pos (Succ zzz34200)) == LT)",fontsize=16,color="black",shape="box"];8010 -> 8841[label="",style="solid", color="black", weight=3]; 130.29/78.15 8011[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];8011 -> 8842[label="",style="solid", color="black", weight=3]; 130.29/78.15 8012[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg Zero) (Neg (Succ zzz34200)) == LT)",fontsize=16,color="black",shape="box"];8012 -> 8843[label="",style="solid", color="black", weight=3]; 130.29/78.15 8013[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];8013 -> 8844[label="",style="solid", color="black", weight=3]; 130.29/78.15 6856[label="FiniteMap.splitLT1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Neg Zero) (primCmpNat (Succ zzz3000) Zero == GT)",fontsize=16,color="black",shape="box"];6856 -> 7618[label="",style="solid", color="black", weight=3]; 130.29/78.15 20481 -> 13521[label="",style="dashed", color="red", weight=0]; 130.29/78.15 20481[label="FiniteMap.splitGT (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero)",fontsize=16,color="magenta"];20481 -> 20517[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20482 -> 12653[label="",style="dashed", color="red", weight=0]; 130.29/78.15 20482[label="FiniteMap.splitLT (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero)",fontsize=16,color="magenta"];20482 -> 20518[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20483 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.15 20483[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero)) zzz1601",fontsize=16,color="magenta"];20483 -> 20519[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20483 -> 20520[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20484 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.15 20484[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero)) zzz1602",fontsize=16,color="magenta"];20484 -> 20521[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20484 -> 20522[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 20485[label="FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero)) zzz1599",fontsize=16,color="black",shape="box"];20485 -> 20523[label="",style="solid", color="black", weight=3]; 130.29/78.15 33710 -> 33577[label="",style="dashed", color="red", weight=0]; 130.29/78.15 33710[label="FiniteMap.splitGT2 (Pos (Succ zzz3396)) zzz3397 zzz3398 zzz3399 zzz3400 (Pos (Succ zzz3401)) (primCmpNat zzz34020 zzz34030 == GT)",fontsize=16,color="magenta"];33710 -> 33730[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 33710 -> 33731[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 33711[label="FiniteMap.splitGT2 (Pos (Succ zzz3396)) zzz3397 zzz3398 zzz3399 zzz3400 (Pos (Succ zzz3401)) (GT == GT)",fontsize=16,color="black",shape="box"];33711 -> 33732[label="",style="solid", color="black", weight=3]; 130.29/78.15 33712[label="FiniteMap.splitGT2 (Pos (Succ zzz3396)) zzz3397 zzz3398 zzz3399 zzz3400 (Pos (Succ zzz3401)) (LT == GT)",fontsize=16,color="black",shape="box"];33712 -> 33733[label="",style="solid", color="black", weight=3]; 130.29/78.15 33713[label="FiniteMap.splitGT2 (Pos (Succ zzz3396)) zzz3397 zzz3398 zzz3399 zzz3400 (Pos (Succ zzz3401)) (EQ == GT)",fontsize=16,color="black",shape="box"];33713 -> 33734[label="",style="solid", color="black", weight=3]; 130.29/78.15 34770[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) zzz3530 zzz3531 zzz3532 zzz3533 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3534)) zzz3535 zzz3536 zzz3537 zzz3538 (Pos (Succ zzz3529)) (primCmpNat (Succ zzz35390) (Succ zzz35400) == GT)))",fontsize=16,color="black",shape="box"];34770 -> 34836[label="",style="solid", color="black", weight=3]; 130.29/78.15 34771[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) zzz3530 zzz3531 zzz3532 zzz3533 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3534)) zzz3535 zzz3536 zzz3537 zzz3538 (Pos (Succ zzz3529)) (primCmpNat (Succ zzz35390) Zero == GT)))",fontsize=16,color="black",shape="box"];34771 -> 34837[label="",style="solid", color="black", weight=3]; 130.29/78.15 34772[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) zzz3530 zzz3531 zzz3532 zzz3533 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3534)) zzz3535 zzz3536 zzz3537 zzz3538 (Pos (Succ zzz3529)) (primCmpNat Zero (Succ zzz35400) == GT)))",fontsize=16,color="black",shape="box"];34772 -> 34838[label="",style="solid", color="black", weight=3]; 130.29/78.15 34773[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) zzz3530 zzz3531 zzz3532 zzz3533 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3534)) zzz3535 zzz3536 zzz3537 zzz3538 (Pos (Succ zzz3529)) (primCmpNat Zero Zero == GT)))",fontsize=16,color="black",shape="box"];34773 -> 34839[label="",style="solid", color="black", weight=3]; 130.29/78.15 29598 -> 288[label="",style="dashed", color="red", weight=0]; 130.29/78.15 29598[label="FiniteMap.glueVBal (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738))) zzz2741) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738))) zzz2742)",fontsize=16,color="magenta"];29598 -> 29670[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 29598 -> 29671[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31955[label="FiniteMap.splitLT1 (Pos (Succ zzz3133)) zzz3134 zzz3135 zzz3136 zzz3137 (Pos (Succ zzz3138)) (Pos (Succ zzz3138) > Pos (Succ zzz3133))",fontsize=16,color="black",shape="box"];31955 -> 32030[label="",style="solid", color="black", weight=3]; 130.29/78.15 31956 -> 23112[label="",style="dashed", color="red", weight=0]; 130.29/78.15 31956[label="FiniteMap.splitLT zzz3136 (Pos (Succ zzz3138))",fontsize=16,color="magenta"];31956 -> 32031[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 31956 -> 32032[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 22667[label="FiniteMap.splitLT1 (Pos Zero) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) (GT == GT)",fontsize=16,color="black",shape="box"];22667 -> 22796[label="",style="solid", color="black", weight=3]; 130.29/78.15 22668[label="FiniteMap.mkVBalBranch (Neg zzz19700) zzz1971 FiniteMap.EmptyFM (FiniteMap.splitLT zzz1974 (Pos (Succ zzz1975)))",fontsize=16,color="black",shape="box"];22668 -> 22797[label="",style="solid", color="black", weight=3]; 130.29/78.15 22669[label="FiniteMap.mkVBalBranch (Neg zzz19700) zzz1971 (FiniteMap.Branch zzz19730 zzz19731 zzz19732 zzz19733 zzz19734) (FiniteMap.splitLT zzz1974 (Pos (Succ zzz1975)))",fontsize=16,color="burlywood",shape="box"];65200[label="zzz1974/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];22669 -> 65200[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65200 -> 22798[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65201[label="zzz1974/FiniteMap.Branch zzz19740 zzz19741 zzz19742 zzz19743 zzz19744",fontsize=10,color="white",style="solid",shape="box"];22669 -> 65201[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65201 -> 22799[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 32217 -> 18275[label="",style="dashed", color="red", weight=0]; 130.29/78.15 32217[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) zzz3169 zzz3170 zzz3171 zzz3172 (Maybe.isJust (FiniteMap.lookupFM zzz3177 (Pos (Succ zzz3168))))",fontsize=16,color="magenta"];32217 -> 32249[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 32217 -> 32250[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 32217 -> 32251[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 32217 -> 32252[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 32217 -> 32253[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 32217 -> 32254[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 32217 -> 32255[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 32217 -> 32256[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 32217 -> 32257[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 32217 -> 32258[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 32217 -> 32259[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 32218[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) zzz3169 zzz3170 zzz3171 zzz3172 (Maybe.isJust (FiniteMap.lookupFM0 (Pos (Succ zzz3173)) zzz3174 zzz3175 zzz3176 zzz3177 (Pos (Succ zzz3168)) otherwise))",fontsize=16,color="black",shape="box"];32218 -> 32260[label="",style="solid", color="black", weight=3]; 130.29/78.15 19449 -> 19598[label="",style="dashed", color="red", weight=0]; 130.29/78.15 19449[label="FiniteMap.splitGT (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387))",fontsize=16,color="magenta"];19449 -> 19689[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 19449 -> 19690[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 19450[label="FiniteMap.splitLT (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387))",fontsize=16,color="black",shape="box"];19450 -> 19691[label="",style="solid", color="black", weight=3]; 130.29/78.15 12173[label="FiniteMap.splitGT2 (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622 (Pos Zero) (LT == GT)",fontsize=16,color="black",shape="box"];12173 -> 12254[label="",style="solid", color="black", weight=3]; 130.29/78.15 12174[label="FiniteMap.splitLT2 (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622 (Pos Zero) (LT == LT)",fontsize=16,color="black",shape="box"];12174 -> 12255[label="",style="solid", color="black", weight=3]; 130.29/78.15 32219[label="zzz31890",fontsize=16,color="green",shape="box"];32220[label="zzz31880",fontsize=16,color="green",shape="box"];32221[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz3181)) zzz3182 zzz3183 zzz3184 zzz3185 (Pos (Succ zzz3186)) zzz3187 False",fontsize=16,color="black",shape="triangle"];32221 -> 32261[label="",style="solid", color="black", weight=3]; 130.29/78.15 32222[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz3181)) zzz3182 zzz3183 zzz3184 zzz3185 (Pos (Succ zzz3186)) zzz3187 True",fontsize=16,color="black",shape="box"];32222 -> 32262[label="",style="solid", color="black", weight=3]; 130.29/78.15 32223 -> 32221[label="",style="dashed", color="red", weight=0]; 130.29/78.15 32223[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Pos (Succ zzz3181)) zzz3182 zzz3183 zzz3184 zzz3185 (Pos (Succ zzz3186)) zzz3187 False",fontsize=16,color="magenta"];7158[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 (primCmpNat (Succ zzz3000) Zero == GT)",fontsize=16,color="black",shape="box"];7158 -> 9982[label="",style="solid", color="black", weight=3]; 130.29/78.15 7159 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.15 7159[label="FiniteMap.mkBalBranch (Neg zzz3400) zzz341 zzz343 (FiniteMap.addToFM_C FiniteMap.addToFM0 zzz344 (Pos (Succ zzz3000)) zzz31)",fontsize=16,color="magenta"];7159 -> 63105[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 7159 -> 63106[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 7159 -> 63107[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 7159 -> 63108[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 7161[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 False",fontsize=16,color="black",shape="box"];7161 -> 9983[label="",style="solid", color="black", weight=3]; 130.29/78.15 7162[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz34000)) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 True",fontsize=16,color="black",shape="box"];7162 -> 9984[label="",style="solid", color="black", weight=3]; 130.29/78.15 7163[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 False",fontsize=16,color="black",shape="box"];7163 -> 9985[label="",style="solid", color="black", weight=3]; 130.29/78.15 7164[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat Zero (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];7164 -> 9986[label="",style="solid", color="black", weight=3]; 130.29/78.15 7165[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (primCmpNat Zero (Succ zzz34200) == LT)",fontsize=16,color="black",shape="box"];7165 -> 9987[label="",style="solid", color="black", weight=3]; 130.29/78.15 7166[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (EQ == LT)",fontsize=16,color="black",shape="box"];7166 -> 9988[label="",style="solid", color="black", weight=3]; 130.29/78.15 7167[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (GT == LT)",fontsize=16,color="black",shape="box"];7167 -> 9989[label="",style="solid", color="black", weight=3]; 130.29/78.15 7168[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (EQ == LT)",fontsize=16,color="black",shape="box"];7168 -> 9990[label="",style="solid", color="black", weight=3]; 130.29/78.15 7169[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat Zero (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];7169 -> 9991[label="",style="solid", color="black", weight=3]; 130.29/78.15 7170[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];7170 -> 9992[label="",style="solid", color="black", weight=3]; 130.29/78.15 7171[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (EQ == LT)",fontsize=16,color="black",shape="box"];7171 -> 9993[label="",style="solid", color="black", weight=3]; 130.29/78.15 7172[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpNat (Succ zzz34200) Zero == LT)",fontsize=16,color="black",shape="box"];7172 -> 9994[label="",style="solid", color="black", weight=3]; 130.29/78.15 7173[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (EQ == LT)",fontsize=16,color="black",shape="box"];7173 -> 9995[label="",style="solid", color="black", weight=3]; 130.29/78.15 18140[label="FiniteMap.splitGT2 (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196 (Pos Zero) (Pos Zero > Neg (Succ zzz1192))",fontsize=16,color="black",shape="box"];18140 -> 18166[label="",style="solid", color="black", weight=3]; 130.29/78.15 12733[label="FiniteMap.splitLT FiniteMap.EmptyFM (Pos Zero)",fontsize=16,color="black",shape="box"];12733 -> 13598[label="",style="solid", color="black", weight=3]; 130.29/78.15 12734[label="FiniteMap.splitLT (FiniteMap.Branch zzz6210 zzz6211 zzz6212 zzz6213 zzz6214) (Pos Zero)",fontsize=16,color="black",shape="box"];12734 -> 13599[label="",style="solid", color="black", weight=3]; 130.29/78.15 44331 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.15 44331[label="primPlusNat (primMulNat (Succ Zero) (Succ zzz4739)) (Succ zzz4739)",fontsize=16,color="magenta"];44331 -> 44356[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 44331 -> 44357[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 62631[label="zzz6319000",fontsize=16,color="green",shape="box"];62632[label="zzz633800",fontsize=16,color="green",shape="box"];62633[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.glueVBal3Size_r zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464)) zzz6343 == LT)",fontsize=16,color="black",shape="box"];62633 -> 62641[label="",style="solid", color="black", weight=3]; 130.29/78.15 63594[label="FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464",fontsize=16,color="green",shape="box"];63595 -> 62159[label="",style="dashed", color="red", weight=0]; 130.29/78.15 63595[label="FiniteMap.glueVBal3GlueVBal2 zzz4740330 zzz4740331 zzz4740332 zzz4740333 zzz4740334 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz4740330 zzz4740331 zzz4740332 zzz4740333 zzz4740334 (FiniteMap.sIZE_RATIO * FiniteMap.glueVBal3Size_l zzz4740330 zzz4740331 zzz4740332 zzz4740333 zzz4740334 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 < FiniteMap.glueVBal3Size_r zzz4740330 zzz4740331 zzz4740332 zzz4740333 zzz4740334 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464)",fontsize=16,color="magenta"];63595 -> 63655[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 63595 -> 63656[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 63595 -> 63657[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 63595 -> 63658[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 63595 -> 63659[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 63595 -> 63660[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 63596[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (compare (FiniteMap.mkBalBranch6Size_l zzz474034 zzz474030 zzz474031 zzz6373 + FiniteMap.mkBalBranch6Size_r zzz474034 zzz474030 zzz474031 zzz6373) (Pos (Succ (Succ Zero))) == LT)",fontsize=16,color="black",shape="box"];63596 -> 63661[label="",style="solid", color="black", weight=3]; 130.29/78.15 13542[label="FiniteMap.splitGT1 (Pos zzz742) zzz743 zzz744 zzz745 zzz746 (Neg (Succ zzz747)) (LT == LT)",fontsize=16,color="black",shape="box"];13542 -> 13837[label="",style="solid", color="black", weight=3]; 130.29/78.15 28925[label="zzz2760",fontsize=16,color="green",shape="box"];28926 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.15 28926[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760))) zzz2764",fontsize=16,color="magenta"];28926 -> 29000[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 28926 -> 29001[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 28927 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.15 28927[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760))) zzz2763",fontsize=16,color="magenta"];28927 -> 29002[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 28927 -> 29003[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 28928[label="FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760))) zzz2761",fontsize=16,color="black",shape="box"];28928 -> 29004[label="",style="solid", color="black", weight=3]; 130.29/78.15 10990[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz332) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 zzz332 zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="burlywood",shape="box"];65202[label="zzz332/Pos zzz3320",fontsize=10,color="white",style="solid",shape="box"];10990 -> 65202[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65202 -> 11173[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65203[label="zzz332/Neg zzz3320",fontsize=10,color="white",style="solid",shape="box"];10990 -> 65203[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65203 -> 11174[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 34466 -> 34162[label="",style="dashed", color="red", weight=0]; 130.29/78.15 34466[label="FiniteMap.splitGT2 (Neg (Succ zzz3494)) zzz3495 zzz3496 zzz3497 zzz3498 (Neg (Succ zzz3499)) (primCmpNat zzz35000 zzz35010 == GT)",fontsize=16,color="magenta"];34466 -> 34704[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 34466 -> 34705[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 34467[label="FiniteMap.splitGT2 (Neg (Succ zzz3494)) zzz3495 zzz3496 zzz3497 zzz3498 (Neg (Succ zzz3499)) (GT == GT)",fontsize=16,color="black",shape="box"];34467 -> 34706[label="",style="solid", color="black", weight=3]; 130.29/78.15 34468[label="FiniteMap.splitGT2 (Neg (Succ zzz3494)) zzz3495 zzz3496 zzz3497 zzz3498 (Neg (Succ zzz3499)) (LT == GT)",fontsize=16,color="black",shape="box"];34468 -> 34707[label="",style="solid", color="black", weight=3]; 130.29/78.15 34469[label="FiniteMap.splitGT2 (Neg (Succ zzz3494)) zzz3495 zzz3496 zzz3497 zzz3498 (Neg (Succ zzz3499)) (EQ == GT)",fontsize=16,color="black",shape="box"];34469 -> 34708[label="",style="solid", color="black", weight=3]; 130.29/78.15 15050[label="FiniteMap.splitGT1 (Neg Zero) zzz884 zzz885 zzz886 zzz887 (Neg (Succ zzz888)) (compare (Neg (Succ zzz888)) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];15050 -> 15213[label="",style="solid", color="black", weight=3]; 130.29/78.15 34700 -> 34273[label="",style="dashed", color="red", weight=0]; 130.29/78.15 34700[label="FiniteMap.splitLT2 (Neg (Succ zzz3503)) zzz3504 zzz3505 zzz3506 zzz3507 (Neg (Succ zzz3508)) (primCmpNat zzz35090 zzz35100 == LT)",fontsize=16,color="magenta"];34700 -> 34774[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 34700 -> 34775[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 34701[label="FiniteMap.splitLT2 (Neg (Succ zzz3503)) zzz3504 zzz3505 zzz3506 zzz3507 (Neg (Succ zzz3508)) (GT == LT)",fontsize=16,color="black",shape="box"];34701 -> 34776[label="",style="solid", color="black", weight=3]; 130.29/78.15 34702[label="FiniteMap.splitLT2 (Neg (Succ zzz3503)) zzz3504 zzz3505 zzz3506 zzz3507 (Neg (Succ zzz3508)) (LT == LT)",fontsize=16,color="black",shape="box"];34702 -> 34777[label="",style="solid", color="black", weight=3]; 130.29/78.15 34703[label="FiniteMap.splitLT2 (Neg (Succ zzz3503)) zzz3504 zzz3505 zzz3506 zzz3507 (Neg (Succ zzz3508)) (EQ == LT)",fontsize=16,color="black",shape="box"];34703 -> 34778[label="",style="solid", color="black", weight=3]; 130.29/78.15 29965[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888)) zzz2889 zzz2890 zzz2891 zzz2892 True",fontsize=16,color="black",shape="box"];29965 -> 29995[label="",style="solid", color="black", weight=3]; 130.29/78.15 14563[label="FiniteMap.splitGT2 zzz8330 zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (primCmpInt (Neg Zero) zzz8330 == GT)",fontsize=16,color="burlywood",shape="triangle"];65204[label="zzz8330/Pos zzz83300",fontsize=10,color="white",style="solid",shape="box"];14563 -> 65204[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65204 -> 14935[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 65205[label="zzz8330/Neg zzz83300",fontsize=10,color="white",style="solid",shape="box"];14563 -> 65205[label="",style="solid", color="burlywood", weight=9]; 130.29/78.15 65205 -> 14936[label="",style="solid", color="burlywood", weight=3]; 130.29/78.15 14564[label="FiniteMap.splitLT1 (Neg (Succ zzz833000)) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (Neg Zero > Neg (Succ zzz833000))",fontsize=16,color="black",shape="box"];14564 -> 14937[label="",style="solid", color="black", weight=3]; 130.29/78.15 33695 -> 33397[label="",style="dashed", color="red", weight=0]; 130.29/78.15 33695[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz3386)) zzz3387 zzz3388 zzz3389 zzz3390 (Neg (Succ zzz3391)) zzz3392 (primCmpNat zzz33930 zzz33940 == LT)",fontsize=16,color="magenta"];33695 -> 33714[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 33695 -> 33715[label="",style="dashed", color="magenta", weight=3]; 130.29/78.15 33696[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz3386)) zzz3387 zzz3388 zzz3389 zzz3390 (Neg (Succ zzz3391)) zzz3392 (GT == LT)",fontsize=16,color="black",shape="box"];33696 -> 33716[label="",style="solid", color="black", weight=3]; 130.29/78.15 33697[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz3386)) zzz3387 zzz3388 zzz3389 zzz3390 (Neg (Succ zzz3391)) zzz3392 (LT == LT)",fontsize=16,color="black",shape="box"];33697 -> 33717[label="",style="solid", color="black", weight=3]; 130.29/78.15 33698[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz3386)) zzz3387 zzz3388 zzz3389 zzz3390 (Neg (Succ zzz3391)) zzz3392 (EQ == LT)",fontsize=16,color="black",shape="box"];33698 -> 33718[label="",style="solid", color="black", weight=3]; 130.29/78.15 63367[label="zzz9823",fontsize=16,color="green",shape="box"];63368[label="Succ zzz3000",fontsize=16,color="green",shape="box"];14461[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (EQ == GT)",fontsize=16,color="black",shape="box"];14461 -> 14579[label="",style="solid", color="black", weight=3]; 130.29/78.15 14462[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz982000)) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (primCmpInt (Neg Zero) (Neg (Succ zzz982000)) == GT)",fontsize=16,color="black",shape="box"];14462 -> 14580[label="",style="solid", color="black", weight=3]; 130.29/78.15 14463[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (EQ == GT)",fontsize=16,color="black",shape="box"];14463 -> 14581[label="",style="solid", color="black", weight=3]; 130.29/78.15 8835[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat Zero (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];8835 -> 10793[label="",style="solid", color="black", weight=3]; 130.29/78.15 8836[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (primCmpNat Zero (Succ zzz34200) == LT)",fontsize=16,color="black",shape="box"];8836 -> 10794[label="",style="solid", color="black", weight=3]; 130.29/78.15 8837[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (EQ == LT)",fontsize=16,color="black",shape="box"];8837 -> 10795[label="",style="solid", color="black", weight=3]; 130.29/78.16 8838[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (GT == LT)",fontsize=16,color="black",shape="box"];8838 -> 10796[label="",style="solid", color="black", weight=3]; 130.29/78.16 8839[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (EQ == LT)",fontsize=16,color="black",shape="box"];8839 -> 10797[label="",style="solid", color="black", weight=3]; 130.29/78.16 8840[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat Zero (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];8840 -> 10798[label="",style="solid", color="black", weight=3]; 130.29/78.16 8841[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];8841 -> 10799[label="",style="solid", color="black", weight=3]; 130.29/78.16 8842[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (EQ == LT)",fontsize=16,color="black",shape="box"];8842 -> 10800[label="",style="solid", color="black", weight=3]; 130.29/78.16 8843[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpNat (Succ zzz34200) Zero == LT)",fontsize=16,color="black",shape="box"];8843 -> 10801[label="",style="solid", color="black", weight=3]; 130.29/78.16 8844[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (EQ == LT)",fontsize=16,color="black",shape="box"];8844 -> 10802[label="",style="solid", color="black", weight=3]; 130.29/78.16 7618[label="FiniteMap.splitLT1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Neg Zero) (GT == GT)",fontsize=16,color="black",shape="box"];7618 -> 10803[label="",style="solid", color="black", weight=3]; 130.29/78.16 20517[label="FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598",fontsize=16,color="green",shape="box"];20518[label="FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598",fontsize=16,color="green",shape="box"];20519 -> 20411[label="",style="dashed", color="red", weight=0]; 130.29/78.16 20519[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero)",fontsize=16,color="magenta"];20520[label="zzz1601",fontsize=16,color="green",shape="box"];20521 -> 20409[label="",style="dashed", color="red", weight=0]; 130.29/78.16 20521[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg (Succ zzz1594)) zzz1595 zzz1596 zzz1597 zzz1598) (Neg Zero)",fontsize=16,color="magenta"];20522[label="zzz1602",fontsize=16,color="green",shape="box"];20523[label="zzz1599",fontsize=16,color="green",shape="box"];33730[label="zzz34030",fontsize=16,color="green",shape="box"];33731[label="zzz34020",fontsize=16,color="green",shape="box"];33732[label="FiniteMap.splitGT2 (Pos (Succ zzz3396)) zzz3397 zzz3398 zzz3399 zzz3400 (Pos (Succ zzz3401)) True",fontsize=16,color="black",shape="box"];33732 -> 33824[label="",style="solid", color="black", weight=3]; 130.29/78.16 33733[label="FiniteMap.splitGT2 (Pos (Succ zzz3396)) zzz3397 zzz3398 zzz3399 zzz3400 (Pos (Succ zzz3401)) False",fontsize=16,color="black",shape="triangle"];33733 -> 33825[label="",style="solid", color="black", weight=3]; 130.29/78.16 33734 -> 33733[label="",style="dashed", color="red", weight=0]; 130.29/78.16 33734[label="FiniteMap.splitGT2 (Pos (Succ zzz3396)) zzz3397 zzz3398 zzz3399 zzz3400 (Pos (Succ zzz3401)) False",fontsize=16,color="magenta"];34836 -> 34521[label="",style="dashed", color="red", weight=0]; 130.29/78.16 34836[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) zzz3530 zzz3531 zzz3532 zzz3533 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3534)) zzz3535 zzz3536 zzz3537 zzz3538 (Pos (Succ zzz3529)) (primCmpNat zzz35390 zzz35400 == GT)))",fontsize=16,color="magenta"];34836 -> 34879[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34836 -> 34880[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34837[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) zzz3530 zzz3531 zzz3532 zzz3533 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3534)) zzz3535 zzz3536 zzz3537 zzz3538 (Pos (Succ zzz3529)) (GT == GT)))",fontsize=16,color="black",shape="box"];34837 -> 34881[label="",style="solid", color="black", weight=3]; 130.29/78.16 34838[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) zzz3530 zzz3531 zzz3532 zzz3533 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3534)) zzz3535 zzz3536 zzz3537 zzz3538 (Pos (Succ zzz3529)) (LT == GT)))",fontsize=16,color="black",shape="box"];34838 -> 34882[label="",style="solid", color="black", weight=3]; 130.29/78.16 34839[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) zzz3530 zzz3531 zzz3532 zzz3533 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3534)) zzz3535 zzz3536 zzz3537 zzz3538 (Pos (Succ zzz3529)) (EQ == GT)))",fontsize=16,color="black",shape="box"];34839 -> 34883[label="",style="solid", color="black", weight=3]; 130.29/78.16 29670 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.16 29670[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738))) zzz2742",fontsize=16,color="magenta"];29670 -> 29705[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29670 -> 29706[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29671 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.16 29671[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738))) zzz2741",fontsize=16,color="magenta"];29671 -> 29707[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29671 -> 29708[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32030[label="FiniteMap.splitLT1 (Pos (Succ zzz3133)) zzz3134 zzz3135 zzz3136 zzz3137 (Pos (Succ zzz3138)) (compare (Pos (Succ zzz3138)) (Pos (Succ zzz3133)) == GT)",fontsize=16,color="black",shape="box"];32030 -> 32066[label="",style="solid", color="black", weight=3]; 130.29/78.16 32031[label="zzz3138",fontsize=16,color="green",shape="box"];32032[label="zzz3136",fontsize=16,color="green",shape="box"];22796[label="FiniteMap.splitLT1 (Pos Zero) zzz1971 zzz1972 zzz1973 zzz1974 (Pos (Succ zzz1975)) True",fontsize=16,color="black",shape="box"];22796 -> 23046[label="",style="solid", color="black", weight=3]; 130.29/78.16 22797[label="FiniteMap.mkVBalBranch5 (Neg zzz19700) zzz1971 FiniteMap.EmptyFM (FiniteMap.splitLT zzz1974 (Pos (Succ zzz1975)))",fontsize=16,color="black",shape="box"];22797 -> 23047[label="",style="solid", color="black", weight=3]; 130.29/78.16 22798[label="FiniteMap.mkVBalBranch (Neg zzz19700) zzz1971 (FiniteMap.Branch zzz19730 zzz19731 zzz19732 zzz19733 zzz19734) (FiniteMap.splitLT FiniteMap.EmptyFM (Pos (Succ zzz1975)))",fontsize=16,color="black",shape="box"];22798 -> 23048[label="",style="solid", color="black", weight=3]; 130.29/78.16 22799[label="FiniteMap.mkVBalBranch (Neg zzz19700) zzz1971 (FiniteMap.Branch zzz19730 zzz19731 zzz19732 zzz19733 zzz19734) (FiniteMap.splitLT (FiniteMap.Branch zzz19740 zzz19741 zzz19742 zzz19743 zzz19744) (Pos (Succ zzz1975)))",fontsize=16,color="black",shape="box"];22799 -> 23049[label="",style="solid", color="black", weight=3]; 130.29/78.16 32249[label="zzz3167",fontsize=16,color="green",shape="box"];32250[label="zzz3165",fontsize=16,color="green",shape="box"];32251[label="zzz3168",fontsize=16,color="green",shape="box"];32252[label="zzz3164",fontsize=16,color="green",shape="box"];32253[label="zzz3171",fontsize=16,color="green",shape="box"];32254[label="zzz3163",fontsize=16,color="green",shape="box"];32255[label="zzz3172",fontsize=16,color="green",shape="box"];32256[label="zzz3166",fontsize=16,color="green",shape="box"];32257[label="zzz3169",fontsize=16,color="green",shape="box"];32258[label="zzz3177",fontsize=16,color="green",shape="box"];32259[label="zzz3170",fontsize=16,color="green",shape="box"];32260[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) zzz3169 zzz3170 zzz3171 zzz3172 (Maybe.isJust (FiniteMap.lookupFM0 (Pos (Succ zzz3173)) zzz3174 zzz3175 zzz3176 zzz3177 (Pos (Succ zzz3168)) True))",fontsize=16,color="black",shape="box"];32260 -> 32288[label="",style="solid", color="black", weight=3]; 130.29/78.16 19689[label="FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386",fontsize=16,color="green",shape="box"];19690[label="zzz1387",fontsize=16,color="green",shape="box"];19691[label="FiniteMap.splitLT3 (FiniteMap.Branch (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386) (Pos (Succ zzz1387))",fontsize=16,color="black",shape="box"];19691 -> 19842[label="",style="solid", color="black", weight=3]; 130.29/78.16 12254[label="FiniteMap.splitGT2 (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622 (Pos Zero) False",fontsize=16,color="black",shape="box"];12254 -> 12321[label="",style="solid", color="black", weight=3]; 130.29/78.16 12255[label="FiniteMap.splitLT2 (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622 (Pos Zero) True",fontsize=16,color="black",shape="box"];12255 -> 12322[label="",style="solid", color="black", weight=3]; 130.29/78.16 32261[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ zzz3181)) zzz3182 zzz3183 zzz3184 zzz3185 (Pos (Succ zzz3186)) zzz3187 (Pos (Succ zzz3186) > Pos (Succ zzz3181))",fontsize=16,color="black",shape="box"];32261 -> 32289[label="",style="solid", color="black", weight=3]; 130.29/78.16 32262 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.16 32262[label="FiniteMap.mkBalBranch (Pos (Succ zzz3181)) zzz3182 (FiniteMap.addToFM_C FiniteMap.addToFM0 zzz3184 (Pos (Succ zzz3186)) zzz3187) zzz3185",fontsize=16,color="magenta"];32262 -> 63109[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32262 -> 63110[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32262 -> 63111[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32262 -> 63112[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 9982[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 (GT == GT)",fontsize=16,color="black",shape="box"];9982 -> 11219[label="",style="solid", color="black", weight=3]; 130.29/78.16 63105[label="Neg zzz3400",fontsize=16,color="green",shape="box"];63106 -> 4379[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63106[label="FiniteMap.addToFM_C FiniteMap.addToFM0 zzz344 (Pos (Succ zzz3000)) zzz31",fontsize=16,color="magenta"];63106 -> 63369[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63106 -> 63370[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63107[label="zzz343",fontsize=16,color="green",shape="box"];63108[label="zzz341",fontsize=16,color="green",shape="box"];9983[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Pos Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 otherwise",fontsize=16,color="black",shape="box"];9983 -> 11222[label="",style="solid", color="black", weight=3]; 130.29/78.16 9984 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.16 9984[label="FiniteMap.mkBalBranch (Neg (Succ zzz34000)) zzz341 zzz343 (FiniteMap.addToFM_C FiniteMap.addToFM0 zzz344 (Pos Zero) zzz31)",fontsize=16,color="magenta"];9984 -> 63113[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 9984 -> 63114[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 9984 -> 63115[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 9984 -> 63116[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 9985[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Neg Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 otherwise",fontsize=16,color="black",shape="box"];9985 -> 11227[label="",style="solid", color="black", weight=3]; 130.29/78.16 9986[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primPlusNat (Succ zzz250200) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];9986 -> 11228[label="",style="solid", color="black", weight=3]; 130.29/78.16 9987[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];9987 -> 11229[label="",style="solid", color="black", weight=3]; 130.29/78.16 9988[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];9988 -> 11230[label="",style="solid", color="black", weight=3]; 130.29/78.16 9989[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];9989 -> 11231[label="",style="solid", color="black", weight=3]; 130.29/78.16 9990[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];9990 -> 11232[label="",style="solid", color="black", weight=3]; 130.29/78.16 9991[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (Succ zzz250200) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];9991 -> 11233[label="",style="solid", color="black", weight=3]; 130.29/78.16 9992[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];9992 -> 11234[label="",style="solid", color="black", weight=3]; 130.29/78.16 9993[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];9993 -> 11235[label="",style="solid", color="black", weight=3]; 130.29/78.16 9994[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (GT == LT)",fontsize=16,color="black",shape="box"];9994 -> 11236[label="",style="solid", color="black", weight=3]; 130.29/78.16 9995[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];9995 -> 11237[label="",style="solid", color="black", weight=3]; 130.29/78.16 18166[label="FiniteMap.splitGT2 (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196 (Pos Zero) (compare (Pos Zero) (Neg (Succ zzz1192)) == GT)",fontsize=16,color="black",shape="box"];18166 -> 18196[label="",style="solid", color="black", weight=3]; 130.29/78.16 13598 -> 2403[label="",style="dashed", color="red", weight=0]; 130.29/78.16 13598[label="FiniteMap.splitLT4 FiniteMap.EmptyFM (Pos Zero)",fontsize=16,color="magenta"];13599[label="FiniteMap.splitLT3 (FiniteMap.Branch zzz6210 zzz6211 zzz6212 zzz6213 zzz6214) (Pos Zero)",fontsize=16,color="black",shape="box"];13599 -> 14687[label="",style="solid", color="black", weight=3]; 130.29/78.16 44356[label="Succ zzz4739",fontsize=16,color="green",shape="box"];44357[label="primMulNat (Succ Zero) (Succ zzz4739)",fontsize=16,color="black",shape="triangle"];44357 -> 44382[label="",style="solid", color="black", weight=3]; 130.29/78.16 62641 -> 62672[label="",style="dashed", color="red", weight=0]; 130.29/78.16 62641[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.glueVBal3Size_r zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464)) zzz6343 == LT)",fontsize=16,color="magenta"];62641 -> 62673[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63655[label="zzz4740330",fontsize=16,color="green",shape="box"];63656 -> 62673[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63656[label="FiniteMap.glueVBal3Size_r zzz4740330 zzz4740331 zzz4740332 zzz4740333 zzz4740334 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464",fontsize=16,color="magenta"];63656 -> 63702[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63656 -> 63703[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63656 -> 63704[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63656 -> 63705[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63656 -> 63706[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63657[label="zzz4740334",fontsize=16,color="green",shape="box"];63658[label="zzz4740333",fontsize=16,color="green",shape="box"];63659[label="zzz4740331",fontsize=16,color="green",shape="box"];63660[label="zzz4740332",fontsize=16,color="green",shape="box"];63661 -> 63758[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63661[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (FiniteMap.mkBalBranch6Size_l zzz474034 zzz474030 zzz474031 zzz6373 + FiniteMap.mkBalBranch6Size_r zzz474034 zzz474030 zzz474031 zzz6373) (Pos (Succ (Succ Zero))) == LT)",fontsize=16,color="magenta"];63661 -> 63759[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 13837[label="FiniteMap.splitGT1 (Pos zzz742) zzz743 zzz744 zzz745 zzz746 (Neg (Succ zzz747)) True",fontsize=16,color="black",shape="box"];13837 -> 14067[label="",style="solid", color="black", weight=3]; 130.29/78.16 29000 -> 12144[label="",style="dashed", color="red", weight=0]; 130.29/78.16 29000[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760))",fontsize=16,color="magenta"];29000 -> 29214[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29000 -> 29215[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29000 -> 29216[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29000 -> 29217[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29000 -> 29218[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29000 -> 29219[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29001[label="zzz2764",fontsize=16,color="green",shape="box"];29002 -> 12146[label="",style="dashed", color="red", weight=0]; 130.29/78.16 29002[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos zzz2755) zzz2756 zzz2757 zzz2758 zzz2759) (Neg (Succ zzz2760))",fontsize=16,color="magenta"];29002 -> 29220[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29002 -> 29221[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29002 -> 29222[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29002 -> 29223[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29002 -> 29224[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29002 -> 29225[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29003[label="zzz2763",fontsize=16,color="green",shape="box"];29004[label="zzz2761",fontsize=16,color="green",shape="box"];11173[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos zzz3320) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos zzz3320) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos zzz3320)) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos zzz3320) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];11173 -> 11434[label="",style="solid", color="black", weight=3]; 130.29/78.16 11174[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg zzz3320) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg zzz3320) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg zzz3320)) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg zzz3320) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];11174 -> 11435[label="",style="solid", color="black", weight=3]; 130.29/78.16 34704[label="zzz35010",fontsize=16,color="green",shape="box"];34705[label="zzz35000",fontsize=16,color="green",shape="box"];34706[label="FiniteMap.splitGT2 (Neg (Succ zzz3494)) zzz3495 zzz3496 zzz3497 zzz3498 (Neg (Succ zzz3499)) True",fontsize=16,color="black",shape="box"];34706 -> 34779[label="",style="solid", color="black", weight=3]; 130.29/78.16 34707[label="FiniteMap.splitGT2 (Neg (Succ zzz3494)) zzz3495 zzz3496 zzz3497 zzz3498 (Neg (Succ zzz3499)) False",fontsize=16,color="black",shape="triangle"];34707 -> 34780[label="",style="solid", color="black", weight=3]; 130.29/78.16 34708 -> 34707[label="",style="dashed", color="red", weight=0]; 130.29/78.16 34708[label="FiniteMap.splitGT2 (Neg (Succ zzz3494)) zzz3495 zzz3496 zzz3497 zzz3498 (Neg (Succ zzz3499)) False",fontsize=16,color="magenta"];15213[label="FiniteMap.splitGT1 (Neg Zero) zzz884 zzz885 zzz886 zzz887 (Neg (Succ zzz888)) (primCmpInt (Neg (Succ zzz888)) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];15213 -> 15439[label="",style="solid", color="black", weight=3]; 130.29/78.16 34774[label="zzz35100",fontsize=16,color="green",shape="box"];34775[label="zzz35090",fontsize=16,color="green",shape="box"];34776[label="FiniteMap.splitLT2 (Neg (Succ zzz3503)) zzz3504 zzz3505 zzz3506 zzz3507 (Neg (Succ zzz3508)) False",fontsize=16,color="black",shape="triangle"];34776 -> 34840[label="",style="solid", color="black", weight=3]; 130.29/78.16 34777[label="FiniteMap.splitLT2 (Neg (Succ zzz3503)) zzz3504 zzz3505 zzz3506 zzz3507 (Neg (Succ zzz3508)) True",fontsize=16,color="black",shape="box"];34777 -> 34841[label="",style="solid", color="black", weight=3]; 130.29/78.16 34778 -> 34776[label="",style="dashed", color="red", weight=0]; 130.29/78.16 34778[label="FiniteMap.splitLT2 (Neg (Succ zzz3503)) zzz3504 zzz3505 zzz3506 zzz3507 (Neg (Succ zzz3508)) False",fontsize=16,color="magenta"];29995 -> 6244[label="",style="dashed", color="red", weight=0]; 130.29/78.16 29995[label="FiniteMap.mkVBalBranch (Neg (Succ zzz2888)) (FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888))) zzz2889) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888))) zzz2891) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888))) zzz2892)",fontsize=16,color="magenta"];29995 -> 30012[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29995 -> 30013[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29995 -> 30014[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29995 -> 30015[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 14935[label="FiniteMap.splitGT2 (Pos zzz83300) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (primCmpInt (Neg Zero) (Pos zzz83300) == GT)",fontsize=16,color="burlywood",shape="box"];65206[label="zzz83300/Succ zzz833000",fontsize=10,color="white",style="solid",shape="box"];14935 -> 65206[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65206 -> 15218[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65207[label="zzz83300/Zero",fontsize=10,color="white",style="solid",shape="box"];14935 -> 65207[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65207 -> 15219[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 14936[label="FiniteMap.splitGT2 (Neg zzz83300) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (primCmpInt (Neg Zero) (Neg zzz83300) == GT)",fontsize=16,color="burlywood",shape="box"];65208[label="zzz83300/Succ zzz833000",fontsize=10,color="white",style="solid",shape="box"];14936 -> 65208[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65208 -> 15220[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65209[label="zzz83300/Zero",fontsize=10,color="white",style="solid",shape="box"];14936 -> 65209[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65209 -> 15221[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 14937[label="FiniteMap.splitLT1 (Neg (Succ zzz833000)) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (compare (Neg Zero) (Neg (Succ zzz833000)) == GT)",fontsize=16,color="black",shape="box"];14937 -> 15222[label="",style="solid", color="black", weight=3]; 130.29/78.16 33714[label="zzz33940",fontsize=16,color="green",shape="box"];33715[label="zzz33930",fontsize=16,color="green",shape="box"];33716[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz3386)) zzz3387 zzz3388 zzz3389 zzz3390 (Neg (Succ zzz3391)) zzz3392 False",fontsize=16,color="black",shape="triangle"];33716 -> 33735[label="",style="solid", color="black", weight=3]; 130.29/78.16 33717[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz3386)) zzz3387 zzz3388 zzz3389 zzz3390 (Neg (Succ zzz3391)) zzz3392 True",fontsize=16,color="black",shape="box"];33717 -> 33736[label="",style="solid", color="black", weight=3]; 130.29/78.16 33718 -> 33716[label="",style="dashed", color="red", weight=0]; 130.29/78.16 33718[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 (Neg (Succ zzz3386)) zzz3387 zzz3388 zzz3389 zzz3390 (Neg (Succ zzz3391)) zzz3392 False",fontsize=16,color="magenta"];14579[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 False",fontsize=16,color="black",shape="box"];14579 -> 14950[label="",style="solid", color="black", weight=3]; 130.29/78.16 14580[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz982000)) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (primCmpNat (Succ zzz982000) Zero == GT)",fontsize=16,color="black",shape="box"];14580 -> 14951[label="",style="solid", color="black", weight=3]; 130.29/78.16 14581[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 False",fontsize=16,color="black",shape="box"];14581 -> 14952[label="",style="solid", color="black", weight=3]; 130.29/78.16 10793[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primPlusNat (Succ zzz353200) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];10793 -> 11849[label="",style="solid", color="black", weight=3]; 130.29/78.16 10794[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];10794 -> 11850[label="",style="solid", color="black", weight=3]; 130.29/78.16 10795[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];10795 -> 11851[label="",style="solid", color="black", weight=3]; 130.29/78.16 10796[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];10796 -> 11852[label="",style="solid", color="black", weight=3]; 130.29/78.16 10797[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];10797 -> 11853[label="",style="solid", color="black", weight=3]; 130.29/78.16 10798[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (Succ zzz353200) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];10798 -> 11854[label="",style="solid", color="black", weight=3]; 130.29/78.16 10799[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];10799 -> 11855[label="",style="solid", color="black", weight=3]; 130.29/78.16 10800[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];10800 -> 11856[label="",style="solid", color="black", weight=3]; 130.29/78.16 10801[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (GT == LT)",fontsize=16,color="black",shape="box"];10801 -> 11857[label="",style="solid", color="black", weight=3]; 130.29/78.16 10802[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];10802 -> 11858[label="",style="solid", color="black", weight=3]; 130.29/78.16 10803[label="FiniteMap.splitLT1 (Neg (Succ zzz3000)) zzz31 zzz32 zzz33 FiniteMap.EmptyFM (Neg Zero) True",fontsize=16,color="black",shape="box"];10803 -> 11859[label="",style="solid", color="black", weight=3]; 130.29/78.16 33824 -> 19598[label="",style="dashed", color="red", weight=0]; 130.29/78.16 33824[label="FiniteMap.splitGT zzz3400 (Pos (Succ zzz3401))",fontsize=16,color="magenta"];33824 -> 33844[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33824 -> 33845[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33825[label="FiniteMap.splitGT1 (Pos (Succ zzz3396)) zzz3397 zzz3398 zzz3399 zzz3400 (Pos (Succ zzz3401)) (Pos (Succ zzz3401) < Pos (Succ zzz3396))",fontsize=16,color="black",shape="box"];33825 -> 33846[label="",style="solid", color="black", weight=3]; 130.29/78.16 34879[label="zzz35400",fontsize=16,color="green",shape="box"];34880[label="zzz35390",fontsize=16,color="green",shape="box"];34881[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) zzz3530 zzz3531 zzz3532 zzz3533 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3534)) zzz3535 zzz3536 zzz3537 zzz3538 (Pos (Succ zzz3529)) True))",fontsize=16,color="black",shape="box"];34881 -> 34932[label="",style="solid", color="black", weight=3]; 130.29/78.16 34882[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) zzz3530 zzz3531 zzz3532 zzz3533 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3534)) zzz3535 zzz3536 zzz3537 zzz3538 (Pos (Succ zzz3529)) False))",fontsize=16,color="black",shape="triangle"];34882 -> 34933[label="",style="solid", color="black", weight=3]; 130.29/78.16 34883 -> 34882[label="",style="dashed", color="red", weight=0]; 130.29/78.16 34883[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) zzz3530 zzz3531 zzz3532 zzz3533 (Maybe.isJust (FiniteMap.lookupFM1 (Pos (Succ zzz3534)) zzz3535 zzz3536 zzz3537 zzz3538 (Pos (Succ zzz3529)) False))",fontsize=16,color="magenta"];29705[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738))",fontsize=16,color="black",shape="triangle"];29705 -> 29744[label="",style="solid", color="black", weight=3]; 130.29/78.16 29706[label="zzz2742",fontsize=16,color="green",shape="box"];29707[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738))",fontsize=16,color="black",shape="triangle"];29707 -> 29745[label="",style="solid", color="black", weight=3]; 130.29/78.16 29708[label="zzz2741",fontsize=16,color="green",shape="box"];32066[label="FiniteMap.splitLT1 (Pos (Succ zzz3133)) zzz3134 zzz3135 zzz3136 zzz3137 (Pos (Succ zzz3138)) (primCmpInt (Pos (Succ zzz3138)) (Pos (Succ zzz3133)) == GT)",fontsize=16,color="black",shape="box"];32066 -> 32224[label="",style="solid", color="black", weight=3]; 130.29/78.16 23046 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.16 23046[label="FiniteMap.mkVBalBranch (Pos Zero) zzz1971 zzz1973 (FiniteMap.splitLT zzz1974 (Pos (Succ zzz1975)))",fontsize=16,color="magenta"];23046 -> 23110[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23046 -> 23111[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23046 -> 23112[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23046 -> 23113[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23047[label="FiniteMap.addToFM (FiniteMap.splitLT zzz1974 (Pos (Succ zzz1975))) (Neg zzz19700) zzz1971",fontsize=16,color="black",shape="box"];23047 -> 23114[label="",style="solid", color="black", weight=3]; 130.29/78.16 23048 -> 7670[label="",style="dashed", color="red", weight=0]; 130.29/78.16 23048[label="FiniteMap.mkVBalBranch (Neg zzz19700) zzz1971 (FiniteMap.Branch zzz19730 zzz19731 zzz19732 zzz19733 zzz19734) (FiniteMap.splitLT4 FiniteMap.EmptyFM (Pos (Succ zzz1975)))",fontsize=16,color="magenta"];23048 -> 23115[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23048 -> 23116[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23048 -> 23117[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23048 -> 23118[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23048 -> 23119[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23048 -> 23120[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23048 -> 23121[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23048 -> 23122[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23049 -> 7670[label="",style="dashed", color="red", weight=0]; 130.29/78.16 23049[label="FiniteMap.mkVBalBranch (Neg zzz19700) zzz1971 (FiniteMap.Branch zzz19730 zzz19731 zzz19732 zzz19733 zzz19734) (FiniteMap.splitLT3 (FiniteMap.Branch zzz19740 zzz19741 zzz19742 zzz19743 zzz19744) (Pos (Succ zzz1975)))",fontsize=16,color="magenta"];23049 -> 23123[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23049 -> 23124[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23049 -> 23125[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23049 -> 23126[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23049 -> 23127[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23049 -> 23128[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23049 -> 23129[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23049 -> 23130[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32288[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) zzz3169 zzz3170 zzz3171 zzz3172 (Maybe.isJust (Just zzz3174))",fontsize=16,color="black",shape="box"];32288 -> 32386[label="",style="solid", color="black", weight=3]; 130.29/78.16 19842[label="FiniteMap.splitLT2 (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386 (Pos (Succ zzz1387)) (Pos (Succ zzz1387) < Neg zzz1382)",fontsize=16,color="black",shape="box"];19842 -> 19938[label="",style="solid", color="black", weight=3]; 130.29/78.16 12321[label="FiniteMap.splitGT1 (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622 (Pos Zero) (Pos Zero < Pos (Succ zzz618))",fontsize=16,color="black",shape="box"];12321 -> 12732[label="",style="solid", color="black", weight=3]; 130.29/78.16 32289[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ zzz3181)) zzz3182 zzz3183 zzz3184 zzz3185 (Pos (Succ zzz3186)) zzz3187 (compare (Pos (Succ zzz3186)) (Pos (Succ zzz3181)) == GT)",fontsize=16,color="black",shape="box"];32289 -> 32387[label="",style="solid", color="black", weight=3]; 130.29/78.16 63109[label="Pos (Succ zzz3181)",fontsize=16,color="green",shape="box"];63110[label="zzz3185",fontsize=16,color="green",shape="box"];63111 -> 4379[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63111[label="FiniteMap.addToFM_C FiniteMap.addToFM0 zzz3184 (Pos (Succ zzz3186)) zzz3187",fontsize=16,color="magenta"];63111 -> 63371[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63111 -> 63372[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63111 -> 63373[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63112[label="zzz3182",fontsize=16,color="green",shape="box"];11219[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) zzz341 zzz342 zzz343 zzz344 (Pos (Succ zzz3000)) zzz31 True",fontsize=16,color="black",shape="box"];11219 -> 12744[label="",style="solid", color="black", weight=3]; 130.29/78.16 63369[label="Succ zzz3000",fontsize=16,color="green",shape="box"];63370[label="zzz344",fontsize=16,color="green",shape="box"];11222[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Pos Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 True",fontsize=16,color="black",shape="box"];11222 -> 12745[label="",style="solid", color="black", weight=3]; 130.29/78.16 63113[label="Neg (Succ zzz34000)",fontsize=16,color="green",shape="box"];63114 -> 4379[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63114[label="FiniteMap.addToFM_C FiniteMap.addToFM0 zzz344 (Pos Zero) zzz31",fontsize=16,color="magenta"];63114 -> 63374[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63114 -> 63375[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63115[label="zzz343",fontsize=16,color="green",shape="box"];63116[label="zzz341",fontsize=16,color="green",shape="box"];11227[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Neg Zero) zzz341 zzz342 zzz343 zzz344 (Pos Zero) zzz31 True",fontsize=16,color="black",shape="box"];11227 -> 12748[label="",style="solid", color="black", weight=3]; 130.29/78.16 11228[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (Succ (Succ (primPlusNat zzz250200 zzz250200))) (Succ zzz250200)) (Succ zzz250200)) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];11228 -> 12749[label="",style="solid", color="black", weight=3]; 130.29/78.16 11229[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];11229 -> 12750[label="",style="solid", color="black", weight=3]; 130.29/78.16 11230[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344)",fontsize=16,color="black",shape="box"];11230 -> 12751[label="",style="solid", color="black", weight=3]; 130.29/78.16 11231[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344)",fontsize=16,color="black",shape="box"];11231 -> 12752[label="",style="solid", color="black", weight=3]; 130.29/78.16 11232[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344)",fontsize=16,color="black",shape="box"];11232 -> 12753[label="",style="solid", color="black", weight=3]; 130.29/78.16 11233[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg 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11235[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344)",fontsize=16,color="black",shape="box"];11235 -> 12759[label="",style="solid", color="black", weight=3]; 130.29/78.16 11236[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];11236 -> 12760[label="",style="solid", color="black", weight=3]; 130.29/78.16 11237[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344)",fontsize=16,color="black",shape="box"];11237 -> 12761[label="",style="solid", color="black", weight=3]; 130.29/78.16 18196[label="FiniteMap.splitGT2 (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ zzz1192)) == GT)",fontsize=16,color="black",shape="box"];18196 -> 18244[label="",style="solid", color="black", weight=3]; 130.29/78.16 14687[label="FiniteMap.splitLT2 zzz6210 zzz6211 zzz6212 zzz6213 zzz6214 (Pos Zero) (Pos Zero < zzz6210)",fontsize=16,color="black",shape="box"];14687 -> 16618[label="",style="solid", color="black", weight=3]; 130.29/78.16 44382 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.16 44382[label="primPlusNat (primMulNat Zero (Succ zzz4739)) (Succ zzz4739)",fontsize=16,color="magenta"];44382 -> 44417[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 44382 -> 44418[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 62673[label="FiniteMap.glueVBal3Size_r zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464",fontsize=16,color="black",shape="triangle"];62673 -> 62675[label="",style="solid", color="black", weight=3]; 130.29/78.16 62672[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz6348) zzz6343 == LT)",fontsize=16,color="burlywood",shape="triangle"];65210[label="zzz6348/Pos zzz63480",fontsize=10,color="white",style="solid",shape="box"];62672 -> 65210[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65210 -> 62676[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65211[label="zzz6348/Neg zzz63480",fontsize=10,color="white",style="solid",shape="box"];62672 -> 65211[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65211 -> 62677[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 63702[label="zzz4740330",fontsize=16,color="green",shape="box"];63703[label="zzz4740334",fontsize=16,color="green",shape="box"];63704[label="zzz4740333",fontsize=16,color="green",shape="box"];63705[label="zzz4740331",fontsize=16,color="green",shape="box"];63706[label="zzz4740332",fontsize=16,color="green",shape="box"];63759[label="FiniteMap.mkBalBranch6Size_l zzz474034 zzz474030 zzz474031 zzz6373 + FiniteMap.mkBalBranch6Size_r zzz474034 zzz474030 zzz474031 zzz6373",fontsize=16,color="black",shape="box"];63759 -> 63764[label="",style="solid", color="black", weight=3]; 130.29/78.16 63758[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt zzz6375 (Pos (Succ (Succ Zero))) == LT)",fontsize=16,color="burlywood",shape="triangle"];65212[label="zzz6375/Pos zzz63750",fontsize=10,color="white",style="solid",shape="box"];63758 -> 65212[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65212 -> 63765[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65213[label="zzz6375/Neg zzz63750",fontsize=10,color="white",style="solid",shape="box"];63758 -> 65213[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65213 -> 63766[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 14067 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.16 14067[label="FiniteMap.mkVBalBranch (Pos zzz742) zzz743 (FiniteMap.splitGT zzz745 (Neg (Succ zzz747))) zzz746",fontsize=16,color="magenta"];14067 -> 14393[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 14067 -> 14394[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 14067 -> 14395[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 14067 -> 14396[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29214[label="zzz2757",fontsize=16,color="green",shape="box"];29215[label="zzz2758",fontsize=16,color="green",shape="box"];29216[label="zzz2759",fontsize=16,color="green",shape="box"];29217[label="zzz2755",fontsize=16,color="green",shape="box"];29218[label="zzz2756",fontsize=16,color="green",shape="box"];29219[label="zzz2760",fontsize=16,color="green",shape="box"];29220[label="zzz2757",fontsize=16,color="green",shape="box"];29221[label="zzz2758",fontsize=16,color="green",shape="box"];29222[label="zzz2759",fontsize=16,color="green",shape="box"];29223[label="zzz2755",fontsize=16,color="green",shape="box"];29224[label="zzz2756",fontsize=16,color="green",shape="box"];29225[label="zzz2760",fontsize=16,color="green",shape="box"];11434[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos zzz3320) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos zzz3320) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz3320)) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos zzz3320) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="burlywood",shape="box"];65214[label="zzz3320/Succ zzz33200",fontsize=10,color="white",style="solid",shape="box"];11434 -> 65214[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65214 -> 12825[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65215[label="zzz3320/Zero",fontsize=10,color="white",style="solid",shape="box"];11434 -> 65215[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65215 -> 12826[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 11435[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg zzz3320) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg zzz3320) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz3320)) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg zzz3320) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="burlywood",shape="box"];65216[label="zzz3320/Succ zzz33200",fontsize=10,color="white",style="solid",shape="box"];11435 -> 65216[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65216 -> 12827[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65217[label="zzz3320/Zero",fontsize=10,color="white",style="solid",shape="box"];11435 -> 65217[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65217 -> 12828[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 34779 -> 14393[label="",style="dashed", color="red", weight=0]; 130.29/78.16 34779[label="FiniteMap.splitGT zzz3498 (Neg (Succ zzz3499))",fontsize=16,color="magenta"];34779 -> 34842[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34779 -> 34843[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34780[label="FiniteMap.splitGT1 (Neg (Succ zzz3494)) zzz3495 zzz3496 zzz3497 zzz3498 (Neg (Succ zzz3499)) (Neg (Succ zzz3499) < Neg (Succ zzz3494))",fontsize=16,color="black",shape="box"];34780 -> 34844[label="",style="solid", color="black", weight=3]; 130.29/78.16 15439[label="FiniteMap.splitGT1 (Neg Zero) zzz884 zzz885 zzz886 zzz887 (Neg (Succ zzz888)) (primCmpNat Zero (Succ zzz888) == LT)",fontsize=16,color="black",shape="box"];15439 -> 15646[label="",style="solid", color="black", weight=3]; 130.29/78.16 34840[label="FiniteMap.splitLT1 (Neg (Succ zzz3503)) zzz3504 zzz3505 zzz3506 zzz3507 (Neg (Succ zzz3508)) (Neg (Succ zzz3508) > Neg (Succ zzz3503))",fontsize=16,color="black",shape="box"];34840 -> 34884[label="",style="solid", color="black", weight=3]; 130.29/78.16 34841 -> 13018[label="",style="dashed", color="red", weight=0]; 130.29/78.16 34841[label="FiniteMap.splitLT zzz3506 (Neg (Succ zzz3508))",fontsize=16,color="magenta"];34841 -> 34885[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34841 -> 34886[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 30012[label="zzz2888",fontsize=16,color="green",shape="box"];30013 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.16 30013[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888))) zzz2892",fontsize=16,color="magenta"];30013 -> 30045[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 30013 -> 30046[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 30014 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.16 30014[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888))) zzz2891",fontsize=16,color="magenta"];30014 -> 30047[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 30014 -> 30048[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 30015[label="FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888))) zzz2889",fontsize=16,color="black",shape="box"];30015 -> 30049[label="",style="solid", color="black", weight=3]; 130.29/78.16 15218[label="FiniteMap.splitGT2 (Pos (Succ zzz833000)) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (primCmpInt (Neg Zero) (Pos (Succ zzz833000)) == GT)",fontsize=16,color="black",shape="box"];15218 -> 15459[label="",style="solid", color="black", weight=3]; 130.29/78.16 15219[label="FiniteMap.splitGT2 (Pos Zero) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];15219 -> 15460[label="",style="solid", color="black", weight=3]; 130.29/78.16 15220[label="FiniteMap.splitGT2 (Neg (Succ zzz833000)) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ zzz833000)) == GT)",fontsize=16,color="black",shape="box"];15220 -> 15461[label="",style="solid", color="black", weight=3]; 130.29/78.16 15221[label="FiniteMap.splitGT2 (Neg Zero) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];15221 -> 15462[label="",style="solid", color="black", weight=3]; 130.29/78.16 15222[label="FiniteMap.splitLT1 (Neg (Succ zzz833000)) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ zzz833000)) == GT)",fontsize=16,color="black",shape="box"];15222 -> 15463[label="",style="solid", color="black", weight=3]; 130.29/78.16 33735[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz3386)) zzz3387 zzz3388 zzz3389 zzz3390 (Neg (Succ zzz3391)) zzz3392 (Neg (Succ zzz3391) > Neg (Succ zzz3386))",fontsize=16,color="black",shape="box"];33735 -> 33826[label="",style="solid", color="black", weight=3]; 130.29/78.16 33736 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.16 33736[label="FiniteMap.mkBalBranch (Neg (Succ zzz3386)) zzz3387 (FiniteMap.addToFM_C FiniteMap.addToFM0 zzz3389 (Neg (Succ zzz3391)) zzz3392) zzz3390",fontsize=16,color="magenta"];33736 -> 63121[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33736 -> 63122[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33736 -> 63123[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33736 -> 63124[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 14950[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Pos Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 otherwise",fontsize=16,color="black",shape="box"];14950 -> 15239[label="",style="solid", color="black", weight=3]; 130.29/78.16 14951[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz982000)) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 (GT == GT)",fontsize=16,color="black",shape="box"];14951 -> 15240[label="",style="solid", color="black", weight=3]; 130.29/78.16 14952[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Neg Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 otherwise",fontsize=16,color="black",shape="box"];14952 -> 15241[label="",style="solid", color="black", weight=3]; 130.29/78.16 11849[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (Succ (Succ (primPlusNat zzz353200 zzz353200))) (Succ zzz353200)) (Succ zzz353200)) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];11849 -> 13075[label="",style="solid", color="black", weight=3]; 130.29/78.16 11850[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];11850 -> 13076[label="",style="solid", color="black", weight=3]; 130.29/78.16 11851[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344)",fontsize=16,color="black",shape="box"];11851 -> 13077[label="",style="solid", color="black", weight=3]; 130.29/78.16 11852[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344)",fontsize=16,color="black",shape="box"];11852 -> 13078[label="",style="solid", color="black", weight=3]; 130.29/78.16 11853[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) 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11855[label="FiniteMap.mkBalBranch zzz340 zzz341 (FiniteMap.mkVBalBranch (Neg Zero) zzz31 (FiniteMap.Branch zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534) zzz343) zzz344",fontsize=16,color="magenta"];11855 -> 63125[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 11855 -> 63126[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 11855 -> 63127[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 11855 -> 63128[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 11856[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 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zzz344)",fontsize=16,color="black",shape="box"];11858 -> 13087[label="",style="solid", color="black", weight=3]; 130.29/78.16 11859 -> 6244[label="",style="dashed", color="red", weight=0]; 130.29/78.16 11859[label="FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 zzz33 (FiniteMap.splitLT FiniteMap.EmptyFM (Neg Zero))",fontsize=16,color="magenta"];11859 -> 13088[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33844[label="zzz3400",fontsize=16,color="green",shape="box"];33845[label="zzz3401",fontsize=16,color="green",shape="box"];33846[label="FiniteMap.splitGT1 (Pos (Succ zzz3396)) zzz3397 zzz3398 zzz3399 zzz3400 (Pos (Succ zzz3401)) (compare (Pos (Succ zzz3401)) (Pos (Succ zzz3396)) == LT)",fontsize=16,color="black",shape="box"];33846 -> 33860[label="",style="solid", color="black", weight=3]; 130.29/78.16 34932 -> 28738[label="",style="dashed", color="red", weight=0]; 130.29/78.16 34932[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) zzz3530 zzz3531 zzz3532 zzz3533 (Maybe.isJust (FiniteMap.lookupFM zzz3538 (Pos (Succ zzz3529))))",fontsize=16,color="magenta"];34932 -> 34971[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34932 -> 34972[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34932 -> 34973[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34932 -> 34974[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34932 -> 34975[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34932 -> 34976[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34932 -> 34977[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34932 -> 34978[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34932 -> 34979[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34932 -> 34980[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34933[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) zzz3530 zzz3531 zzz3532 zzz3533 (Maybe.isJust (FiniteMap.lookupFM0 (Pos (Succ zzz3534)) zzz3535 zzz3536 zzz3537 zzz3538 (Pos (Succ zzz3529)) otherwise))",fontsize=16,color="black",shape="box"];34933 -> 34981[label="",style="solid", color="black", weight=3]; 130.29/78.16 29744 -> 19598[label="",style="dashed", color="red", weight=0]; 130.29/78.16 29744[label="FiniteMap.splitGT (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738))",fontsize=16,color="magenta"];29744 -> 29877[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29744 -> 29878[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29745 -> 23112[label="",style="dashed", color="red", weight=0]; 130.29/78.16 29745[label="FiniteMap.splitLT (FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737) (Pos (Succ zzz2738))",fontsize=16,color="magenta"];29745 -> 29879[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 29745 -> 29880[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32224 -> 38000[label="",style="dashed", color="red", weight=0]; 130.29/78.16 32224[label="FiniteMap.splitLT1 (Pos (Succ zzz3133)) zzz3134 zzz3135 zzz3136 zzz3137 (Pos (Succ zzz3138)) (primCmpNat (Succ zzz3138) (Succ zzz3133) == GT)",fontsize=16,color="magenta"];32224 -> 38001[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32224 -> 38002[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32224 -> 38003[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32224 -> 38004[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32224 -> 38005[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32224 -> 38006[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32224 -> 38007[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32224 -> 38008[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23110[label="zzz1973",fontsize=16,color="green",shape="box"];23111[label="Zero",fontsize=16,color="green",shape="box"];23113[label="zzz1971",fontsize=16,color="green",shape="box"];23114 -> 12360[label="",style="dashed", color="red", weight=0]; 130.29/78.16 23114[label="FiniteMap.addToFM_C FiniteMap.addToFM0 (FiniteMap.splitLT zzz1974 (Pos (Succ zzz1975))) (Neg zzz19700) zzz1971",fontsize=16,color="magenta"];23114 -> 23294[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23114 -> 23295[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23114 -> 23296[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23115[label="zzz19732",fontsize=16,color="green",shape="box"];23116[label="zzz19700",fontsize=16,color="green",shape="box"];23117[label="zzz19734",fontsize=16,color="green",shape="box"];23118 -> 7671[label="",style="dashed", color="red", weight=0]; 130.29/78.16 23118[label="FiniteMap.splitLT4 FiniteMap.EmptyFM (Pos (Succ zzz1975))",fontsize=16,color="magenta"];23118 -> 23297[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 23119[label="zzz19730",fontsize=16,color="green",shape="box"];23120[label="zzz19733",fontsize=16,color="green",shape="box"];23121[label="zzz1971",fontsize=16,color="green",shape="box"];23122[label="zzz19731",fontsize=16,color="green",shape="box"];7670[label="FiniteMap.mkVBalBranch (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) zzz523",fontsize=16,color="burlywood",shape="triangle"];65218[label="zzz523/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];7670 -> 65218[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65218 -> 7786[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65219[label="zzz523/FiniteMap.Branch zzz5230 zzz5231 zzz5232 zzz5233 zzz5234",fontsize=10,color="white",style="solid",shape="box"];7670 -> 65219[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65219 -> 7787[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 23123[label="zzz19732",fontsize=16,color="green",shape="box"];23124[label="zzz19700",fontsize=16,color="green",shape="box"];23125[label="zzz19734",fontsize=16,color="green",shape="box"];23127[label="zzz19730",fontsize=16,color="green",shape="box"];23128[label="zzz19733",fontsize=16,color="green",shape="box"];23129[label="zzz1971",fontsize=16,color="green",shape="box"];23130[label="zzz19731",fontsize=16,color="green",shape="box"];32386[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) FiniteMap.intersectFM0 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168)) zzz3169 zzz3170 zzz3171 zzz3172 True",fontsize=16,color="black",shape="box"];32386 -> 32434[label="",style="solid", color="black", weight=3]; 130.29/78.16 19938 -> 21896[label="",style="dashed", color="red", weight=0]; 130.29/78.16 19938[label="FiniteMap.splitLT2 (Neg zzz1382) zzz1383 zzz1384 zzz1385 zzz1386 (Pos (Succ zzz1387)) (compare (Pos (Succ zzz1387)) (Neg zzz1382) == LT)",fontsize=16,color="magenta"];19938 -> 21921[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 19938 -> 21922[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 19938 -> 21923[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 19938 -> 21924[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 19938 -> 21925[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 19938 -> 21926[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 12732[label="FiniteMap.splitGT1 (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622 (Pos Zero) (compare (Pos Zero) (Pos (Succ zzz618)) == LT)",fontsize=16,color="black",shape="box"];12732 -> 13597[label="",style="solid", color="black", weight=3]; 130.29/78.16 32387[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ zzz3181)) zzz3182 zzz3183 zzz3184 zzz3185 (Pos (Succ zzz3186)) zzz3187 (primCmpInt (Pos (Succ zzz3186)) (Pos (Succ zzz3181)) == GT)",fontsize=16,color="black",shape="box"];32387 -> 32435[label="",style="solid", color="black", weight=3]; 130.29/78.16 63371[label="Succ zzz3186",fontsize=16,color="green",shape="box"];63372[label="zzz3184",fontsize=16,color="green",shape="box"];63373[label="zzz3187",fontsize=16,color="green",shape="box"];12744 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.16 12744[label="FiniteMap.mkBalBranch (Pos Zero) zzz341 zzz343 (FiniteMap.addToFM_C FiniteMap.addToFM0 zzz344 (Pos (Succ zzz3000)) zzz31)",fontsize=16,color="magenta"];12744 -> 63129[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 12744 -> 63130[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 12744 -> 63131[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 12744 -> 63132[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 12745[label="FiniteMap.Branch (Pos Zero) (FiniteMap.addToFM0 zzz341 zzz31) zzz342 zzz343 zzz344",fontsize=16,color="green",shape="box"];12745 -> 13616[label="",style="dashed", color="green", weight=3]; 130.29/78.16 63374[label="Zero",fontsize=16,color="green",shape="box"];63375[label="zzz344",fontsize=16,color="green",shape="box"];12748[label="FiniteMap.Branch (Pos Zero) (FiniteMap.addToFM0 zzz341 zzz31) zzz342 zzz343 zzz344",fontsize=16,color="green",shape="box"];12748 -> 13617[label="",style="dashed", color="green", weight=3]; 130.29/78.16 12749[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200))) (Succ zzz250200)) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];12749 -> 13618[label="",style="solid", color="black", weight=3]; 130.29/78.16 12750 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.16 12750[label="FiniteMap.mkBalBranch zzz340 zzz341 (FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504) zzz343) zzz344",fontsize=16,color="magenta"];12750 -> 63133[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 12750 -> 63134[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 12750 -> 63135[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 12750 -> 63136[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 12751[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];12751 -> 13623[label="",style="solid", color="black", weight=3]; 130.29/78.16 12752[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];12752 -> 13624[label="",style="solid", color="black", weight=3]; 130.29/78.16 12753[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];12753 -> 13625[label="",style="solid", color="black", weight=3]; 130.29/78.16 12754[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200))) (Succ zzz250200)) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];12754 -> 13626[label="",style="solid", color="black", weight=3]; 130.29/78.16 63117[label="zzz340",fontsize=16,color="green",shape="box"];63118[label="zzz344",fontsize=16,color="green",shape="box"];63119 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63119[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504) zzz343",fontsize=16,color="magenta"];63119 -> 63376[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63119 -> 63377[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63120[label="zzz341",fontsize=16,color="green",shape="box"];12759[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];12759 -> 13629[label="",style="solid", color="black", weight=3]; 130.29/78.16 12760[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344)",fontsize=16,color="black",shape="box"];12760 -> 13630[label="",style="solid", color="black", weight=3]; 130.29/78.16 12761[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];12761 -> 13631[label="",style="solid", color="black", weight=3]; 130.29/78.16 18244[label="FiniteMap.splitGT2 (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196 (Pos Zero) (GT == GT)",fontsize=16,color="black",shape="triangle"];18244 -> 18288[label="",style="solid", color="black", weight=3]; 130.29/78.16 16618[label="FiniteMap.splitLT2 zzz6210 zzz6211 zzz6212 zzz6213 zzz6214 (Pos Zero) (compare (Pos Zero) zzz6210 == LT)",fontsize=16,color="black",shape="box"];16618 -> 17917[label="",style="solid", color="black", weight=3]; 130.29/78.16 44417[label="Succ zzz4739",fontsize=16,color="green",shape="box"];44418[label="primMulNat Zero (Succ zzz4739)",fontsize=16,color="black",shape="triangle"];44418 -> 44446[label="",style="solid", color="black", weight=3]; 130.29/78.16 62675 -> 54589[label="",style="dashed", color="red", weight=0]; 130.29/78.16 62675[label="FiniteMap.sizeFM (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034)",fontsize=16,color="magenta"];62675 -> 62686[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 62676[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos zzz63480)) zzz6343 == LT)",fontsize=16,color="black",shape="box"];62676 -> 62687[label="",style="solid", color="black", weight=3]; 130.29/78.16 62677[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg zzz63480)) zzz6343 == LT)",fontsize=16,color="black",shape="box"];62677 -> 62688[label="",style="solid", color="black", weight=3]; 130.29/78.16 63764 -> 63792[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63764[label="primPlusInt (FiniteMap.mkBalBranch6Size_l zzz474034 zzz474030 zzz474031 zzz6373) (FiniteMap.mkBalBranch6Size_r zzz474034 zzz474030 zzz474031 zzz6373)",fontsize=16,color="magenta"];63764 -> 63793[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63765[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos zzz63750) (Pos (Succ (Succ Zero))) == LT)",fontsize=16,color="burlywood",shape="box"];65220[label="zzz63750/Succ zzz637500",fontsize=10,color="white",style="solid",shape="box"];63765 -> 65220[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65220 -> 63780[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65221[label="zzz63750/Zero",fontsize=10,color="white",style="solid",shape="box"];63765 -> 65221[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65221 -> 63781[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 63766[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg zzz63750) (Pos (Succ (Succ Zero))) == LT)",fontsize=16,color="burlywood",shape="box"];65222[label="zzz63750/Succ zzz637500",fontsize=10,color="white",style="solid",shape="box"];63766 -> 65222[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65222 -> 63782[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65223[label="zzz63750/Zero",fontsize=10,color="white",style="solid",shape="box"];63766 -> 65223[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65223 -> 63783[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 14394[label="zzz742",fontsize=16,color="green",shape="box"];14395[label="zzz746",fontsize=16,color="green",shape="box"];14396[label="zzz743",fontsize=16,color="green",shape="box"];12825[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];12825 -> 13700[label="",style="solid", color="black", weight=3]; 130.29/78.16 12826[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];12826 -> 13701[label="",style="solid", color="black", weight=3]; 130.29/78.16 12827[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];12827 -> 13702[label="",style="solid", color="black", weight=3]; 130.29/78.16 12828[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];12828 -> 13703[label="",style="solid", color="black", weight=3]; 130.29/78.16 34842[label="zzz3498",fontsize=16,color="green",shape="box"];34843[label="zzz3499",fontsize=16,color="green",shape="box"];34844[label="FiniteMap.splitGT1 (Neg (Succ zzz3494)) zzz3495 zzz3496 zzz3497 zzz3498 (Neg (Succ zzz3499)) (compare (Neg (Succ zzz3499)) (Neg (Succ zzz3494)) == LT)",fontsize=16,color="black",shape="box"];34844 -> 34887[label="",style="solid", color="black", weight=3]; 130.29/78.16 15646[label="FiniteMap.splitGT1 (Neg Zero) zzz884 zzz885 zzz886 zzz887 (Neg (Succ zzz888)) (LT == LT)",fontsize=16,color="black",shape="box"];15646 -> 15992[label="",style="solid", color="black", weight=3]; 130.29/78.16 34884[label="FiniteMap.splitLT1 (Neg (Succ zzz3503)) zzz3504 zzz3505 zzz3506 zzz3507 (Neg (Succ zzz3508)) (compare (Neg (Succ zzz3508)) (Neg (Succ zzz3503)) == GT)",fontsize=16,color="black",shape="box"];34884 -> 34934[label="",style="solid", color="black", weight=3]; 130.29/78.16 34885[label="zzz3506",fontsize=16,color="green",shape="box"];34886[label="zzz3508",fontsize=16,color="green",shape="box"];30045 -> 13437[label="",style="dashed", color="red", weight=0]; 130.29/78.16 30045[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888))",fontsize=16,color="magenta"];30045 -> 30086[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 30045 -> 30087[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 30045 -> 30088[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 30045 -> 30089[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 30045 -> 30090[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 30046[label="zzz2892",fontsize=16,color="green",shape="box"];30047 -> 13439[label="",style="dashed", color="red", weight=0]; 130.29/78.16 30047[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg Zero) zzz2884 zzz2885 zzz2886 zzz2887) (Neg (Succ zzz2888))",fontsize=16,color="magenta"];30047 -> 30091[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 30047 -> 30092[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 30047 -> 30093[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 30047 -> 30094[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 30047 -> 30095[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 30048[label="zzz2891",fontsize=16,color="green",shape="box"];30049[label="zzz2889",fontsize=16,color="green",shape="box"];15459 -> 12472[label="",style="dashed", color="red", weight=0]; 130.29/78.16 15459[label="FiniteMap.splitGT2 (Pos (Succ zzz833000)) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (LT == GT)",fontsize=16,color="magenta"];15459 -> 15661[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 15459 -> 15662[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 15459 -> 15663[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 15459 -> 15664[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 15459 -> 15665[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 15460 -> 6084[label="",style="dashed", color="red", weight=0]; 130.29/78.16 15460[label="FiniteMap.splitGT2 (Pos Zero) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (EQ == GT)",fontsize=16,color="magenta"];15460 -> 15666[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 15460 -> 15667[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 15460 -> 15668[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 15460 -> 15669[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 15461[label="FiniteMap.splitGT2 (Neg (Succ zzz833000)) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (primCmpNat (Succ zzz833000) Zero == GT)",fontsize=16,color="black",shape="box"];15461 -> 15670[label="",style="solid", color="black", weight=3]; 130.29/78.16 15462 -> 6089[label="",style="dashed", color="red", weight=0]; 130.29/78.16 15462[label="FiniteMap.splitGT2 (Neg Zero) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (EQ == GT)",fontsize=16,color="magenta"];15462 -> 15671[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 15462 -> 15672[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 15462 -> 15673[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 15462 -> 15674[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 15463[label="FiniteMap.splitLT1 (Neg (Succ zzz833000)) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (primCmpNat (Succ zzz833000) Zero == GT)",fontsize=16,color="black",shape="box"];15463 -> 15675[label="",style="solid", color="black", weight=3]; 130.29/78.16 33826[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz3386)) zzz3387 zzz3388 zzz3389 zzz3390 (Neg (Succ zzz3391)) zzz3392 (compare (Neg (Succ zzz3391)) (Neg (Succ zzz3386)) == GT)",fontsize=16,color="black",shape="box"];33826 -> 33847[label="",style="solid", color="black", weight=3]; 130.29/78.16 63121[label="Neg (Succ zzz3386)",fontsize=16,color="green",shape="box"];63122[label="zzz3390",fontsize=16,color="green",shape="box"];63123 -> 12360[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63123[label="FiniteMap.addToFM_C FiniteMap.addToFM0 zzz3389 (Neg (Succ zzz3391)) zzz3392",fontsize=16,color="magenta"];63123 -> 63378[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63123 -> 63379[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63123 -> 63380[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63124[label="zzz3387",fontsize=16,color="green",shape="box"];15239[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Pos Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 True",fontsize=16,color="black",shape="box"];15239 -> 15474[label="",style="solid", color="black", weight=3]; 130.29/78.16 15240[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz982000)) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 True",fontsize=16,color="black",shape="box"];15240 -> 15475[label="",style="solid", color="black", weight=3]; 130.29/78.16 15241[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Neg Zero) zzz9821 zzz9822 zzz9823 zzz9824 (Neg Zero) zzz31 True",fontsize=16,color="black",shape="box"];15241 -> 15476[label="",style="solid", color="black", weight=3]; 130.29/78.16 13075[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200))) (Succ zzz353200)) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];13075 -> 14132[label="",style="solid", color="black", weight=3]; 130.29/78.16 13076 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.16 13076[label="FiniteMap.mkBalBranch zzz340 zzz341 (FiniteMap.mkVBalBranch (Neg Zero) zzz31 (FiniteMap.Branch zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534) zzz343) zzz344",fontsize=16,color="magenta"];13076 -> 63137[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 13076 -> 63138[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 13076 -> 63139[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 13076 -> 63140[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 13077[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];13077 -> 14137[label="",style="solid", color="black", weight=3]; 130.29/78.16 13078[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];13078 -> 14138[label="",style="solid", color="black", weight=3]; 130.29/78.16 13079[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];13079 -> 14139[label="",style="solid", color="black", weight=3]; 130.29/78.16 13080[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200))) (Succ zzz353200)) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];13080 -> 14140[label="",style="solid", color="black", weight=3]; 130.29/78.16 63125[label="zzz340",fontsize=16,color="green",shape="box"];63126[label="zzz344",fontsize=16,color="green",shape="box"];63127 -> 7670[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63127[label="FiniteMap.mkVBalBranch (Neg Zero) zzz31 (FiniteMap.Branch zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534) zzz343",fontsize=16,color="magenta"];63127 -> 63381[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63127 -> 63382[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63127 -> 63383[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63127 -> 63384[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63127 -> 63385[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63127 -> 63386[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63127 -> 63387[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63128[label="zzz341",fontsize=16,color="green",shape="box"];13085[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];13085 -> 14148[label="",style="solid", color="black", weight=3]; 130.29/78.16 13086[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344)",fontsize=16,color="black",shape="box"];13086 -> 14149[label="",style="solid", color="black", weight=3]; 130.29/78.16 13087[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];13087 -> 14150[label="",style="solid", color="black", weight=3]; 130.29/78.16 13088 -> 12653[label="",style="dashed", color="red", weight=0]; 130.29/78.16 13088[label="FiniteMap.splitLT FiniteMap.EmptyFM (Neg Zero)",fontsize=16,color="magenta"];13088 -> 14151[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33860[label="FiniteMap.splitGT1 (Pos (Succ zzz3396)) zzz3397 zzz3398 zzz3399 zzz3400 (Pos (Succ zzz3401)) (primCmpInt (Pos (Succ zzz3401)) (Pos (Succ zzz3396)) == LT)",fontsize=16,color="black",shape="box"];33860 -> 33873[label="",style="solid", color="black", weight=3]; 130.29/78.16 34971[label="zzz3533",fontsize=16,color="green",shape="box"];34972[label="zzz3528",fontsize=16,color="green",shape="box"];34973[label="zzz3530",fontsize=16,color="green",shape="box"];34974[label="zzz3527",fontsize=16,color="green",shape="box"];34975[label="zzz3531",fontsize=16,color="green",shape="box"];34976[label="zzz3538",fontsize=16,color="green",shape="box"];34977[label="zzz3525",fontsize=16,color="green",shape="box"];34978[label="zzz3526",fontsize=16,color="green",shape="box"];34979[label="zzz3529",fontsize=16,color="green",shape="box"];34980[label="zzz3532",fontsize=16,color="green",shape="box"];34981[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) zzz3530 zzz3531 zzz3532 zzz3533 (Maybe.isJust (FiniteMap.lookupFM0 (Pos (Succ zzz3534)) zzz3535 zzz3536 zzz3537 zzz3538 (Pos (Succ zzz3529)) True))",fontsize=16,color="black",shape="box"];34981 -> 35042[label="",style="solid", color="black", weight=3]; 130.29/78.16 29877[label="FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737",fontsize=16,color="green",shape="box"];29878[label="zzz2738",fontsize=16,color="green",shape="box"];29879[label="zzz2738",fontsize=16,color="green",shape="box"];29880[label="FiniteMap.Branch (Pos Zero) zzz2734 zzz2735 zzz2736 zzz2737",fontsize=16,color="green",shape="box"];38001[label="zzz3133",fontsize=16,color="green",shape="box"];38002[label="Succ zzz3133",fontsize=16,color="green",shape="box"];38003[label="Succ zzz3138",fontsize=16,color="green",shape="box"];38004[label="zzz3136",fontsize=16,color="green",shape="box"];38005[label="zzz3134",fontsize=16,color="green",shape="box"];38006[label="zzz3138",fontsize=16,color="green",shape="box"];38007[label="zzz3137",fontsize=16,color="green",shape="box"];38008[label="zzz3135",fontsize=16,color="green",shape="box"];38000[label="FiniteMap.splitLT1 (Pos (Succ zzz4178)) zzz4179 zzz4180 zzz4181 zzz4182 (Pos (Succ zzz4183)) (primCmpNat zzz4184 zzz4185 == GT)",fontsize=16,color="burlywood",shape="triangle"];65224[label="zzz4184/Succ zzz41840",fontsize=10,color="white",style="solid",shape="box"];38000 -> 65224[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65224 -> 38089[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65225[label="zzz4184/Zero",fontsize=10,color="white",style="solid",shape="box"];38000 -> 65225[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65225 -> 38090[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 23294 -> 23112[label="",style="dashed", color="red", weight=0]; 130.29/78.16 23294[label="FiniteMap.splitLT zzz1974 (Pos (Succ zzz1975))",fontsize=16,color="magenta"];23295[label="zzz19700",fontsize=16,color="green",shape="box"];23296[label="zzz1971",fontsize=16,color="green",shape="box"];23297[label="zzz1975",fontsize=16,color="green",shape="box"];7786[label="FiniteMap.mkVBalBranch (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];7786 -> 11067[label="",style="solid", color="black", weight=3]; 130.29/78.16 7787[label="FiniteMap.mkVBalBranch (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) (FiniteMap.Branch zzz5230 zzz5231 zzz5232 zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];7787 -> 11068[label="",style="solid", color="black", weight=3]; 130.29/78.16 32434 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.16 32434[label="FiniteMap.mkVBalBranch (Pos (Succ zzz3168)) (FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168))) zzz3169) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168))) zzz3171) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168))) zzz3172)",fontsize=16,color="magenta"];32434 -> 32536[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32434 -> 32537[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32434 -> 32538[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32434 -> 32539[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 21921[label="zzz1385",fontsize=16,color="green",shape="box"];21922[label="Neg zzz1382",fontsize=16,color="green",shape="box"];21923[label="zzz1387",fontsize=16,color="green",shape="box"];21924[label="zzz1386",fontsize=16,color="green",shape="box"];21925[label="zzz1384",fontsize=16,color="green",shape="box"];21926[label="zzz1383",fontsize=16,color="green",shape="box"];13597[label="FiniteMap.splitGT1 (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622 (Pos Zero) (primCmpInt (Pos Zero) (Pos (Succ zzz618)) == LT)",fontsize=16,color="black",shape="box"];13597 -> 14686[label="",style="solid", color="black", weight=3]; 130.29/78.16 32435 -> 38579[label="",style="dashed", color="red", weight=0]; 130.29/78.16 32435[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ zzz3181)) zzz3182 zzz3183 zzz3184 zzz3185 (Pos (Succ zzz3186)) zzz3187 (primCmpNat (Succ zzz3186) (Succ zzz3181) == GT)",fontsize=16,color="magenta"];32435 -> 38580[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32435 -> 38581[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32435 -> 38582[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32435 -> 38583[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32435 -> 38584[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32435 -> 38585[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32435 -> 38586[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32435 -> 38587[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32435 -> 38588[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63129[label="Pos Zero",fontsize=16,color="green",shape="box"];63130 -> 4379[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63130[label="FiniteMap.addToFM_C FiniteMap.addToFM0 zzz344 (Pos (Succ zzz3000)) zzz31",fontsize=16,color="magenta"];63130 -> 63388[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63130 -> 63389[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63131[label="zzz343",fontsize=16,color="green",shape="box"];63132[label="zzz341",fontsize=16,color="green",shape="box"];13616[label="FiniteMap.addToFM0 zzz341 zzz31",fontsize=16,color="black",shape="triangle"];13616 -> 14701[label="",style="solid", color="black", weight=3]; 130.29/78.16 13617 -> 13616[label="",style="dashed", color="red", weight=0]; 130.29/78.16 13617[label="FiniteMap.addToFM0 zzz341 zzz31",fontsize=16,color="magenta"];13618[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200))) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];13618 -> 14702[label="",style="solid", color="black", weight=3]; 130.29/78.16 63133[label="zzz340",fontsize=16,color="green",shape="box"];63134[label="zzz344",fontsize=16,color="green",shape="box"];63135 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63135[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504) zzz343",fontsize=16,color="magenta"];63135 -> 63390[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63135 -> 63391[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63136[label="zzz341",fontsize=16,color="green",shape="box"];13623[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];13623 -> 14705[label="",style="solid", color="black", weight=3]; 130.29/78.16 13624[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];13624 -> 14706[label="",style="solid", color="black", weight=3]; 130.29/78.16 13625[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];13625 -> 14707[label="",style="solid", color="black", weight=3]; 130.29/78.16 13626[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200))) (Succ zzz250200))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];13626 -> 14708[label="",style="solid", color="black", weight=3]; 130.29/78.16 63376[label="FiniteMap.Branch zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504",fontsize=16,color="green",shape="box"];63377[label="zzz343",fontsize=16,color="green",shape="box"];13629[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];13629 -> 14709[label="",style="solid", color="black", weight=3]; 130.29/78.16 13630[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];13630 -> 14710[label="",style="solid", color="black", weight=3]; 130.29/78.16 13631[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];13631 -> 14711[label="",style="solid", color="black", weight=3]; 130.29/78.16 18288[label="FiniteMap.splitGT2 (Neg (Succ zzz1192)) zzz1193 zzz1194 zzz1195 zzz1196 (Pos Zero) True",fontsize=16,color="black",shape="box"];18288 -> 18327[label="",style="solid", color="black", weight=3]; 130.29/78.16 17917[label="FiniteMap.splitLT2 zzz6210 zzz6211 zzz6212 zzz6213 zzz6214 (Pos Zero) (primCmpInt (Pos Zero) zzz6210 == LT)",fontsize=16,color="burlywood",shape="box"];65226[label="zzz6210/Pos zzz62100",fontsize=10,color="white",style="solid",shape="box"];17917 -> 65226[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65226 -> 18141[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65227[label="zzz6210/Neg zzz62100",fontsize=10,color="white",style="solid",shape="box"];17917 -> 65227[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65227 -> 18142[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 44446[label="Zero",fontsize=16,color="green",shape="box"];62686[label="FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034",fontsize=16,color="green",shape="box"];62687 -> 62699[label="",style="dashed", color="red", weight=0]; 130.29/78.16 62687[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz63480)) zzz6343 == LT)",fontsize=16,color="magenta"];62687 -> 62700[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 62688 -> 62701[label="",style="dashed", color="red", weight=0]; 130.29/78.16 62688[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz63480)) zzz6343 == LT)",fontsize=16,color="magenta"];62688 -> 62702[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63793[label="FiniteMap.mkBalBranch6Size_l zzz474034 zzz474030 zzz474031 zzz6373",fontsize=16,color="black",shape="triangle"];63793 -> 63795[label="",style="solid", color="black", weight=3]; 130.29/78.16 63792[label="primPlusInt zzz6377 (FiniteMap.mkBalBranch6Size_r zzz474034 zzz474030 zzz474031 zzz6373)",fontsize=16,color="burlywood",shape="triangle"];65228[label="zzz6377/Pos zzz63770",fontsize=10,color="white",style="solid",shape="box"];63792 -> 65228[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65228 -> 63796[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65229[label="zzz6377/Neg zzz63770",fontsize=10,color="white",style="solid",shape="box"];63792 -> 65229[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65229 -> 63797[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 63780[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos (Succ zzz637500)) (Pos (Succ (Succ Zero))) == LT)",fontsize=16,color="black",shape="box"];63780 -> 63798[label="",style="solid", color="black", weight=3]; 130.29/78.16 63781[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (Pos (Succ (Succ Zero))) == LT)",fontsize=16,color="black",shape="box"];63781 -> 63799[label="",style="solid", color="black", weight=3]; 130.29/78.16 63782[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg (Succ zzz637500)) (Pos (Succ (Succ Zero))) == LT)",fontsize=16,color="black",shape="box"];63782 -> 63800[label="",style="solid", color="black", weight=3]; 130.29/78.16 63783[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (Pos (Succ (Succ Zero))) == LT)",fontsize=16,color="black",shape="box"];63783 -> 63801[label="",style="solid", color="black", weight=3]; 130.29/78.16 13700[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Pos (primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];13700 -> 15272[label="",style="solid", color="black", weight=3]; 130.29/78.16 13701[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];13701 -> 15273[label="",style="solid", color="black", weight=3]; 130.29/78.16 13702[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Neg (primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];13702 -> 15274[label="",style="solid", color="black", weight=3]; 130.29/78.16 13703[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];13703 -> 15275[label="",style="solid", color="black", weight=3]; 130.29/78.16 34887[label="FiniteMap.splitGT1 (Neg (Succ zzz3494)) zzz3495 zzz3496 zzz3497 zzz3498 (Neg (Succ zzz3499)) (primCmpInt (Neg (Succ zzz3499)) (Neg (Succ zzz3494)) == LT)",fontsize=16,color="black",shape="box"];34887 -> 34935[label="",style="solid", color="black", weight=3]; 130.29/78.16 15992[label="FiniteMap.splitGT1 (Neg Zero) zzz884 zzz885 zzz886 zzz887 (Neg (Succ zzz888)) True",fontsize=16,color="black",shape="box"];15992 -> 17239[label="",style="solid", color="black", weight=3]; 130.29/78.16 34934[label="FiniteMap.splitLT1 (Neg (Succ zzz3503)) zzz3504 zzz3505 zzz3506 zzz3507 (Neg (Succ zzz3508)) (primCmpInt (Neg (Succ zzz3508)) (Neg (Succ zzz3503)) == GT)",fontsize=16,color="black",shape="box"];34934 -> 34982[label="",style="solid", color="black", weight=3]; 130.29/78.16 30086[label="zzz2885",fontsize=16,color="green",shape="box"];30087[label="zzz2884",fontsize=16,color="green",shape="box"];30088[label="zzz2886",fontsize=16,color="green",shape="box"];30089[label="zzz2888",fontsize=16,color="green",shape="box"];30090[label="zzz2887",fontsize=16,color="green",shape="box"];30091[label="zzz2885",fontsize=16,color="green",shape="box"];30092[label="zzz2884",fontsize=16,color="green",shape="box"];30093[label="zzz2886",fontsize=16,color="green",shape="box"];30094[label="zzz2888",fontsize=16,color="green",shape="box"];30095[label="zzz2887",fontsize=16,color="green",shape="box"];15661[label="zzz8331",fontsize=16,color="green",shape="box"];15662[label="zzz833000",fontsize=16,color="green",shape="box"];15663[label="zzz8332",fontsize=16,color="green",shape="box"];15664[label="zzz8334",fontsize=16,color="green",shape="box"];15665[label="zzz8333",fontsize=16,color="green",shape="box"];15666[label="zzz8332",fontsize=16,color="green",shape="box"];15667[label="zzz8334",fontsize=16,color="green",shape="box"];15668[label="zzz8333",fontsize=16,color="green",shape="box"];15669[label="zzz8331",fontsize=16,color="green",shape="box"];15670[label="FiniteMap.splitGT2 (Neg (Succ zzz833000)) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (GT == GT)",fontsize=16,color="black",shape="box"];15670 -> 16011[label="",style="solid", color="black", weight=3]; 130.29/78.16 15671[label="zzz8332",fontsize=16,color="green",shape="box"];15672[label="zzz8334",fontsize=16,color="green",shape="box"];15673[label="zzz8333",fontsize=16,color="green",shape="box"];15674[label="zzz8331",fontsize=16,color="green",shape="box"];15675[label="FiniteMap.splitLT1 (Neg (Succ zzz833000)) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) (GT == GT)",fontsize=16,color="black",shape="box"];15675 -> 16012[label="",style="solid", color="black", weight=3]; 130.29/78.16 33847[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz3386)) zzz3387 zzz3388 zzz3389 zzz3390 (Neg (Succ zzz3391)) zzz3392 (primCmpInt (Neg (Succ zzz3391)) (Neg (Succ zzz3386)) == GT)",fontsize=16,color="black",shape="box"];33847 -> 33861[label="",style="solid", color="black", weight=3]; 130.29/78.16 63378[label="zzz3389",fontsize=16,color="green",shape="box"];63379[label="Succ zzz3391",fontsize=16,color="green",shape="box"];63380[label="zzz3392",fontsize=16,color="green",shape="box"];15474[label="FiniteMap.Branch (Neg Zero) (FiniteMap.addToFM0 zzz9821 zzz31) zzz9822 zzz9823 zzz9824",fontsize=16,color="green",shape="box"];15474 -> 15753[label="",style="dashed", color="green", weight=3]; 130.29/78.16 15475 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.16 15475[label="FiniteMap.mkBalBranch (Neg (Succ zzz982000)) zzz9821 zzz9823 (FiniteMap.addToFM_C FiniteMap.addToFM0 zzz9824 (Neg Zero) zzz31)",fontsize=16,color="magenta"];15475 -> 63141[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 15475 -> 63142[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 15475 -> 63143[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 15475 -> 63144[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 15476[label="FiniteMap.Branch (Neg Zero) (FiniteMap.addToFM0 zzz9821 zzz31) zzz9822 zzz9823 zzz9824",fontsize=16,color="green",shape="box"];15476 -> 15758[label="",style="dashed", color="green", weight=3]; 130.29/78.16 14132[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200))) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];14132 -> 15759[label="",style="solid", color="black", weight=3]; 130.29/78.16 63137[label="zzz340",fontsize=16,color="green",shape="box"];63138[label="zzz344",fontsize=16,color="green",shape="box"];63139 -> 7670[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63139[label="FiniteMap.mkVBalBranch (Neg Zero) zzz31 (FiniteMap.Branch zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534) zzz343",fontsize=16,color="magenta"];63139 -> 63392[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63139 -> 63393[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63139 -> 63394[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63139 -> 63395[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63139 -> 63396[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63139 -> 63397[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63139 -> 63398[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63140[label="zzz341",fontsize=16,color="green",shape="box"];14137[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];14137 -> 15767[label="",style="solid", color="black", weight=3]; 130.29/78.16 14138[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];14138 -> 15768[label="",style="solid", color="black", weight=3]; 130.29/78.16 14139[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];14139 -> 15769[label="",style="solid", color="black", weight=3]; 130.29/78.16 14140[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200))) (Succ zzz353200))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];14140 -> 15770[label="",style="solid", color="black", weight=3]; 130.29/78.16 63381[label="Neg Zero",fontsize=16,color="green",shape="box"];63382[label="Zero",fontsize=16,color="green",shape="box"];63383[label="zzz3534",fontsize=16,color="green",shape="box"];63384[label="zzz343",fontsize=16,color="green",shape="box"];63385[label="zzz3530",fontsize=16,color="green",shape="box"];63386[label="zzz3533",fontsize=16,color="green",shape="box"];63387[label="zzz3531",fontsize=16,color="green",shape="box"];14148[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];14148 -> 15771[label="",style="solid", color="black", weight=3]; 130.29/78.16 14149[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];14149 -> 15772[label="",style="solid", color="black", weight=3]; 130.29/78.16 14150[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];14150 -> 15773[label="",style="solid", color="black", weight=3]; 130.29/78.16 14151[label="FiniteMap.EmptyFM",fontsize=16,color="green",shape="box"];33873 -> 39386[label="",style="dashed", color="red", weight=0]; 130.29/78.16 33873[label="FiniteMap.splitGT1 (Pos (Succ zzz3396)) zzz3397 zzz3398 zzz3399 zzz3400 (Pos (Succ zzz3401)) (primCmpNat (Succ zzz3401) (Succ zzz3396) == LT)",fontsize=16,color="magenta"];33873 -> 39387[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33873 -> 39388[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33873 -> 39389[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33873 -> 39390[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33873 -> 39391[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33873 -> 39392[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33873 -> 39393[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33873 -> 39394[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 35042[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) zzz3530 zzz3531 zzz3532 zzz3533 (Maybe.isJust (Just zzz3535))",fontsize=16,color="black",shape="box"];35042 -> 35187[label="",style="solid", color="black", weight=3]; 130.29/78.16 38089[label="FiniteMap.splitLT1 (Pos (Succ zzz4178)) zzz4179 zzz4180 zzz4181 zzz4182 (Pos (Succ zzz4183)) (primCmpNat (Succ zzz41840) zzz4185 == GT)",fontsize=16,color="burlywood",shape="box"];65230[label="zzz4185/Succ zzz41850",fontsize=10,color="white",style="solid",shape="box"];38089 -> 65230[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65230 -> 38110[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65231[label="zzz4185/Zero",fontsize=10,color="white",style="solid",shape="box"];38089 -> 65231[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65231 -> 38111[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 38090[label="FiniteMap.splitLT1 (Pos (Succ zzz4178)) zzz4179 zzz4180 zzz4181 zzz4182 (Pos (Succ zzz4183)) (primCmpNat Zero zzz4185 == GT)",fontsize=16,color="burlywood",shape="box"];65232[label="zzz4185/Succ zzz41850",fontsize=10,color="white",style="solid",shape="box"];38090 -> 65232[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65232 -> 38112[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65233[label="zzz4185/Zero",fontsize=10,color="white",style="solid",shape="box"];38090 -> 65233[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65233 -> 38113[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 11067[label="FiniteMap.mkVBalBranch4 (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];11067 -> 12428[label="",style="solid", color="black", weight=3]; 130.29/78.16 11068[label="FiniteMap.mkVBalBranch3 (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) (FiniteMap.Branch zzz5230 zzz5231 zzz5232 zzz5233 zzz5234)",fontsize=16,color="black",shape="triangle"];11068 -> 12429[label="",style="solid", color="black", weight=3]; 130.29/78.16 32536 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.16 32536[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168))) zzz3171",fontsize=16,color="magenta"];32536 -> 32670[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32536 -> 32671[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32537[label="Succ zzz3168",fontsize=16,color="green",shape="box"];32538 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.16 32538[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168))) zzz3172",fontsize=16,color="magenta"];32538 -> 32672[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32538 -> 32673[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32539[label="FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168))) zzz3169",fontsize=16,color="black",shape="box"];32539 -> 32674[label="",style="solid", color="black", weight=3]; 130.29/78.16 14686[label="FiniteMap.splitGT1 (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622 (Pos Zero) (primCmpNat Zero (Succ zzz618) == LT)",fontsize=16,color="black",shape="box"];14686 -> 16617[label="",style="solid", color="black", weight=3]; 130.29/78.16 38580[label="zzz3184",fontsize=16,color="green",shape="box"];38581[label="zzz3181",fontsize=16,color="green",shape="box"];38582[label="zzz3183",fontsize=16,color="green",shape="box"];38583[label="zzz3185",fontsize=16,color="green",shape="box"];38584[label="zzz3186",fontsize=16,color="green",shape="box"];38585[label="zzz3187",fontsize=16,color="green",shape="box"];38586[label="Succ zzz3181",fontsize=16,color="green",shape="box"];38587[label="zzz3182",fontsize=16,color="green",shape="box"];38588[label="Succ zzz3186",fontsize=16,color="green",shape="box"];38579[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ zzz4303)) zzz4304 zzz4305 zzz4306 zzz4307 (Pos (Succ zzz4308)) zzz4309 (primCmpNat zzz4310 zzz4311 == GT)",fontsize=16,color="burlywood",shape="triangle"];65234[label="zzz4310/Succ zzz43100",fontsize=10,color="white",style="solid",shape="box"];38579 -> 65234[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65234 -> 38679[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65235[label="zzz4310/Zero",fontsize=10,color="white",style="solid",shape="box"];38579 -> 65235[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65235 -> 38680[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 63388[label="Succ zzz3000",fontsize=16,color="green",shape="box"];63389[label="zzz344",fontsize=16,color="green",shape="box"];14701[label="zzz31",fontsize=16,color="green",shape="box"];14702[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200)))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];14702 -> 16630[label="",style="solid", color="black", weight=3]; 130.29/78.16 63390[label="FiniteMap.Branch zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504",fontsize=16,color="green",shape="box"];63391[label="zzz343",fontsize=16,color="green",shape="box"];14705[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];14705 -> 16631[label="",style="solid", color="black", weight=3]; 130.29/78.16 14706[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];14706 -> 16632[label="",style="solid", color="black", weight=3]; 130.29/78.16 14707[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];14707 -> 16633[label="",style="solid", color="black", weight=3]; 130.29/78.16 14708[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200)))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];14708 -> 16634[label="",style="solid", color="black", weight=3]; 130.29/78.16 14709[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];14709 -> 16635[label="",style="solid", color="black", weight=3]; 130.29/78.16 14710[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];14710 -> 16636[label="",style="solid", color="black", weight=3]; 130.29/78.16 14711[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];14711 -> 16637[label="",style="solid", color="black", weight=3]; 130.29/78.16 18327[label="FiniteMap.splitGT zzz1196 (Pos Zero)",fontsize=16,color="burlywood",shape="triangle"];65236[label="zzz1196/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];18327 -> 65236[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65236 -> 18410[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65237[label="zzz1196/FiniteMap.Branch zzz11960 zzz11961 zzz11962 zzz11963 zzz11964",fontsize=10,color="white",style="solid",shape="box"];18327 -> 65237[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65237 -> 18411[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 18141[label="FiniteMap.splitLT2 (Pos zzz62100) zzz6211 zzz6212 zzz6213 zzz6214 (Pos Zero) (primCmpInt (Pos Zero) (Pos zzz62100) == LT)",fontsize=16,color="burlywood",shape="box"];65238[label="zzz62100/Succ zzz621000",fontsize=10,color="white",style="solid",shape="box"];18141 -> 65238[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65238 -> 18167[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65239[label="zzz62100/Zero",fontsize=10,color="white",style="solid",shape="box"];18141 -> 65239[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65239 -> 18168[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 18142[label="FiniteMap.splitLT2 (Neg zzz62100) zzz6211 zzz6212 zzz6213 zzz6214 (Pos Zero) (primCmpInt (Pos Zero) (Neg zzz62100) == LT)",fontsize=16,color="burlywood",shape="box"];65240[label="zzz62100/Succ zzz621000",fontsize=10,color="white",style="solid",shape="box"];18142 -> 65240[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65240 -> 18169[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65241[label="zzz62100/Zero",fontsize=10,color="white",style="solid",shape="box"];18142 -> 65241[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65241 -> 18170[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 62700 -> 62524[label="",style="dashed", color="red", weight=0]; 130.29/78.16 62700[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz63480",fontsize=16,color="magenta"];62700 -> 62712[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 62699[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos zzz6349) zzz6343 == LT)",fontsize=16,color="burlywood",shape="triangle"];65242[label="zzz6349/Succ zzz63490",fontsize=10,color="white",style="solid",shape="box"];62699 -> 65242[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65242 -> 62713[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65243[label="zzz6349/Zero",fontsize=10,color="white",style="solid",shape="box"];62699 -> 65243[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65243 -> 62714[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 62702 -> 62524[label="",style="dashed", color="red", weight=0]; 130.29/78.16 62702[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz63480",fontsize=16,color="magenta"];62702 -> 62715[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 62701[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg zzz6350) zzz6343 == LT)",fontsize=16,color="burlywood",shape="triangle"];65244[label="zzz6350/Succ zzz63500",fontsize=10,color="white",style="solid",shape="box"];62701 -> 65244[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65244 -> 62716[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65245[label="zzz6350/Zero",fontsize=10,color="white",style="solid",shape="box"];62701 -> 65245[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65245 -> 62717[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 63795 -> 54589[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63795[label="FiniteMap.sizeFM zzz6373",fontsize=16,color="magenta"];63795 -> 63814[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63796[label="primPlusInt (Pos zzz63770) (FiniteMap.mkBalBranch6Size_r zzz474034 zzz474030 zzz474031 zzz6373)",fontsize=16,color="black",shape="box"];63796 -> 63815[label="",style="solid", color="black", weight=3]; 130.29/78.16 63797[label="primPlusInt (Neg zzz63770) (FiniteMap.mkBalBranch6Size_r zzz474034 zzz474030 zzz474031 zzz6373)",fontsize=16,color="black",shape="box"];63797 -> 63816[label="",style="solid", color="black", weight=3]; 130.29/78.16 63798[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat (Succ zzz637500) (Succ (Succ Zero)) == LT)",fontsize=16,color="black",shape="box"];63798 -> 63817[label="",style="solid", color="black", weight=3]; 130.29/78.16 63799[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat Zero (Succ (Succ Zero)) == LT)",fontsize=16,color="black",shape="box"];63799 -> 63818[label="",style="solid", color="black", weight=3]; 130.29/78.16 63800[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (LT == LT)",fontsize=16,color="black",shape="triangle"];63800 -> 63819[label="",style="solid", color="black", weight=3]; 130.29/78.16 63801 -> 63800[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63801[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (LT == LT)",fontsize=16,color="magenta"];15272[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Pos (primPlusNat (primPlusNat (primMulNat (Succ (Succ (Succ Zero))) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];15272 -> 16883[label="",style="solid", color="black", weight=3]; 130.29/78.16 15273[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz4260 zzz4261 zzz4262 zzz4263 zzz4264)) == LT)",fontsize=16,color="black",shape="box"];15273 -> 16884[label="",style="solid", color="black", weight=3]; 130.29/78.16 15274[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Neg (primPlusNat (primPlusNat (primMulNat (Succ (Succ (Succ Zero))) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];15274 -> 16885[label="",style="solid", color="black", weight=3]; 130.29/78.16 15275[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz4260 zzz4261 zzz4262 zzz4263 zzz4264)) == LT)",fontsize=16,color="black",shape="box"];15275 -> 16886[label="",style="solid", color="black", weight=3]; 130.29/78.16 34935 -> 40102[label="",style="dashed", color="red", weight=0]; 130.29/78.16 34935[label="FiniteMap.splitGT1 (Neg (Succ zzz3494)) zzz3495 zzz3496 zzz3497 zzz3498 (Neg (Succ zzz3499)) (primCmpNat (Succ zzz3494) (Succ zzz3499) == LT)",fontsize=16,color="magenta"];34935 -> 40103[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34935 -> 40104[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34935 -> 40105[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34935 -> 40106[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34935 -> 40107[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34935 -> 40108[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34935 -> 40109[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34935 -> 40110[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 17239 -> 5407[label="",style="dashed", color="red", weight=0]; 130.29/78.16 17239[label="FiniteMap.mkVBalBranch (Neg Zero) zzz884 (FiniteMap.splitGT zzz886 (Neg (Succ zzz888))) zzz887",fontsize=16,color="magenta"];17239 -> 18016[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 17239 -> 18017[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 17239 -> 18018[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34982 -> 40193[label="",style="dashed", color="red", weight=0]; 130.29/78.16 34982[label="FiniteMap.splitLT1 (Neg (Succ zzz3503)) zzz3504 zzz3505 zzz3506 zzz3507 (Neg (Succ zzz3508)) (primCmpNat (Succ zzz3503) (Succ zzz3508) == GT)",fontsize=16,color="magenta"];34982 -> 40194[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34982 -> 40195[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34982 -> 40196[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34982 -> 40197[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34982 -> 40198[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34982 -> 40199[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34982 -> 40200[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 34982 -> 40201[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 16011[label="FiniteMap.splitGT2 (Neg (Succ zzz833000)) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) True",fontsize=16,color="black",shape="triangle"];16011 -> 17266[label="",style="solid", color="black", weight=3]; 130.29/78.16 16012[label="FiniteMap.splitLT1 (Neg (Succ zzz833000)) zzz8331 zzz8332 zzz8333 zzz8334 (Neg Zero) True",fontsize=16,color="black",shape="box"];16012 -> 17267[label="",style="solid", color="black", weight=3]; 130.29/78.16 33861 -> 40457[label="",style="dashed", color="red", weight=0]; 130.29/78.16 33861[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz3386)) zzz3387 zzz3388 zzz3389 zzz3390 (Neg (Succ zzz3391)) zzz3392 (primCmpNat (Succ zzz3386) (Succ zzz3391) == GT)",fontsize=16,color="magenta"];33861 -> 40458[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33861 -> 40459[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33861 -> 40460[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33861 -> 40461[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33861 -> 40462[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33861 -> 40463[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33861 -> 40464[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33861 -> 40465[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 33861 -> 40466[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 15753 -> 13616[label="",style="dashed", color="red", weight=0]; 130.29/78.16 15753[label="FiniteMap.addToFM0 zzz9821 zzz31",fontsize=16,color="magenta"];15753 -> 17282[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63141[label="Neg (Succ zzz982000)",fontsize=16,color="green",shape="box"];63142 -> 12360[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63142[label="FiniteMap.addToFM_C FiniteMap.addToFM0 zzz9824 (Neg Zero) zzz31",fontsize=16,color="magenta"];63142 -> 63399[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63142 -> 63400[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63143[label="zzz9823",fontsize=16,color="green",shape="box"];63144[label="zzz9821",fontsize=16,color="green",shape="box"];15758 -> 13616[label="",style="dashed", color="red", weight=0]; 130.29/78.16 15758[label="FiniteMap.addToFM0 zzz9821 zzz31",fontsize=16,color="magenta"];15758 -> 17285[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 15759[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200)))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];15759 -> 17286[label="",style="solid", color="black", weight=3]; 130.29/78.16 63392[label="Pos Zero",fontsize=16,color="green",shape="box"];63393[label="Zero",fontsize=16,color="green",shape="box"];63394[label="zzz3534",fontsize=16,color="green",shape="box"];63395[label="zzz343",fontsize=16,color="green",shape="box"];63396[label="zzz3530",fontsize=16,color="green",shape="box"];63397[label="zzz3533",fontsize=16,color="green",shape="box"];63398[label="zzz3531",fontsize=16,color="green",shape="box"];15767[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];15767 -> 17287[label="",style="solid", color="black", weight=3]; 130.29/78.16 15768[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];15768 -> 17288[label="",style="solid", color="black", weight=3]; 130.29/78.16 15769[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];15769 -> 17289[label="",style="solid", color="black", weight=3]; 130.29/78.16 15770[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200)))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];15770 -> 17290[label="",style="solid", color="black", weight=3]; 130.29/78.16 15771[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];15771 -> 17291[label="",style="solid", color="black", weight=3]; 130.29/78.16 15772[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];15772 -> 17292[label="",style="solid", color="black", weight=3]; 130.29/78.16 15773[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];15773 -> 17293[label="",style="solid", color="black", weight=3]; 130.29/78.16 39387[label="zzz3398",fontsize=16,color="green",shape="box"];39388[label="zzz3397",fontsize=16,color="green",shape="box"];39389[label="zzz3399",fontsize=16,color="green",shape="box"];39390[label="zzz3400",fontsize=16,color="green",shape="box"];39391[label="zzz3401",fontsize=16,color="green",shape="box"];39392[label="Succ zzz3401",fontsize=16,color="green",shape="box"];39393[label="Succ zzz3396",fontsize=16,color="green",shape="box"];39394[label="zzz3396",fontsize=16,color="green",shape="box"];39386[label="FiniteMap.splitGT1 (Pos (Succ zzz4428)) zzz4429 zzz4430 zzz4431 zzz4432 (Pos (Succ zzz4433)) (primCmpNat zzz4434 zzz4435 == LT)",fontsize=16,color="burlywood",shape="triangle"];65246[label="zzz4434/Succ zzz44340",fontsize=10,color="white",style="solid",shape="box"];39386 -> 65246[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65246 -> 39475[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65247[label="zzz4434/Zero",fontsize=10,color="white",style="solid",shape="box"];39386 -> 65247[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65247 -> 39476[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 35187[label="FiniteMap.intersectFM_C2IntersectFM_C1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) FiniteMap.intersectFM0 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529)) zzz3530 zzz3531 zzz3532 zzz3533 True",fontsize=16,color="black",shape="box"];35187 -> 35229[label="",style="solid", color="black", weight=3]; 130.29/78.16 38110[label="FiniteMap.splitLT1 (Pos (Succ zzz4178)) zzz4179 zzz4180 zzz4181 zzz4182 (Pos (Succ zzz4183)) (primCmpNat (Succ zzz41840) (Succ zzz41850) == GT)",fontsize=16,color="black",shape="box"];38110 -> 38135[label="",style="solid", color="black", weight=3]; 130.29/78.16 38111[label="FiniteMap.splitLT1 (Pos (Succ zzz4178)) zzz4179 zzz4180 zzz4181 zzz4182 (Pos (Succ zzz4183)) (primCmpNat (Succ zzz41840) Zero == GT)",fontsize=16,color="black",shape="box"];38111 -> 38136[label="",style="solid", color="black", weight=3]; 130.29/78.16 38112[label="FiniteMap.splitLT1 (Pos (Succ zzz4178)) zzz4179 zzz4180 zzz4181 zzz4182 (Pos (Succ zzz4183)) (primCmpNat Zero (Succ zzz41850) == GT)",fontsize=16,color="black",shape="box"];38112 -> 38137[label="",style="solid", color="black", weight=3]; 130.29/78.16 38113[label="FiniteMap.splitLT1 (Pos (Succ zzz4178)) zzz4179 zzz4180 zzz4181 zzz4182 (Pos (Succ zzz4183)) (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];38113 -> 38138[label="",style="solid", color="black", weight=3]; 130.29/78.16 12428[label="FiniteMap.addToFM (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) (Neg zzz300) zzz31",fontsize=16,color="black",shape="triangle"];12428 -> 13329[label="",style="solid", color="black", weight=3]; 130.29/78.16 12429[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 < FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];12429 -> 13330[label="",style="solid", color="black", weight=3]; 130.29/78.16 32670 -> 19225[label="",style="dashed", color="red", weight=0]; 130.29/78.16 32670[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168))",fontsize=16,color="magenta"];32670 -> 32702[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32670 -> 32703[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32670 -> 32704[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32670 -> 32705[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32670 -> 32706[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32670 -> 32707[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32671[label="zzz3171",fontsize=16,color="green",shape="box"];32672 -> 19223[label="",style="dashed", color="red", weight=0]; 130.29/78.16 32672[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Neg zzz3163) zzz3164 zzz3165 zzz3166 zzz3167) (Pos (Succ zzz3168))",fontsize=16,color="magenta"];32672 -> 32708[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32672 -> 32709[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32672 -> 32710[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32672 -> 32711[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32672 -> 32712[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32672 -> 32713[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 32673[label="zzz3172",fontsize=16,color="green",shape="box"];32674[label="zzz3169",fontsize=16,color="green",shape="box"];16617[label="FiniteMap.splitGT1 (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622 (Pos Zero) (LT == LT)",fontsize=16,color="black",shape="box"];16617 -> 17916[label="",style="solid", color="black", weight=3]; 130.29/78.16 38679[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ zzz4303)) zzz4304 zzz4305 zzz4306 zzz4307 (Pos (Succ zzz4308)) zzz4309 (primCmpNat (Succ zzz43100) zzz4311 == GT)",fontsize=16,color="burlywood",shape="box"];65248[label="zzz4311/Succ zzz43110",fontsize=10,color="white",style="solid",shape="box"];38679 -> 65248[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65248 -> 38768[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65249[label="zzz4311/Zero",fontsize=10,color="white",style="solid",shape="box"];38679 -> 65249[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65249 -> 38769[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 38680[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ zzz4303)) zzz4304 zzz4305 zzz4306 zzz4307 (Pos (Succ zzz4308)) zzz4309 (primCmpNat Zero zzz4311 == GT)",fontsize=16,color="burlywood",shape="box"];65250[label="zzz4311/Succ zzz43110",fontsize=10,color="white",style="solid",shape="box"];38680 -> 65250[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65250 -> 38770[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65251[label="zzz4311/Zero",fontsize=10,color="white",style="solid",shape="box"];38680 -> 65251[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65251 -> 38771[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 16630[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200)))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) == LT)",fontsize=16,color="black",shape="box"];16630 -> 17932[label="",style="solid", color="black", weight=3]; 130.29/78.16 16631[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];16631 -> 17933[label="",style="solid", color="black", weight=3]; 130.29/78.16 16632[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];16632 -> 17934[label="",style="solid", color="black", weight=3]; 130.29/78.16 16633[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];16633 -> 17935[label="",style="solid", color="black", weight=3]; 130.29/78.16 16634[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200)))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) == LT)",fontsize=16,color="black",shape="box"];16634 -> 17936[label="",style="solid", color="black", weight=3]; 130.29/78.16 16635[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];16635 -> 17937[label="",style="solid", color="black", weight=3]; 130.29/78.16 16636[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];16636 -> 17938[label="",style="solid", color="black", weight=3]; 130.29/78.16 16637[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];16637 -> 17939[label="",style="solid", color="black", weight=3]; 130.29/78.16 18410[label="FiniteMap.splitGT FiniteMap.EmptyFM (Pos Zero)",fontsize=16,color="black",shape="box"];18410 -> 18590[label="",style="solid", color="black", weight=3]; 130.29/78.16 18411[label="FiniteMap.splitGT (FiniteMap.Branch zzz11960 zzz11961 zzz11962 zzz11963 zzz11964) (Pos Zero)",fontsize=16,color="black",shape="box"];18411 -> 18591[label="",style="solid", color="black", weight=3]; 130.29/78.16 18167[label="FiniteMap.splitLT2 (Pos (Succ zzz621000)) zzz6211 zzz6212 zzz6213 zzz6214 (Pos Zero) (primCmpInt (Pos Zero) (Pos (Succ zzz621000)) == LT)",fontsize=16,color="black",shape="box"];18167 -> 18197[label="",style="solid", color="black", weight=3]; 130.29/78.16 18168[label="FiniteMap.splitLT2 (Pos Zero) zzz6211 zzz6212 zzz6213 zzz6214 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];18168 -> 18198[label="",style="solid", color="black", weight=3]; 130.29/78.16 18169[label="FiniteMap.splitLT2 (Neg (Succ zzz621000)) zzz6211 zzz6212 zzz6213 zzz6214 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ zzz621000)) == LT)",fontsize=16,color="black",shape="box"];18169 -> 18199[label="",style="solid", color="black", weight=3]; 130.29/78.16 18170[label="FiniteMap.splitLT2 (Neg Zero) zzz6211 zzz6212 zzz6213 zzz6214 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];18170 -> 18200[label="",style="solid", color="black", weight=3]; 130.29/78.16 62712[label="zzz63480",fontsize=16,color="green",shape="box"];62713[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos (Succ zzz63490)) zzz6343 == LT)",fontsize=16,color="burlywood",shape="box"];65252[label="zzz6343/Pos zzz63430",fontsize=10,color="white",style="solid",shape="box"];62713 -> 65252[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65252 -> 62721[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65253[label="zzz6343/Neg zzz63430",fontsize=10,color="white",style="solid",shape="box"];62713 -> 65253[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65253 -> 62722[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 62714[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos Zero) zzz6343 == LT)",fontsize=16,color="burlywood",shape="box"];65254[label="zzz6343/Pos zzz63430",fontsize=10,color="white",style="solid",shape="box"];62714 -> 65254[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65254 -> 62723[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65255[label="zzz6343/Neg zzz63430",fontsize=10,color="white",style="solid",shape="box"];62714 -> 65255[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65255 -> 62724[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 62715[label="zzz63480",fontsize=16,color="green",shape="box"];62716[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg (Succ zzz63500)) zzz6343 == LT)",fontsize=16,color="burlywood",shape="box"];65256[label="zzz6343/Pos zzz63430",fontsize=10,color="white",style="solid",shape="box"];62716 -> 65256[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65256 -> 62725[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65257[label="zzz6343/Neg zzz63430",fontsize=10,color="white",style="solid",shape="box"];62716 -> 65257[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65257 -> 62726[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 62717[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg Zero) zzz6343 == LT)",fontsize=16,color="burlywood",shape="box"];65258[label="zzz6343/Pos zzz63430",fontsize=10,color="white",style="solid",shape="box"];62717 -> 65258[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65258 -> 62727[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65259[label="zzz6343/Neg zzz63430",fontsize=10,color="white",style="solid",shape="box"];62717 -> 65259[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65259 -> 62728[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 63814[label="zzz6373",fontsize=16,color="green",shape="box"];63815 -> 55581[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63815[label="primPlusInt (Pos zzz63770) (FiniteMap.sizeFM zzz474034)",fontsize=16,color="magenta"];63815 -> 63828[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63815 -> 63829[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63816 -> 55610[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63816[label="primPlusInt (Neg zzz63770) (FiniteMap.sizeFM zzz474034)",fontsize=16,color="magenta"];63816 -> 63830[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63816 -> 63831[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63817[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat zzz637500 (Succ Zero) == LT)",fontsize=16,color="burlywood",shape="box"];65260[label="zzz637500/Succ zzz6375000",fontsize=10,color="white",style="solid",shape="box"];63817 -> 65260[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65260 -> 63832[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65261[label="zzz637500/Zero",fontsize=10,color="white",style="solid",shape="box"];63817 -> 65261[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65261 -> 63833[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 63818 -> 63800[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63818[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (LT == LT)",fontsize=16,color="magenta"];63819[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 True",fontsize=16,color="black",shape="box"];63819 -> 63834[label="",style="solid", color="black", weight=3]; 130.29/78.16 16883[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ (Succ Zero)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];16883 -> 17973[label="",style="solid", color="black", weight=3]; 130.29/78.16 16884[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Pos Zero) zzz4262 == LT)",fontsize=16,color="burlywood",shape="box"];65262[label="zzz4262/Pos zzz42620",fontsize=10,color="white",style="solid",shape="box"];16884 -> 65262[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65262 -> 17974[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65263[label="zzz4262/Neg zzz42620",fontsize=10,color="white",style="solid",shape="box"];16884 -> 65263[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65263 -> 17975[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 16885[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ (Succ Zero)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];16885 -> 17976[label="",style="solid", color="black", weight=3]; 130.29/78.16 16886[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Neg Zero) zzz4262 == LT)",fontsize=16,color="burlywood",shape="box"];65264[label="zzz4262/Pos zzz42620",fontsize=10,color="white",style="solid",shape="box"];16886 -> 65264[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65264 -> 17977[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65265[label="zzz4262/Neg zzz42620",fontsize=10,color="white",style="solid",shape="box"];16886 -> 65265[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65265 -> 17978[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 40103[label="zzz3498",fontsize=16,color="green",shape="box"];40104[label="zzz3494",fontsize=16,color="green",shape="box"];40105[label="Succ zzz3494",fontsize=16,color="green",shape="box"];40106[label="zzz3496",fontsize=16,color="green",shape="box"];40107[label="Succ zzz3499",fontsize=16,color="green",shape="box"];40108[label="zzz3497",fontsize=16,color="green",shape="box"];40109[label="zzz3495",fontsize=16,color="green",shape="box"];40110[label="zzz3499",fontsize=16,color="green",shape="box"];40102[label="FiniteMap.splitGT1 (Neg (Succ zzz4495)) zzz4496 zzz4497 zzz4498 zzz4499 (Neg (Succ zzz4500)) (primCmpNat zzz4501 zzz4502 == LT)",fontsize=16,color="burlywood",shape="triangle"];65266[label="zzz4501/Succ zzz45010",fontsize=10,color="white",style="solid",shape="box"];40102 -> 65266[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65266 -> 40191[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65267[label="zzz4501/Zero",fontsize=10,color="white",style="solid",shape="box"];40102 -> 65267[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65267 -> 40192[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 18016 -> 14393[label="",style="dashed", color="red", weight=0]; 130.29/78.16 18016[label="FiniteMap.splitGT zzz886 (Neg (Succ zzz888))",fontsize=16,color="magenta"];18016 -> 19018[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 18016 -> 19019[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 18017[label="zzz887",fontsize=16,color="green",shape="box"];18018[label="zzz884",fontsize=16,color="green",shape="box"];40194[label="Succ zzz3503",fontsize=16,color="green",shape="box"];40195[label="Succ zzz3508",fontsize=16,color="green",shape="box"];40196[label="zzz3505",fontsize=16,color="green",shape="box"];40197[label="zzz3503",fontsize=16,color="green",shape="box"];40198[label="zzz3506",fontsize=16,color="green",shape="box"];40199[label="zzz3507",fontsize=16,color="green",shape="box"];40200[label="zzz3504",fontsize=16,color="green",shape="box"];40201[label="zzz3508",fontsize=16,color="green",shape="box"];40193[label="FiniteMap.splitLT1 (Neg (Succ zzz4504)) zzz4505 zzz4506 zzz4507 zzz4508 (Neg (Succ zzz4509)) (primCmpNat zzz4510 zzz4511 == GT)",fontsize=16,color="burlywood",shape="triangle"];65268[label="zzz4510/Succ zzz45100",fontsize=10,color="white",style="solid",shape="box"];40193 -> 65268[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65268 -> 40282[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65269[label="zzz4510/Zero",fontsize=10,color="white",style="solid",shape="box"];40193 -> 65269[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65269 -> 40283[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 17266 -> 13521[label="",style="dashed", color="red", weight=0]; 130.29/78.16 17266[label="FiniteMap.splitGT zzz8334 (Neg Zero)",fontsize=16,color="magenta"];17266 -> 18070[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 17267 -> 6244[label="",style="dashed", color="red", weight=0]; 130.29/78.16 17267[label="FiniteMap.mkVBalBranch (Neg (Succ zzz833000)) zzz8331 zzz8333 (FiniteMap.splitLT zzz8334 (Neg Zero))",fontsize=16,color="magenta"];17267 -> 18071[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 17267 -> 18072[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 17267 -> 18073[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 17267 -> 18074[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 40458[label="zzz3389",fontsize=16,color="green",shape="box"];40459[label="zzz3391",fontsize=16,color="green",shape="box"];40460[label="zzz3387",fontsize=16,color="green",shape="box"];40461[label="Succ zzz3386",fontsize=16,color="green",shape="box"];40462[label="zzz3390",fontsize=16,color="green",shape="box"];40463[label="Succ zzz3391",fontsize=16,color="green",shape="box"];40464[label="zzz3388",fontsize=16,color="green",shape="box"];40465[label="zzz3386",fontsize=16,color="green",shape="box"];40466[label="zzz3392",fontsize=16,color="green",shape="box"];40457[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz4538)) zzz4539 zzz4540 zzz4541 zzz4542 (Neg (Succ zzz4543)) zzz4544 (primCmpNat zzz4545 zzz4546 == GT)",fontsize=16,color="burlywood",shape="triangle"];65270[label="zzz4545/Succ zzz45450",fontsize=10,color="white",style="solid",shape="box"];40457 -> 65270[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65270 -> 40557[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65271[label="zzz4545/Zero",fontsize=10,color="white",style="solid",shape="box"];40457 -> 65271[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65271 -> 40558[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 17282[label="zzz9821",fontsize=16,color="green",shape="box"];63399[label="zzz9824",fontsize=16,color="green",shape="box"];63400[label="Zero",fontsize=16,color="green",shape="box"];17285[label="zzz9821",fontsize=16,color="green",shape="box"];17286[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200)))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) == LT)",fontsize=16,color="black",shape="box"];17286 -> 18090[label="",style="solid", color="black", weight=3]; 130.29/78.16 17287[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];17287 -> 18091[label="",style="solid", color="black", weight=3]; 130.29/78.16 17288[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];17288 -> 18092[label="",style="solid", color="black", weight=3]; 130.29/78.16 17289[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];17289 -> 18093[label="",style="solid", color="black", weight=3]; 130.29/78.16 17290[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200)))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 zzz342 zzz343 zzz344)) == LT)",fontsize=16,color="black",shape="box"];17290 -> 18094[label="",style="solid", color="black", weight=3]; 130.29/78.16 17291[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];17291 -> 18095[label="",style="solid", color="black", weight=3]; 130.29/78.16 17292[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];17292 -> 18096[label="",style="solid", color="black", weight=3]; 130.29/78.16 17293[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];17293 -> 18097[label="",style="solid", color="black", weight=3]; 130.29/78.16 39475[label="FiniteMap.splitGT1 (Pos (Succ zzz4428)) zzz4429 zzz4430 zzz4431 zzz4432 (Pos (Succ zzz4433)) (primCmpNat (Succ zzz44340) zzz4435 == LT)",fontsize=16,color="burlywood",shape="box"];65272[label="zzz4435/Succ zzz44350",fontsize=10,color="white",style="solid",shape="box"];39475 -> 65272[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65272 -> 39557[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65273[label="zzz4435/Zero",fontsize=10,color="white",style="solid",shape="box"];39475 -> 65273[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65273 -> 39558[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 39476[label="FiniteMap.splitGT1 (Pos (Succ zzz4428)) zzz4429 zzz4430 zzz4431 zzz4432 (Pos (Succ zzz4433)) (primCmpNat Zero zzz4435 == LT)",fontsize=16,color="burlywood",shape="box"];65274[label="zzz4435/Succ zzz44350",fontsize=10,color="white",style="solid",shape="box"];39476 -> 65274[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65274 -> 39559[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65275[label="zzz4435/Zero",fontsize=10,color="white",style="solid",shape="box"];39476 -> 65275[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65275 -> 39560[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 35229 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.16 35229[label="FiniteMap.mkVBalBranch (Pos (Succ zzz3529)) (FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529))) zzz3530) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529))) zzz3532) (FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529))) zzz3533)",fontsize=16,color="magenta"];35229 -> 35257[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 35229 -> 35258[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 35229 -> 35259[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 35229 -> 35260[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 38135 -> 38000[label="",style="dashed", color="red", weight=0]; 130.29/78.16 38135[label="FiniteMap.splitLT1 (Pos (Succ zzz4178)) zzz4179 zzz4180 zzz4181 zzz4182 (Pos (Succ zzz4183)) (primCmpNat zzz41840 zzz41850 == GT)",fontsize=16,color="magenta"];38135 -> 38185[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 38135 -> 38186[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 38136[label="FiniteMap.splitLT1 (Pos (Succ zzz4178)) zzz4179 zzz4180 zzz4181 zzz4182 (Pos (Succ zzz4183)) (GT == GT)",fontsize=16,color="black",shape="box"];38136 -> 38187[label="",style="solid", color="black", weight=3]; 130.29/78.16 38137[label="FiniteMap.splitLT1 (Pos (Succ zzz4178)) zzz4179 zzz4180 zzz4181 zzz4182 (Pos (Succ zzz4183)) (LT == GT)",fontsize=16,color="black",shape="box"];38137 -> 38188[label="",style="solid", color="black", weight=3]; 130.29/78.16 38138[label="FiniteMap.splitLT1 (Pos (Succ zzz4178)) zzz4179 zzz4180 zzz4181 zzz4182 (Pos (Succ zzz4183)) (EQ == GT)",fontsize=16,color="black",shape="box"];38138 -> 38189[label="",style="solid", color="black", weight=3]; 130.29/78.16 13329 -> 12360[label="",style="dashed", color="red", weight=0]; 130.29/78.16 13329[label="FiniteMap.addToFM_C FiniteMap.addToFM0 (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334) (Neg zzz300) zzz31",fontsize=16,color="magenta"];13329 -> 14624[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 13330[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];13330 -> 14625[label="",style="solid", color="black", weight=3]; 130.29/78.16 32702[label="zzz3167",fontsize=16,color="green",shape="box"];32703[label="zzz3165",fontsize=16,color="green",shape="box"];32704[label="zzz3168",fontsize=16,color="green",shape="box"];32705[label="zzz3164",fontsize=16,color="green",shape="box"];32706[label="zzz3163",fontsize=16,color="green",shape="box"];32707[label="zzz3166",fontsize=16,color="green",shape="box"];32708[label="zzz3167",fontsize=16,color="green",shape="box"];32709[label="zzz3165",fontsize=16,color="green",shape="box"];32710[label="zzz3168",fontsize=16,color="green",shape="box"];32711[label="zzz3164",fontsize=16,color="green",shape="box"];32712[label="zzz3163",fontsize=16,color="green",shape="box"];32713[label="zzz3166",fontsize=16,color="green",shape="box"];17916[label="FiniteMap.splitGT1 (Pos (Succ zzz618)) zzz619 zzz620 zzz621 zzz622 (Pos Zero) True",fontsize=16,color="black",shape="box"];17916 -> 18445[label="",style="solid", color="black", weight=3]; 130.29/78.16 38768[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ zzz4303)) zzz4304 zzz4305 zzz4306 zzz4307 (Pos (Succ zzz4308)) zzz4309 (primCmpNat (Succ zzz43100) (Succ zzz43110) == GT)",fontsize=16,color="black",shape="box"];38768 -> 38843[label="",style="solid", color="black", weight=3]; 130.29/78.16 38769[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ zzz4303)) zzz4304 zzz4305 zzz4306 zzz4307 (Pos (Succ zzz4308)) zzz4309 (primCmpNat (Succ zzz43100) Zero == GT)",fontsize=16,color="black",shape="box"];38769 -> 38844[label="",style="solid", color="black", weight=3]; 130.29/78.16 38770[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ zzz4303)) zzz4304 zzz4305 zzz4306 zzz4307 (Pos (Succ zzz4308)) zzz4309 (primCmpNat Zero (Succ zzz43110) == GT)",fontsize=16,color="black",shape="box"];38770 -> 38845[label="",style="solid", color="black", weight=3]; 130.29/78.16 38771[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ zzz4303)) zzz4304 zzz4305 zzz4306 zzz4307 (Pos (Succ zzz4308)) zzz4309 (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];38771 -> 38846[label="",style="solid", color="black", weight=3]; 130.29/78.16 17932[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200)))) zzz342 == LT)",fontsize=16,color="burlywood",shape="box"];65276[label="zzz342/Pos zzz3420",fontsize=10,color="white",style="solid",shape="box"];17932 -> 65276[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65276 -> 18462[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65277[label="zzz342/Neg zzz3420",fontsize=10,color="white",style="solid",shape="box"];17932 -> 65277[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65277 -> 18463[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 17933[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Pos Zero) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];17933 -> 18464[label="",style="solid", color="black", weight=3]; 130.29/78.16 17934[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];17934 -> 18465[label="",style="solid", color="black", weight=3]; 130.29/78.16 17935[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Neg Zero) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];17935 -> 18466[label="",style="solid", color="black", weight=3]; 130.29/78.16 17936[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200)))) zzz342 == LT)",fontsize=16,color="burlywood",shape="box"];65278[label="zzz342/Pos zzz3420",fontsize=10,color="white",style="solid",shape="box"];17936 -> 65278[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65278 -> 18467[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65279[label="zzz342/Neg zzz3420",fontsize=10,color="white",style="solid",shape="box"];17936 -> 65279[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65279 -> 18468[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 17937[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Pos Zero) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];17937 -> 18469[label="",style="solid", color="black", weight=3]; 130.29/78.16 17938[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];17938 -> 18470[label="",style="solid", color="black", weight=3]; 130.29/78.16 17939[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Neg Zero) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];17939 -> 18471[label="",style="solid", color="black", weight=3]; 130.29/78.16 18590 -> 3761[label="",style="dashed", color="red", weight=0]; 130.29/78.16 18590[label="FiniteMap.splitGT4 FiniteMap.EmptyFM (Pos Zero)",fontsize=16,color="magenta"];18591[label="FiniteMap.splitGT3 (FiniteMap.Branch zzz11960 zzz11961 zzz11962 zzz11963 zzz11964) (Pos Zero)",fontsize=16,color="black",shape="box"];18591 -> 18662[label="",style="solid", color="black", weight=3]; 130.29/78.16 18197 -> 12108[label="",style="dashed", color="red", weight=0]; 130.29/78.16 18197[label="FiniteMap.splitLT2 (Pos (Succ zzz621000)) zzz6211 zzz6212 zzz6213 zzz6214 (Pos Zero) (primCmpNat Zero (Succ zzz621000) == LT)",fontsize=16,color="magenta"];18197 -> 18472[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 18197 -> 18473[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 18197 -> 18474[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 18197 -> 18475[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 18197 -> 18476[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 18198 -> 4942[label="",style="dashed", color="red", weight=0]; 130.29/78.16 18198[label="FiniteMap.splitLT2 (Pos Zero) zzz6211 zzz6212 zzz6213 zzz6214 (Pos Zero) (EQ == LT)",fontsize=16,color="magenta"];18198 -> 18477[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 18198 -> 18478[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 18198 -> 18479[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 18198 -> 18480[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 18199[label="FiniteMap.splitLT2 (Neg (Succ zzz621000)) zzz6211 zzz6212 zzz6213 zzz6214 (Pos Zero) (GT == LT)",fontsize=16,color="black",shape="box"];18199 -> 18481[label="",style="solid", color="black", weight=3]; 130.29/78.16 18200 -> 4947[label="",style="dashed", color="red", weight=0]; 130.29/78.16 18200[label="FiniteMap.splitLT2 (Neg Zero) zzz6211 zzz6212 zzz6213 zzz6214 (Pos Zero) (EQ == LT)",fontsize=16,color="magenta"];18200 -> 18482[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 18200 -> 18483[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 18200 -> 18484[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 18200 -> 18485[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 62721[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos (Succ zzz63490)) (Pos zzz63430) == LT)",fontsize=16,color="black",shape="box"];62721 -> 62732[label="",style="solid", color="black", weight=3]; 130.29/78.16 62722[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos (Succ zzz63490)) (Neg zzz63430) == LT)",fontsize=16,color="black",shape="box"];62722 -> 62733[label="",style="solid", color="black", weight=3]; 130.29/78.16 62723[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos Zero) (Pos zzz63430) == LT)",fontsize=16,color="burlywood",shape="box"];65280[label="zzz63430/Succ zzz634300",fontsize=10,color="white",style="solid",shape="box"];62723 -> 65280[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65280 -> 62734[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65281[label="zzz63430/Zero",fontsize=10,color="white",style="solid",shape="box"];62723 -> 65281[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65281 -> 62735[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 62724[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos Zero) (Neg zzz63430) == LT)",fontsize=16,color="burlywood",shape="box"];65282[label="zzz63430/Succ zzz634300",fontsize=10,color="white",style="solid",shape="box"];62724 -> 65282[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65282 -> 62736[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65283[label="zzz63430/Zero",fontsize=10,color="white",style="solid",shape="box"];62724 -> 65283[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65283 -> 62737[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 62725[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg (Succ zzz63500)) (Pos zzz63430) == LT)",fontsize=16,color="black",shape="box"];62725 -> 62738[label="",style="solid", color="black", weight=3]; 130.29/78.16 62726[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg (Succ zzz63500)) (Neg zzz63430) == LT)",fontsize=16,color="black",shape="box"];62726 -> 62739[label="",style="solid", color="black", weight=3]; 130.29/78.16 62727[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg Zero) (Pos zzz63430) == LT)",fontsize=16,color="burlywood",shape="box"];65284[label="zzz63430/Succ zzz634300",fontsize=10,color="white",style="solid",shape="box"];62727 -> 65284[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65284 -> 62740[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65285[label="zzz63430/Zero",fontsize=10,color="white",style="solid",shape="box"];62727 -> 65285[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65285 -> 62741[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 62728[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg Zero) (Neg zzz63430) == LT)",fontsize=16,color="burlywood",shape="box"];65286[label="zzz63430/Succ zzz634300",fontsize=10,color="white",style="solid",shape="box"];62728 -> 65286[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65286 -> 62742[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65287[label="zzz63430/Zero",fontsize=10,color="white",style="solid",shape="box"];62728 -> 65287[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65287 -> 62743[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 63828[label="zzz63770",fontsize=16,color="green",shape="box"];63829 -> 54589[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63829[label="FiniteMap.sizeFM zzz474034",fontsize=16,color="magenta"];63829 -> 63927[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 55581[label="primPlusInt (Pos zzz58960) zzz5900",fontsize=16,color="burlywood",shape="triangle"];65288[label="zzz5900/Pos zzz59000",fontsize=10,color="white",style="solid",shape="box"];55581 -> 65288[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65288 -> 55607[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65289[label="zzz5900/Neg zzz59000",fontsize=10,color="white",style="solid",shape="box"];55581 -> 65289[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65289 -> 55608[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 63830[label="zzz63770",fontsize=16,color="green",shape="box"];63831 -> 54589[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63831[label="FiniteMap.sizeFM zzz474034",fontsize=16,color="magenta"];63831 -> 63928[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 55610[label="primPlusInt (Neg zzz58960) zzz5901",fontsize=16,color="burlywood",shape="triangle"];65290[label="zzz5901/Pos zzz59010",fontsize=10,color="white",style="solid",shape="box"];55610 -> 65290[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65290 -> 55626[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65291[label="zzz5901/Neg zzz59010",fontsize=10,color="white",style="solid",shape="box"];55610 -> 65291[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65291 -> 55627[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 63832[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat (Succ zzz6375000) (Succ Zero) == LT)",fontsize=16,color="black",shape="box"];63832 -> 63929[label="",style="solid", color="black", weight=3]; 130.29/78.16 63833[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat Zero (Succ Zero) == LT)",fontsize=16,color="black",shape="box"];63833 -> 63930[label="",style="solid", color="black", weight=3]; 130.29/78.16 63834 -> 60457[label="",style="dashed", color="red", weight=0]; 130.29/78.16 63834[label="FiniteMap.mkBranch (Pos (Succ Zero)) zzz474030 zzz474031 zzz6373 zzz474034",fontsize=16,color="magenta"];63834 -> 63931[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63834 -> 63932[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63834 -> 63933[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63834 -> 63934[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 63834 -> 63935[label="",style="dashed", color="magenta", weight=3]; 130.29/78.16 17973[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ Zero) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];17973 -> 18517[label="",style="solid", color="black", weight=3]; 130.29/78.16 17974[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos zzz42620) zzz4263 zzz4264 (primCmpInt (Pos Zero) (Pos zzz42620) == LT)",fontsize=16,color="burlywood",shape="box"];65292[label="zzz42620/Succ zzz426200",fontsize=10,color="white",style="solid",shape="box"];17974 -> 65292[label="",style="solid", color="burlywood", weight=9]; 130.29/78.16 65292 -> 18518[label="",style="solid", color="burlywood", weight=3]; 130.29/78.16 65293[label="zzz42620/Zero",fontsize=10,color="white",style="solid",shape="box"];17974 -> 65293[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65293 -> 18519[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 17975[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (primCmpInt (Pos Zero) (Neg zzz42620) == LT)",fontsize=16,color="burlywood",shape="box"];65294[label="zzz42620/Succ zzz426200",fontsize=10,color="white",style="solid",shape="box"];17975 -> 65294[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65294 -> 18520[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 65295[label="zzz42620/Zero",fontsize=10,color="white",style="solid",shape="box"];17975 -> 65295[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65295 -> 18521[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 17976[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ Zero) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];17976 -> 18522[label="",style="solid", color="black", weight=3]; 130.29/78.17 17977[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos zzz42620) zzz4263 zzz4264 (primCmpInt (Neg Zero) (Pos zzz42620) == LT)",fontsize=16,color="burlywood",shape="box"];65296[label="zzz42620/Succ zzz426200",fontsize=10,color="white",style="solid",shape="box"];17977 -> 65296[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65296 -> 18523[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 65297[label="zzz42620/Zero",fontsize=10,color="white",style="solid",shape="box"];17977 -> 65297[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65297 -> 18524[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 17978[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (primCmpInt (Neg Zero) (Neg zzz42620) == LT)",fontsize=16,color="burlywood",shape="box"];65298[label="zzz42620/Succ zzz426200",fontsize=10,color="white",style="solid",shape="box"];17978 -> 65298[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65298 -> 18525[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 65299[label="zzz42620/Zero",fontsize=10,color="white",style="solid",shape="box"];17978 -> 65299[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65299 -> 18526[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 40191[label="FiniteMap.splitGT1 (Neg (Succ zzz4495)) zzz4496 zzz4497 zzz4498 zzz4499 (Neg (Succ zzz4500)) (primCmpNat (Succ zzz45010) zzz4502 == LT)",fontsize=16,color="burlywood",shape="box"];65300[label="zzz4502/Succ zzz45020",fontsize=10,color="white",style="solid",shape="box"];40191 -> 65300[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65300 -> 40284[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 65301[label="zzz4502/Zero",fontsize=10,color="white",style="solid",shape="box"];40191 -> 65301[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65301 -> 40285[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 40192[label="FiniteMap.splitGT1 (Neg (Succ zzz4495)) zzz4496 zzz4497 zzz4498 zzz4499 (Neg (Succ zzz4500)) (primCmpNat Zero zzz4502 == LT)",fontsize=16,color="burlywood",shape="box"];65302[label="zzz4502/Succ zzz45020",fontsize=10,color="white",style="solid",shape="box"];40192 -> 65302[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65302 -> 40286[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 65303[label="zzz4502/Zero",fontsize=10,color="white",style="solid",shape="box"];40192 -> 65303[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65303 -> 40287[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 19018[label="zzz886",fontsize=16,color="green",shape="box"];19019[label="zzz888",fontsize=16,color="green",shape="box"];40282[label="FiniteMap.splitLT1 (Neg (Succ zzz4504)) zzz4505 zzz4506 zzz4507 zzz4508 (Neg (Succ zzz4509)) (primCmpNat (Succ zzz45100) zzz4511 == GT)",fontsize=16,color="burlywood",shape="box"];65304[label="zzz4511/Succ zzz45110",fontsize=10,color="white",style="solid",shape="box"];40282 -> 65304[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65304 -> 40336[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 65305[label="zzz4511/Zero",fontsize=10,color="white",style="solid",shape="box"];40282 -> 65305[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65305 -> 40337[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 40283[label="FiniteMap.splitLT1 (Neg (Succ zzz4504)) zzz4505 zzz4506 zzz4507 zzz4508 (Neg (Succ zzz4509)) (primCmpNat Zero zzz4511 == GT)",fontsize=16,color="burlywood",shape="box"];65306[label="zzz4511/Succ zzz45110",fontsize=10,color="white",style="solid",shape="box"];40283 -> 65306[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65306 -> 40338[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 65307[label="zzz4511/Zero",fontsize=10,color="white",style="solid",shape="box"];40283 -> 65307[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65307 -> 40339[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 18070[label="zzz8334",fontsize=16,color="green",shape="box"];18071[label="zzz833000",fontsize=16,color="green",shape="box"];18072 -> 12653[label="",style="dashed", color="red", weight=0]; 130.29/78.17 18072[label="FiniteMap.splitLT zzz8334 (Neg Zero)",fontsize=16,color="magenta"];18072 -> 19277[label="",style="dashed", color="magenta", weight=3]; 130.29/78.17 18073[label="zzz8333",fontsize=16,color="green",shape="box"];18074[label="zzz8331",fontsize=16,color="green",shape="box"];40557[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz4538)) zzz4539 zzz4540 zzz4541 zzz4542 (Neg (Succ zzz4543)) zzz4544 (primCmpNat (Succ zzz45450) zzz4546 == GT)",fontsize=16,color="burlywood",shape="box"];65308[label="zzz4546/Succ zzz45460",fontsize=10,color="white",style="solid",shape="box"];40557 -> 65308[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65308 -> 40631[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 65309[label="zzz4546/Zero",fontsize=10,color="white",style="solid",shape="box"];40557 -> 65309[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65309 -> 40632[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 40558[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz4538)) zzz4539 zzz4540 zzz4541 zzz4542 (Neg (Succ zzz4543)) zzz4544 (primCmpNat Zero zzz4546 == GT)",fontsize=16,color="burlywood",shape="box"];65310[label="zzz4546/Succ zzz45460",fontsize=10,color="white",style="solid",shape="box"];40558 -> 65310[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65310 -> 40633[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 65311[label="zzz4546/Zero",fontsize=10,color="white",style="solid",shape="box"];40558 -> 65311[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65311 -> 40634[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 18090[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200)))) zzz342 == LT)",fontsize=16,color="burlywood",shape="box"];65312[label="zzz342/Pos zzz3420",fontsize=10,color="white",style="solid",shape="box"];18090 -> 65312[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65312 -> 19298[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 65313[label="zzz342/Neg zzz3420",fontsize=10,color="white",style="solid",shape="box"];18090 -> 65313[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65313 -> 19299[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 18091[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Pos Zero) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];18091 -> 19300[label="",style="solid", color="black", weight=3]; 130.29/78.17 18092[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];18092 -> 19301[label="",style="solid", color="black", weight=3]; 130.29/78.17 18093[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Neg Zero) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];18093 -> 19302[label="",style="solid", color="black", weight=3]; 130.29/78.17 18094[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 zzz342 zzz343 zzz344 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200)))) zzz342 == LT)",fontsize=16,color="burlywood",shape="box"];65314[label="zzz342/Pos zzz3420",fontsize=10,color="white",style="solid",shape="box"];18094 -> 65314[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65314 -> 19303[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 65315[label="zzz342/Neg zzz3420",fontsize=10,color="white",style="solid",shape="box"];18094 -> 65315[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65315 -> 19304[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 18095[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Pos Zero) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];18095 -> 19305[label="",style="solid", color="black", weight=3]; 130.29/78.17 18096[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];18096 -> 19306[label="",style="solid", color="black", weight=3]; 130.29/78.17 18097[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Neg Zero) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];18097 -> 19307[label="",style="solid", color="black", weight=3]; 130.29/78.17 39557[label="FiniteMap.splitGT1 (Pos (Succ zzz4428)) zzz4429 zzz4430 zzz4431 zzz4432 (Pos (Succ zzz4433)) (primCmpNat (Succ zzz44340) (Succ zzz44350) == LT)",fontsize=16,color="black",shape="box"];39557 -> 39587[label="",style="solid", color="black", weight=3]; 130.29/78.17 39558[label="FiniteMap.splitGT1 (Pos (Succ zzz4428)) zzz4429 zzz4430 zzz4431 zzz4432 (Pos (Succ zzz4433)) (primCmpNat (Succ zzz44340) Zero == LT)",fontsize=16,color="black",shape="box"];39558 -> 39588[label="",style="solid", color="black", weight=3]; 130.29/78.17 39559[label="FiniteMap.splitGT1 (Pos (Succ zzz4428)) zzz4429 zzz4430 zzz4431 zzz4432 (Pos (Succ zzz4433)) (primCmpNat Zero (Succ zzz44350) == LT)",fontsize=16,color="black",shape="box"];39559 -> 39589[label="",style="solid", color="black", weight=3]; 130.29/78.17 39560[label="FiniteMap.splitGT1 (Pos (Succ zzz4428)) zzz4429 zzz4430 zzz4431 zzz4432 (Pos (Succ zzz4433)) (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];39560 -> 39590[label="",style="solid", color="black", weight=3]; 130.29/78.17 35257 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.17 35257[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529))) zzz3532",fontsize=16,color="magenta"];35257 -> 35279[label="",style="dashed", color="magenta", weight=3]; 130.29/78.17 35257 -> 35280[label="",style="dashed", color="magenta", weight=3]; 130.29/78.17 35258[label="Succ zzz3529",fontsize=16,color="green",shape="box"];35259 -> 5[label="",style="dashed", color="red", weight=0]; 130.29/78.17 35259[label="FiniteMap.intersectFM_C FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529))) zzz3533",fontsize=16,color="magenta"];35259 -> 35281[label="",style="dashed", color="magenta", weight=3]; 130.29/78.17 35259 -> 35282[label="",style="dashed", color="magenta", weight=3]; 130.29/78.17 35260[label="FiniteMap.intersectFM0 (FiniteMap.intersectFM_C2Elt1 (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529))) zzz3530",fontsize=16,color="black",shape="box"];35260 -> 35283[label="",style="solid", color="black", weight=3]; 130.29/78.17 38185[label="zzz41850",fontsize=16,color="green",shape="box"];38186[label="zzz41840",fontsize=16,color="green",shape="box"];38187[label="FiniteMap.splitLT1 (Pos (Succ zzz4178)) zzz4179 zzz4180 zzz4181 zzz4182 (Pos (Succ zzz4183)) True",fontsize=16,color="black",shape="box"];38187 -> 38325[label="",style="solid", color="black", weight=3]; 130.29/78.17 38188[label="FiniteMap.splitLT1 (Pos (Succ zzz4178)) zzz4179 zzz4180 zzz4181 zzz4182 (Pos (Succ zzz4183)) False",fontsize=16,color="black",shape="triangle"];38188 -> 38326[label="",style="solid", color="black", weight=3]; 130.29/78.17 38189 -> 38188[label="",style="dashed", color="red", weight=0]; 130.29/78.17 38189[label="FiniteMap.splitLT1 (Pos (Succ zzz4178)) zzz4179 zzz4180 zzz4181 zzz4182 (Pos (Succ zzz4183)) False",fontsize=16,color="magenta"];14624[label="FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334",fontsize=16,color="green",shape="box"];14625[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];14625 -> 16180[label="",style="solid", color="black", weight=3]; 130.29/78.17 18445 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.17 18445[label="FiniteMap.mkVBalBranch (Pos (Succ zzz618)) zzz619 (FiniteMap.splitGT zzz621 (Pos Zero)) zzz622",fontsize=16,color="magenta"];18445 -> 20896[label="",style="dashed", color="magenta", weight=3]; 130.29/78.17 18445 -> 20897[label="",style="dashed", color="magenta", weight=3]; 130.29/78.17 18445 -> 20898[label="",style="dashed", color="magenta", weight=3]; 130.29/78.17 18445 -> 20899[label="",style="dashed", color="magenta", weight=3]; 130.29/78.17 38843 -> 38579[label="",style="dashed", color="red", weight=0]; 130.29/78.17 38843[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ zzz4303)) zzz4304 zzz4305 zzz4306 zzz4307 (Pos (Succ zzz4308)) zzz4309 (primCmpNat zzz43100 zzz43110 == GT)",fontsize=16,color="magenta"];38843 -> 38905[label="",style="dashed", color="magenta", weight=3]; 130.29/78.17 38843 -> 38906[label="",style="dashed", color="magenta", weight=3]; 130.29/78.17 38844[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ zzz4303)) zzz4304 zzz4305 zzz4306 zzz4307 (Pos (Succ zzz4308)) zzz4309 (GT == GT)",fontsize=16,color="black",shape="box"];38844 -> 38907[label="",style="solid", color="black", weight=3]; 130.29/78.17 38845[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ zzz4303)) zzz4304 zzz4305 zzz4306 zzz4307 (Pos (Succ zzz4308)) zzz4309 (LT == GT)",fontsize=16,color="black",shape="box"];38845 -> 38908[label="",style="solid", color="black", weight=3]; 130.29/78.17 38846[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ zzz4303)) zzz4304 zzz4305 zzz4306 zzz4307 (Pos (Succ zzz4308)) zzz4309 (EQ == GT)",fontsize=16,color="black",shape="box"];38846 -> 38909[label="",style="solid", color="black", weight=3]; 130.29/78.17 18462[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200)))) (Pos zzz3420) == LT)",fontsize=16,color="black",shape="box"];18462 -> 20914[label="",style="solid", color="black", weight=3]; 130.29/78.17 18463[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200)))) (Neg zzz3420) == LT)",fontsize=16,color="black",shape="box"];18463 -> 20915[label="",style="solid", color="black", weight=3]; 130.29/78.17 18464[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos Zero)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];18464 -> 20916[label="",style="solid", color="black", weight=3]; 130.29/78.17 18465[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];18465 -> 20917[label="",style="solid", color="black", weight=3]; 130.29/78.17 18466[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg Zero)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];18466 -> 20918[label="",style="solid", color="black", weight=3]; 130.29/78.17 18467[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200)))) (Pos zzz3420) == LT)",fontsize=16,color="black",shape="box"];18467 -> 20919[label="",style="solid", color="black", weight=3]; 130.29/78.17 18468[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200)))) (Neg zzz3420) == LT)",fontsize=16,color="black",shape="box"];18468 -> 20920[label="",style="solid", color="black", weight=3]; 130.29/78.17 18469[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos Zero)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];18469 -> 20921[label="",style="solid", color="black", weight=3]; 130.29/78.17 18470[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];18470 -> 20922[label="",style="solid", color="black", weight=3]; 130.29/78.17 18471[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg Zero)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];18471 -> 20923[label="",style="solid", color="black", weight=3]; 130.29/78.17 18662[label="FiniteMap.splitGT2 zzz11960 zzz11961 zzz11962 zzz11963 zzz11964 (Pos Zero) (Pos Zero > zzz11960)",fontsize=16,color="black",shape="box"];18662 -> 20924[label="",style="solid", color="black", weight=3]; 130.29/78.17 18472[label="zzz6211",fontsize=16,color="green",shape="box"];18473[label="zzz6214",fontsize=16,color="green",shape="box"];18474[label="zzz6212",fontsize=16,color="green",shape="box"];18475[label="zzz621000",fontsize=16,color="green",shape="box"];18476[label="zzz6213",fontsize=16,color="green",shape="box"];18477[label="zzz6212",fontsize=16,color="green",shape="box"];18478[label="zzz6214",fontsize=16,color="green",shape="box"];18479[label="zzz6213",fontsize=16,color="green",shape="box"];18480[label="zzz6211",fontsize=16,color="green",shape="box"];18481[label="FiniteMap.splitLT2 (Neg (Succ zzz621000)) zzz6211 zzz6212 zzz6213 zzz6214 (Pos Zero) False",fontsize=16,color="black",shape="box"];18481 -> 20925[label="",style="solid", color="black", weight=3]; 130.29/78.17 18482[label="zzz6212",fontsize=16,color="green",shape="box"];18483[label="zzz6214",fontsize=16,color="green",shape="box"];18484[label="zzz6213",fontsize=16,color="green",shape="box"];18485[label="zzz6211",fontsize=16,color="green",shape="box"];62732[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat (Succ zzz63490) zzz63430 == LT)",fontsize=16,color="burlywood",shape="triangle"];65316[label="zzz63430/Succ zzz634300",fontsize=10,color="white",style="solid",shape="box"];62732 -> 65316[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65316 -> 62751[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 65317[label="zzz63430/Zero",fontsize=10,color="white",style="solid",shape="box"];62732 -> 65317[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65317 -> 62752[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 62733[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (GT == LT)",fontsize=16,color="black",shape="triangle"];62733 -> 62753[label="",style="solid", color="black", weight=3]; 130.29/78.17 62734[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos Zero) (Pos (Succ zzz634300)) == LT)",fontsize=16,color="black",shape="box"];62734 -> 62754[label="",style="solid", color="black", weight=3]; 130.29/78.17 62735[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];62735 -> 62755[label="",style="solid", color="black", weight=3]; 130.29/78.17 62736[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos Zero) (Neg (Succ zzz634300)) == LT)",fontsize=16,color="black",shape="box"];62736 -> 62756[label="",style="solid", color="black", weight=3]; 130.29/78.17 62737[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];62737 -> 62757[label="",style="solid", color="black", weight=3]; 130.29/78.17 62738[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (LT == LT)",fontsize=16,color="black",shape="triangle"];62738 -> 62758[label="",style="solid", color="black", weight=3]; 130.29/78.17 62739[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat zzz63430 (Succ zzz63500) == LT)",fontsize=16,color="burlywood",shape="triangle"];65318[label="zzz63430/Succ zzz634300",fontsize=10,color="white",style="solid",shape="box"];62739 -> 65318[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65318 -> 62759[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 65319[label="zzz63430/Zero",fontsize=10,color="white",style="solid",shape="box"];62739 -> 65319[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65319 -> 62760[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 62740[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg Zero) (Pos (Succ zzz634300)) == LT)",fontsize=16,color="black",shape="box"];62740 -> 62761[label="",style="solid", color="black", weight=3]; 130.29/78.17 62741[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];62741 -> 62762[label="",style="solid", color="black", weight=3]; 130.29/78.17 62742[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg Zero) (Neg (Succ zzz634300)) == LT)",fontsize=16,color="black",shape="box"];62742 -> 62763[label="",style="solid", color="black", weight=3]; 130.29/78.17 62743[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];62743 -> 62764[label="",style="solid", color="black", weight=3]; 130.29/78.17 63927[label="zzz474034",fontsize=16,color="green",shape="box"];55607[label="primPlusInt (Pos zzz58960) (Pos zzz59000)",fontsize=16,color="black",shape="box"];55607 -> 55624[label="",style="solid", color="black", weight=3]; 130.29/78.17 55608[label="primPlusInt (Pos zzz58960) (Neg zzz59000)",fontsize=16,color="black",shape="box"];55608 -> 55625[label="",style="solid", color="black", weight=3]; 130.29/78.17 63928[label="zzz474034",fontsize=16,color="green",shape="box"];55626[label="primPlusInt (Neg zzz58960) (Pos zzz59010)",fontsize=16,color="black",shape="box"];55626 -> 55735[label="",style="solid", color="black", weight=3]; 130.29/78.17 55627[label="primPlusInt (Neg zzz58960) (Neg zzz59010)",fontsize=16,color="black",shape="box"];55627 -> 55736[label="",style="solid", color="black", weight=3]; 130.29/78.17 63929[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat zzz6375000 Zero == LT)",fontsize=16,color="burlywood",shape="box"];65320[label="zzz6375000/Succ zzz63750000",fontsize=10,color="white",style="solid",shape="box"];63929 -> 65320[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65320 -> 64030[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 65321[label="zzz6375000/Zero",fontsize=10,color="white",style="solid",shape="box"];63929 -> 65321[label="",style="solid", color="burlywood", weight=9]; 130.29/78.17 65321 -> 64031[label="",style="solid", color="burlywood", weight=3]; 130.29/78.17 63930 -> 63800[label="",style="dashed", color="red", weight=0]; 130.29/78.17 63930[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (LT == LT)",fontsize=16,color="magenta"];63931[label="zzz474031",fontsize=16,color="green",shape="box"];63932[label="zzz474030",fontsize=16,color="green",shape="box"];63933[label="Zero",fontsize=16,color="green",shape="box"];63934[label="zzz474034",fontsize=16,color="green",shape="box"];63935[label="zzz6373",fontsize=16,color="green",shape="box"];60457[label="FiniteMap.mkBranch (Pos (Succ zzz6231)) zzz6232 zzz6233 zzz6234 zzz6235",fontsize=16,color="black",shape="triangle"];60457 -> 60753[label="",style="solid", color="black", weight=3]; 130.29/78.17 18517[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat Zero (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];18517 -> 20964[label="",style="solid", color="black", weight=3]; 130.29/78.17 18518[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ zzz426200)) zzz4263 zzz4264 (primCmpInt (Pos Zero) (Pos (Succ zzz426200)) == LT)",fontsize=16,color="black",shape="box"];18518 -> 20965[label="",style="solid", color="black", weight=3]; 130.29/78.17 18519[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];18519 -> 20966[label="",style="solid", color="black", weight=3]; 130.29/78.17 18520[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (primCmpInt (Pos Zero) (Neg (Succ zzz426200)) == LT)",fontsize=16,color="black",shape="box"];18520 -> 20967[label="",style="solid", color="black", weight=3]; 130.29/78.17 18521[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];18521 -> 20968[label="",style="solid", color="black", weight=3]; 130.29/78.17 18522[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat Zero (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];18522 -> 20969[label="",style="solid", color="black", weight=3]; 130.29/78.17 18523[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ zzz426200)) zzz4263 zzz4264 (primCmpInt (Neg Zero) (Pos (Succ zzz426200)) == LT)",fontsize=16,color="black",shape="box"];18523 -> 20970[label="",style="solid", color="black", weight=3]; 130.29/78.17 18524[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];18524 -> 20971[label="",style="solid", color="black", weight=3]; 130.29/78.17 18525[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (primCmpInt (Neg Zero) (Neg (Succ zzz426200)) == LT)",fontsize=16,color="black",shape="box"];18525 -> 20972[label="",style="solid", color="black", weight=3]; 130.29/78.17 18526[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];18526 -> 20973[label="",style="solid", color="black", weight=3]; 130.29/78.17 40284[label="FiniteMap.splitGT1 (Neg (Succ zzz4495)) zzz4496 zzz4497 zzz4498 zzz4499 (Neg (Succ zzz4500)) (primCmpNat (Succ zzz45010) (Succ zzz45020) == LT)",fontsize=16,color="black",shape="box"];40284 -> 40340[label="",style="solid", color="black", weight=3]; 130.29/78.17 40285[label="FiniteMap.splitGT1 (Neg (Succ zzz4495)) zzz4496 zzz4497 zzz4498 zzz4499 (Neg (Succ zzz4500)) (primCmpNat (Succ zzz45010) Zero == LT)",fontsize=16,color="black",shape="box"];40285 -> 40341[label="",style="solid", color="black", weight=3]; 130.29/78.17 40286[label="FiniteMap.splitGT1 (Neg (Succ zzz4495)) zzz4496 zzz4497 zzz4498 zzz4499 (Neg (Succ zzz4500)) (primCmpNat Zero (Succ zzz45020) == LT)",fontsize=16,color="black",shape="box"];40286 -> 40342[label="",style="solid", color="black", weight=3]; 130.29/78.17 40287[label="FiniteMap.splitGT1 (Neg (Succ zzz4495)) zzz4496 zzz4497 zzz4498 zzz4499 (Neg (Succ zzz4500)) (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];40287 -> 40343[label="",style="solid", color="black", weight=3]; 130.29/78.17 40336[label="FiniteMap.splitLT1 (Neg (Succ zzz4504)) zzz4505 zzz4506 zzz4507 zzz4508 (Neg (Succ zzz4509)) (primCmpNat (Succ zzz45100) (Succ zzz45110) == GT)",fontsize=16,color="black",shape="box"];40336 -> 40398[label="",style="solid", color="black", weight=3]; 130.29/78.17 40337[label="FiniteMap.splitLT1 (Neg (Succ zzz4504)) zzz4505 zzz4506 zzz4507 zzz4508 (Neg (Succ zzz4509)) (primCmpNat (Succ zzz45100) Zero == GT)",fontsize=16,color="black",shape="box"];40337 -> 40399[label="",style="solid", color="black", weight=3]; 130.29/78.17 40338[label="FiniteMap.splitLT1 (Neg (Succ zzz4504)) zzz4505 zzz4506 zzz4507 zzz4508 (Neg (Succ zzz4509)) (primCmpNat Zero (Succ zzz45110) == GT)",fontsize=16,color="black",shape="box"];40338 -> 40400[label="",style="solid", color="black", weight=3]; 130.29/78.17 40339[label="FiniteMap.splitLT1 (Neg (Succ zzz4504)) zzz4505 zzz4506 zzz4507 zzz4508 (Neg (Succ zzz4509)) (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];40339 -> 40401[label="",style="solid", color="black", weight=3]; 130.29/78.17 19277[label="zzz8334",fontsize=16,color="green",shape="box"];40631[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz4538)) zzz4539 zzz4540 zzz4541 zzz4542 (Neg (Succ zzz4543)) zzz4544 (primCmpNat (Succ zzz45450) (Succ zzz45460) == GT)",fontsize=16,color="black",shape="box"];40631 -> 40708[label="",style="solid", color="black", weight=3]; 130.29/78.17 40632[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz4538)) zzz4539 zzz4540 zzz4541 zzz4542 (Neg (Succ zzz4543)) zzz4544 (primCmpNat (Succ zzz45450) Zero == GT)",fontsize=16,color="black",shape="box"];40632 -> 40709[label="",style="solid", color="black", weight=3]; 130.29/78.17 40633[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz4538)) zzz4539 zzz4540 zzz4541 zzz4542 (Neg (Succ zzz4543)) zzz4544 (primCmpNat Zero (Succ zzz45460) == GT)",fontsize=16,color="black",shape="box"];40633 -> 40710[label="",style="solid", color="black", weight=3]; 130.29/78.17 40634[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz4538)) zzz4539 zzz4540 zzz4541 zzz4542 (Neg (Succ zzz4543)) zzz4544 (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];40634 -> 40711[label="",style="solid", color="black", weight=3]; 130.29/78.17 19298[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200)))) (Pos zzz3420) == LT)",fontsize=16,color="black",shape="box"];19298 -> 21155[label="",style="solid", color="black", weight=3]; 130.29/78.17 19299[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200)))) (Neg zzz3420) == LT)",fontsize=16,color="black",shape="box"];19299 -> 21156[label="",style="solid", color="black", weight=3]; 130.29/78.17 19300[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos Zero)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];19300 -> 21157[label="",style="solid", color="black", weight=3]; 130.29/78.17 19301[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];19301 -> 21158[label="",style="solid", color="black", weight=3]; 130.29/78.17 19302[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg Zero)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];19302 -> 21159[label="",style="solid", color="black", weight=3]; 130.29/78.18 19303[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200)))) (Pos zzz3420) == LT)",fontsize=16,color="black",shape="box"];19303 -> 21160[label="",style="solid", color="black", weight=3]; 130.29/78.18 19304[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200)))) (Neg zzz3420) == LT)",fontsize=16,color="black",shape="box"];19304 -> 21161[label="",style="solid", color="black", weight=3]; 130.29/78.18 19305[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos Zero)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];19305 -> 21162[label="",style="solid", color="black", weight=3]; 130.29/78.18 19306[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];19306 -> 21163[label="",style="solid", color="black", weight=3]; 130.29/78.18 19307[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg Zero)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];19307 -> 21164[label="",style="solid", color="black", weight=3]; 130.29/78.18 39587 -> 39386[label="",style="dashed", color="red", weight=0]; 130.29/78.18 39587[label="FiniteMap.splitGT1 (Pos (Succ zzz4428)) zzz4429 zzz4430 zzz4431 zzz4432 (Pos (Succ zzz4433)) (primCmpNat zzz44340 zzz44350 == LT)",fontsize=16,color="magenta"];39587 -> 39664[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 39587 -> 39665[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 39588[label="FiniteMap.splitGT1 (Pos (Succ zzz4428)) zzz4429 zzz4430 zzz4431 zzz4432 (Pos (Succ zzz4433)) (GT == LT)",fontsize=16,color="black",shape="box"];39588 -> 39666[label="",style="solid", color="black", weight=3]; 130.29/78.18 39589[label="FiniteMap.splitGT1 (Pos (Succ zzz4428)) zzz4429 zzz4430 zzz4431 zzz4432 (Pos (Succ zzz4433)) (LT == LT)",fontsize=16,color="black",shape="box"];39589 -> 39667[label="",style="solid", color="black", weight=3]; 130.29/78.18 39590[label="FiniteMap.splitGT1 (Pos (Succ zzz4428)) zzz4429 zzz4430 zzz4431 zzz4432 (Pos (Succ zzz4433)) (EQ == LT)",fontsize=16,color="black",shape="box"];39590 -> 39668[label="",style="solid", color="black", weight=3]; 130.29/78.18 35279 -> 29707[label="",style="dashed", color="red", weight=0]; 130.29/78.18 35279[label="FiniteMap.intersectFM_C2Lts (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529))",fontsize=16,color="magenta"];35279 -> 35303[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 35279 -> 35304[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 35279 -> 35305[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 35279 -> 35306[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 35279 -> 35307[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 35280[label="zzz3532",fontsize=16,color="green",shape="box"];35281 -> 29705[label="",style="dashed", color="red", weight=0]; 130.29/78.18 35281[label="FiniteMap.intersectFM_C2Gts (FiniteMap.Branch (Pos Zero) zzz3525 zzz3526 zzz3527 zzz3528) (Pos (Succ zzz3529))",fontsize=16,color="magenta"];35281 -> 35308[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 35281 -> 35309[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 35281 -> 35310[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 35281 -> 35311[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 35281 -> 35312[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 35282[label="zzz3533",fontsize=16,color="green",shape="box"];35283[label="zzz3530",fontsize=16,color="green",shape="box"];38325 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.18 38325[label="FiniteMap.mkVBalBranch (Pos (Succ zzz4178)) zzz4179 zzz4181 (FiniteMap.splitLT zzz4182 (Pos (Succ zzz4183)))",fontsize=16,color="magenta"];38325 -> 38342[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 38325 -> 38343[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 38325 -> 38344[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 38325 -> 38345[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 38326[label="FiniteMap.splitLT0 (Pos (Succ zzz4178)) zzz4179 zzz4180 zzz4181 zzz4182 (Pos (Succ zzz4183)) otherwise",fontsize=16,color="black",shape="box"];38326 -> 38346[label="",style="solid", color="black", weight=3]; 130.29/78.18 16180[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];16180 -> 17915[label="",style="solid", color="black", weight=3]; 130.29/78.18 20896 -> 18327[label="",style="dashed", color="red", weight=0]; 130.29/78.18 20896[label="FiniteMap.splitGT zzz621 (Pos Zero)",fontsize=16,color="magenta"];20896 -> 21502[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 20897[label="Succ zzz618",fontsize=16,color="green",shape="box"];20898[label="zzz622",fontsize=16,color="green",shape="box"];20899[label="zzz619",fontsize=16,color="green",shape="box"];38905[label="zzz43110",fontsize=16,color="green",shape="box"];38906[label="zzz43100",fontsize=16,color="green",shape="box"];38907[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ zzz4303)) zzz4304 zzz4305 zzz4306 zzz4307 (Pos (Succ zzz4308)) zzz4309 True",fontsize=16,color="black",shape="box"];38907 -> 38927[label="",style="solid", color="black", weight=3]; 130.29/78.18 38908[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ zzz4303)) zzz4304 zzz4305 zzz4306 zzz4307 (Pos (Succ zzz4308)) zzz4309 False",fontsize=16,color="black",shape="triangle"];38908 -> 38928[label="",style="solid", color="black", weight=3]; 130.29/78.18 38909 -> 38908[label="",style="dashed", color="red", weight=0]; 130.29/78.18 38909[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ zzz4303)) zzz4304 zzz4305 zzz4306 zzz4307 (Pos (Succ zzz4308)) zzz4309 False",fontsize=16,color="magenta"];20914[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (primCmpNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200))) zzz3420 == LT)",fontsize=16,color="burlywood",shape="box"];65322[label="zzz3420/Succ zzz34200",fontsize=10,color="white",style="solid",shape="box"];20914 -> 65322[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65322 -> 21518[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65323[label="zzz3420/Zero",fontsize=10,color="white",style="solid",shape="box"];20914 -> 65323[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65323 -> 21519[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 20915[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (GT == LT)",fontsize=16,color="black",shape="box"];20915 -> 21520[label="",style="solid", color="black", weight=3]; 130.29/78.18 20916[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];20916 -> 21521[label="",style="solid", color="black", weight=3]; 130.29/78.18 20917[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];20917 -> 21522[label="",style="solid", color="black", weight=3]; 130.29/78.18 20918[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];20918 -> 21523[label="",style="solid", color="black", weight=3]; 130.29/78.18 20919[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];20919 -> 21524[label="",style="solid", color="black", weight=3]; 130.29/78.18 20920[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpNat zzz3420 (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200))) == LT)",fontsize=16,color="burlywood",shape="box"];65324[label="zzz3420/Succ zzz34200",fontsize=10,color="white",style="solid",shape="box"];20920 -> 65324[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65324 -> 21525[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65325[label="zzz3420/Zero",fontsize=10,color="white",style="solid",shape="box"];20920 -> 65325[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65325 -> 21526[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 20921[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];20921 -> 21527[label="",style="solid", color="black", weight=3]; 130.29/78.18 20922[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];20922 -> 21528[label="",style="solid", color="black", weight=3]; 130.29/78.18 20923[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];20923 -> 21529[label="",style="solid", color="black", weight=3]; 130.29/78.18 20924[label="FiniteMap.splitGT2 zzz11960 zzz11961 zzz11962 zzz11963 zzz11964 (Pos Zero) (compare (Pos Zero) zzz11960 == GT)",fontsize=16,color="black",shape="box"];20924 -> 21530[label="",style="solid", color="black", weight=3]; 130.29/78.18 20925[label="FiniteMap.splitLT1 (Neg (Succ zzz621000)) zzz6211 zzz6212 zzz6213 zzz6214 (Pos Zero) (Pos Zero > Neg (Succ zzz621000))",fontsize=16,color="black",shape="box"];20925 -> 21531[label="",style="solid", color="black", weight=3]; 130.29/78.18 62751[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat (Succ zzz63490) (Succ zzz634300) == LT)",fontsize=16,color="black",shape="box"];62751 -> 62767[label="",style="solid", color="black", weight=3]; 130.29/78.18 62752[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat (Succ zzz63490) Zero == LT)",fontsize=16,color="black",shape="box"];62752 -> 62768[label="",style="solid", color="black", weight=3]; 130.29/78.18 62753[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 False",fontsize=16,color="black",shape="triangle"];62753 -> 62769[label="",style="solid", color="black", weight=3]; 130.29/78.18 62754 -> 62739[label="",style="dashed", color="red", weight=0]; 130.29/78.18 62754[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat Zero (Succ zzz634300) == LT)",fontsize=16,color="magenta"];62754 -> 62770[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 62754 -> 62771[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 62755[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (EQ == LT)",fontsize=16,color="black",shape="triangle"];62755 -> 62772[label="",style="solid", color="black", weight=3]; 130.29/78.18 62756 -> 62733[label="",style="dashed", color="red", weight=0]; 130.29/78.18 62756[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (GT == LT)",fontsize=16,color="magenta"];62757 -> 62755[label="",style="dashed", color="red", weight=0]; 130.29/78.18 62757[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (EQ == LT)",fontsize=16,color="magenta"];62758[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 True",fontsize=16,color="black",shape="box"];62758 -> 62773[label="",style="solid", color="black", weight=3]; 130.29/78.18 62759[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat (Succ zzz634300) (Succ zzz63500) == LT)",fontsize=16,color="black",shape="box"];62759 -> 62774[label="",style="solid", color="black", weight=3]; 130.29/78.18 62760[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat Zero (Succ zzz63500) == LT)",fontsize=16,color="black",shape="box"];62760 -> 62775[label="",style="solid", color="black", weight=3]; 130.29/78.18 62761 -> 62738[label="",style="dashed", color="red", weight=0]; 130.29/78.18 62761[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (LT == LT)",fontsize=16,color="magenta"];62762 -> 62755[label="",style="dashed", color="red", weight=0]; 130.29/78.18 62762[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (EQ == LT)",fontsize=16,color="magenta"];62763 -> 62732[label="",style="dashed", color="red", weight=0]; 130.29/78.18 62763[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat (Succ zzz634300) Zero == LT)",fontsize=16,color="magenta"];62763 -> 62776[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 62763 -> 62777[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 62764 -> 62755[label="",style="dashed", color="red", weight=0]; 130.29/78.18 62764[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (EQ == LT)",fontsize=16,color="magenta"];55624[label="Pos (primPlusNat zzz58960 zzz59000)",fontsize=16,color="green",shape="box"];55624 -> 55732[label="",style="dashed", color="green", weight=3]; 130.29/78.18 55625 -> 43410[label="",style="dashed", color="red", weight=0]; 130.29/78.18 55625[label="primMinusNat zzz58960 zzz59000",fontsize=16,color="magenta"];55625 -> 55733[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 55625 -> 55734[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 55735 -> 43410[label="",style="dashed", color="red", weight=0]; 130.29/78.18 55735[label="primMinusNat zzz59010 zzz58960",fontsize=16,color="magenta"];55735 -> 55777[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 55735 -> 55778[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 55736[label="Neg (primPlusNat zzz58960 zzz59010)",fontsize=16,color="green",shape="box"];55736 -> 55779[label="",style="dashed", color="green", weight=3]; 130.29/78.18 64030[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat (Succ zzz63750000) Zero == LT)",fontsize=16,color="black",shape="box"];64030 -> 64128[label="",style="solid", color="black", weight=3]; 130.29/78.18 64031[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];64031 -> 64129[label="",style="solid", color="black", weight=3]; 130.29/78.18 60753[label="FiniteMap.mkBranchResult zzz6232 zzz6233 zzz6234 zzz6235",fontsize=16,color="black",shape="box"];60753 -> 60762[label="",style="solid", color="black", weight=3]; 130.29/78.18 20964[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat Zero (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];20964 -> 21580[label="",style="solid", color="black", weight=3]; 130.29/78.18 20965[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ zzz426200)) zzz4263 zzz4264 (primCmpNat Zero (Succ zzz426200) == LT)",fontsize=16,color="black",shape="box"];20965 -> 21581[label="",style="solid", color="black", weight=3]; 130.29/78.18 20966[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (EQ == LT)",fontsize=16,color="black",shape="box"];20966 -> 21582[label="",style="solid", color="black", weight=3]; 130.29/78.18 20967[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (GT == LT)",fontsize=16,color="black",shape="box"];20967 -> 21583[label="",style="solid", color="black", weight=3]; 130.29/78.18 20968[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (EQ == LT)",fontsize=16,color="black",shape="box"];20968 -> 21584[label="",style="solid", color="black", weight=3]; 130.29/78.18 20969[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat Zero (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];20969 -> 21585[label="",style="solid", color="black", weight=3]; 130.29/78.18 20970[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ zzz426200)) zzz4263 zzz4264 (LT == LT)",fontsize=16,color="black",shape="box"];20970 -> 21586[label="",style="solid", color="black", weight=3]; 130.29/78.18 20971[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (EQ == LT)",fontsize=16,color="black",shape="box"];20971 -> 21587[label="",style="solid", color="black", weight=3]; 130.29/78.18 20972[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (primCmpNat (Succ zzz426200) Zero == LT)",fontsize=16,color="black",shape="box"];20972 -> 21588[label="",style="solid", color="black", weight=3]; 130.29/78.18 20973[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (EQ == LT)",fontsize=16,color="black",shape="box"];20973 -> 21589[label="",style="solid", color="black", weight=3]; 130.29/78.18 40340 -> 40102[label="",style="dashed", color="red", weight=0]; 130.29/78.18 40340[label="FiniteMap.splitGT1 (Neg (Succ zzz4495)) zzz4496 zzz4497 zzz4498 zzz4499 (Neg (Succ zzz4500)) (primCmpNat zzz45010 zzz45020 == LT)",fontsize=16,color="magenta"];40340 -> 40402[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40340 -> 40403[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40341[label="FiniteMap.splitGT1 (Neg (Succ zzz4495)) zzz4496 zzz4497 zzz4498 zzz4499 (Neg (Succ zzz4500)) (GT == LT)",fontsize=16,color="black",shape="box"];40341 -> 40404[label="",style="solid", color="black", weight=3]; 130.29/78.18 40342[label="FiniteMap.splitGT1 (Neg (Succ zzz4495)) zzz4496 zzz4497 zzz4498 zzz4499 (Neg (Succ zzz4500)) (LT == LT)",fontsize=16,color="black",shape="box"];40342 -> 40405[label="",style="solid", color="black", weight=3]; 130.29/78.18 40343[label="FiniteMap.splitGT1 (Neg (Succ zzz4495)) zzz4496 zzz4497 zzz4498 zzz4499 (Neg (Succ zzz4500)) (EQ == LT)",fontsize=16,color="black",shape="box"];40343 -> 40406[label="",style="solid", color="black", weight=3]; 130.29/78.18 40398 -> 40193[label="",style="dashed", color="red", weight=0]; 130.29/78.18 40398[label="FiniteMap.splitLT1 (Neg (Succ zzz4504)) zzz4505 zzz4506 zzz4507 zzz4508 (Neg (Succ zzz4509)) (primCmpNat zzz45100 zzz45110 == GT)",fontsize=16,color="magenta"];40398 -> 40429[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40398 -> 40430[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40399[label="FiniteMap.splitLT1 (Neg (Succ zzz4504)) zzz4505 zzz4506 zzz4507 zzz4508 (Neg (Succ zzz4509)) (GT == GT)",fontsize=16,color="black",shape="box"];40399 -> 40431[label="",style="solid", color="black", weight=3]; 130.29/78.18 40400[label="FiniteMap.splitLT1 (Neg (Succ zzz4504)) zzz4505 zzz4506 zzz4507 zzz4508 (Neg (Succ zzz4509)) (LT == GT)",fontsize=16,color="black",shape="box"];40400 -> 40432[label="",style="solid", color="black", weight=3]; 130.29/78.18 40401[label="FiniteMap.splitLT1 (Neg (Succ zzz4504)) zzz4505 zzz4506 zzz4507 zzz4508 (Neg (Succ zzz4509)) (EQ == GT)",fontsize=16,color="black",shape="box"];40401 -> 40433[label="",style="solid", color="black", weight=3]; 130.29/78.18 40708 -> 40457[label="",style="dashed", color="red", weight=0]; 130.29/78.18 40708[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz4538)) zzz4539 zzz4540 zzz4541 zzz4542 (Neg (Succ zzz4543)) zzz4544 (primCmpNat zzz45450 zzz45460 == GT)",fontsize=16,color="magenta"];40708 -> 40863[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40708 -> 40864[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40709[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz4538)) zzz4539 zzz4540 zzz4541 zzz4542 (Neg (Succ zzz4543)) zzz4544 (GT == GT)",fontsize=16,color="black",shape="box"];40709 -> 40865[label="",style="solid", color="black", weight=3]; 130.29/78.18 40710[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz4538)) zzz4539 zzz4540 zzz4541 zzz4542 (Neg (Succ zzz4543)) zzz4544 (LT == GT)",fontsize=16,color="black",shape="box"];40710 -> 40866[label="",style="solid", color="black", weight=3]; 130.29/78.18 40711[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz4538)) zzz4539 zzz4540 zzz4541 zzz4542 (Neg (Succ zzz4543)) zzz4544 (EQ == GT)",fontsize=16,color="black",shape="box"];40711 -> 40867[label="",style="solid", color="black", weight=3]; 130.29/78.18 21155[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (primCmpNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200))) zzz3420 == LT)",fontsize=16,color="burlywood",shape="box"];65326[label="zzz3420/Succ zzz34200",fontsize=10,color="white",style="solid",shape="box"];21155 -> 65326[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65326 -> 21663[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65327[label="zzz3420/Zero",fontsize=10,color="white",style="solid",shape="box"];21155 -> 65327[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65327 -> 21664[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 21156[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (GT == LT)",fontsize=16,color="black",shape="box"];21156 -> 21665[label="",style="solid", color="black", weight=3]; 130.29/78.18 21157[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];21157 -> 21666[label="",style="solid", color="black", weight=3]; 130.29/78.18 21158 -> 43855[label="",style="dashed", color="red", weight=0]; 130.29/78.18 21158[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="magenta"];21158 -> 43856[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21158 -> 43857[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21158 -> 43858[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21158 -> 43859[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21158 -> 43860[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21158 -> 43861[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21158 -> 43862[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21158 -> 43863[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21158 -> 43864[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21158 -> 43865[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21158 -> 43866[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21159[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];21159 -> 21668[label="",style="solid", color="black", weight=3]; 130.29/78.18 21160[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];21160 -> 21669[label="",style="solid", color="black", weight=3]; 130.29/78.18 21161[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpNat zzz3420 (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200))) == LT)",fontsize=16,color="burlywood",shape="box"];65328[label="zzz3420/Succ zzz34200",fontsize=10,color="white",style="solid",shape="box"];21161 -> 65328[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65328 -> 21670[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65329[label="zzz3420/Zero",fontsize=10,color="white",style="solid",shape="box"];21161 -> 65329[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65329 -> 21671[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 21162[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];21162 -> 21672[label="",style="solid", color="black", weight=3]; 130.29/78.18 21163[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];21163 -> 21673[label="",style="solid", color="black", weight=3]; 130.29/78.18 21164[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];21164 -> 21674[label="",style="solid", color="black", weight=3]; 130.29/78.18 39664[label="zzz44340",fontsize=16,color="green",shape="box"];39665[label="zzz44350",fontsize=16,color="green",shape="box"];39666[label="FiniteMap.splitGT1 (Pos (Succ zzz4428)) zzz4429 zzz4430 zzz4431 zzz4432 (Pos (Succ zzz4433)) False",fontsize=16,color="black",shape="triangle"];39666 -> 39756[label="",style="solid", color="black", weight=3]; 130.29/78.18 39667[label="FiniteMap.splitGT1 (Pos (Succ zzz4428)) zzz4429 zzz4430 zzz4431 zzz4432 (Pos (Succ zzz4433)) True",fontsize=16,color="black",shape="box"];39667 -> 39757[label="",style="solid", color="black", weight=3]; 130.29/78.18 39668 -> 39666[label="",style="dashed", color="red", weight=0]; 130.29/78.18 39668[label="FiniteMap.splitGT1 (Pos (Succ zzz4428)) zzz4429 zzz4430 zzz4431 zzz4432 (Pos (Succ zzz4433)) False",fontsize=16,color="magenta"];35303[label="zzz3528",fontsize=16,color="green",shape="box"];35304[label="zzz3527",fontsize=16,color="green",shape="box"];35305[label="zzz3525",fontsize=16,color="green",shape="box"];35306[label="zzz3526",fontsize=16,color="green",shape="box"];35307[label="zzz3529",fontsize=16,color="green",shape="box"];35308[label="zzz3528",fontsize=16,color="green",shape="box"];35309[label="zzz3527",fontsize=16,color="green",shape="box"];35310[label="zzz3525",fontsize=16,color="green",shape="box"];35311[label="zzz3526",fontsize=16,color="green",shape="box"];35312[label="zzz3529",fontsize=16,color="green",shape="box"];38342[label="zzz4181",fontsize=16,color="green",shape="box"];38343[label="Succ zzz4178",fontsize=16,color="green",shape="box"];38344 -> 23112[label="",style="dashed", color="red", weight=0]; 130.29/78.18 38344[label="FiniteMap.splitLT zzz4182 (Pos (Succ zzz4183))",fontsize=16,color="magenta"];38344 -> 38360[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 38344 -> 38361[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 38345[label="zzz4179",fontsize=16,color="green",shape="box"];38346[label="FiniteMap.splitLT0 (Pos (Succ zzz4178)) zzz4179 zzz4180 zzz4181 zzz4182 (Pos (Succ zzz4183)) True",fontsize=16,color="black",shape="box"];38346 -> 38362[label="",style="solid", color="black", weight=3]; 130.29/78.18 17915[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];17915 -> 18444[label="",style="solid", color="black", weight=3]; 130.29/78.18 21502[label="zzz621",fontsize=16,color="green",shape="box"];38927 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.18 38927[label="FiniteMap.mkBalBranch (Pos (Succ zzz4303)) zzz4304 zzz4306 (FiniteMap.addToFM_C FiniteMap.addToFM0 zzz4307 (Pos (Succ zzz4308)) zzz4309)",fontsize=16,color="magenta"];38927 -> 63145[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 38927 -> 63146[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 38927 -> 63147[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 38927 -> 63148[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 38928[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Pos (Succ zzz4303)) zzz4304 zzz4305 zzz4306 zzz4307 (Pos (Succ zzz4308)) zzz4309 otherwise",fontsize=16,color="black",shape="box"];38928 -> 38950[label="",style="solid", color="black", weight=3]; 130.29/78.18 21518[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (primCmpNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200))) (Succ zzz34200) == LT)",fontsize=16,color="black",shape="box"];21518 -> 22348[label="",style="solid", color="black", weight=3]; 130.29/78.18 21519[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200))) Zero == LT)",fontsize=16,color="black",shape="box"];21519 -> 22349[label="",style="solid", color="black", weight=3]; 130.29/78.18 21520[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];21520 -> 22350[label="",style="solid", color="black", weight=3]; 130.29/78.18 21521[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];21521 -> 22351[label="",style="solid", color="black", weight=3]; 130.29/78.18 21522[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];21522 -> 22352[label="",style="solid", color="black", weight=3]; 130.29/78.18 21523[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];21523 -> 22353[label="",style="solid", color="black", weight=3]; 130.29/78.18 21524[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];21524 -> 22354[label="",style="solid", color="black", weight=3]; 130.29/78.18 21525[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpNat (Succ zzz34200) (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200))) == LT)",fontsize=16,color="black",shape="box"];21525 -> 22355[label="",style="solid", color="black", weight=3]; 130.29/78.18 21526[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpNat Zero (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200))) == LT)",fontsize=16,color="black",shape="box"];21526 -> 22356[label="",style="solid", color="black", weight=3]; 130.29/78.18 21527[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];21527 -> 22357[label="",style="solid", color="black", weight=3]; 130.29/78.18 21528[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];21528 -> 22358[label="",style="solid", color="black", weight=3]; 130.29/78.18 21529[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];21529 -> 22359[label="",style="solid", color="black", weight=3]; 130.29/78.18 21530[label="FiniteMap.splitGT2 zzz11960 zzz11961 zzz11962 zzz11963 zzz11964 (Pos Zero) (primCmpInt (Pos Zero) zzz11960 == GT)",fontsize=16,color="burlywood",shape="box"];65330[label="zzz11960/Pos zzz119600",fontsize=10,color="white",style="solid",shape="box"];21530 -> 65330[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65330 -> 22360[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65331[label="zzz11960/Neg zzz119600",fontsize=10,color="white",style="solid",shape="box"];21530 -> 65331[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65331 -> 22361[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 21531[label="FiniteMap.splitLT1 (Neg (Succ zzz621000)) zzz6211 zzz6212 zzz6213 zzz6214 (Pos Zero) (compare (Pos Zero) (Neg (Succ zzz621000)) == GT)",fontsize=16,color="black",shape="box"];21531 -> 22362[label="",style="solid", color="black", weight=3]; 130.29/78.18 62767[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat zzz63490 zzz634300 == LT)",fontsize=16,color="burlywood",shape="triangle"];65332[label="zzz63490/Succ zzz634900",fontsize=10,color="white",style="solid",shape="box"];62767 -> 65332[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65332 -> 62780[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65333[label="zzz63490/Zero",fontsize=10,color="white",style="solid",shape="box"];62767 -> 65333[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65333 -> 62781[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 62768 -> 62733[label="",style="dashed", color="red", weight=0]; 130.29/78.18 62768[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (GT == LT)",fontsize=16,color="magenta"];62769[label="FiniteMap.glueVBal3GlueVBal0 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 otherwise",fontsize=16,color="black",shape="box"];62769 -> 62782[label="",style="solid", color="black", weight=3]; 130.29/78.18 62770[label="zzz634300",fontsize=16,color="green",shape="box"];62771[label="Zero",fontsize=16,color="green",shape="box"];62772 -> 62753[label="",style="dashed", color="red", weight=0]; 130.29/78.18 62772[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 False",fontsize=16,color="magenta"];62773 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.18 62773[label="FiniteMap.mkBalBranch zzz47460 zzz47461 zzz47463 (FiniteMap.glueVBal zzz47464 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034))",fontsize=16,color="magenta"];62773 -> 63149[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 62773 -> 63150[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 62773 -> 63151[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 62773 -> 63152[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 62774 -> 62767[label="",style="dashed", color="red", weight=0]; 130.29/78.18 62774[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat zzz634300 zzz63500 == LT)",fontsize=16,color="magenta"];62774 -> 62784[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 62774 -> 62785[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 62775 -> 62738[label="",style="dashed", color="red", weight=0]; 130.29/78.18 62775[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (LT == LT)",fontsize=16,color="magenta"];62776[label="zzz634300",fontsize=16,color="green",shape="box"];62777[label="Zero",fontsize=16,color="green",shape="box"];55732 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.18 55732[label="primPlusNat zzz58960 zzz59000",fontsize=16,color="magenta"];55732 -> 55775[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 55732 -> 55776[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 55733[label="zzz58960",fontsize=16,color="green",shape="box"];55734[label="zzz59000",fontsize=16,color="green",shape="box"];43410[label="primMinusNat zzz48280 zzz4770",fontsize=16,color="burlywood",shape="triangle"];65334[label="zzz48280/Succ zzz482800",fontsize=10,color="white",style="solid",shape="box"];43410 -> 65334[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65334 -> 43438[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65335[label="zzz48280/Zero",fontsize=10,color="white",style="solid",shape="box"];43410 -> 65335[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65335 -> 43439[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 55777[label="zzz59010",fontsize=16,color="green",shape="box"];55778[label="zzz58960",fontsize=16,color="green",shape="box"];55779 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.18 55779[label="primPlusNat zzz58960 zzz59010",fontsize=16,color="magenta"];55779 -> 55793[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 55779 -> 55794[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 64128[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (GT == LT)",fontsize=16,color="black",shape="box"];64128 -> 64232[label="",style="solid", color="black", weight=3]; 130.29/78.18 64129[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (EQ == LT)",fontsize=16,color="black",shape="box"];64129 -> 64233[label="",style="solid", color="black", weight=3]; 130.29/78.18 60762[label="FiniteMap.Branch zzz6232 zzz6233 (FiniteMap.mkBranchUnbox zzz6234 zzz6235 zzz6232 (Pos (Succ Zero) + FiniteMap.mkBranchLeft_size zzz6234 zzz6235 zzz6232 + FiniteMap.mkBranchRight_size zzz6234 zzz6235 zzz6232)) zzz6234 zzz6235",fontsize=16,color="green",shape="box"];60762 -> 60765[label="",style="dashed", color="green", weight=3]; 130.29/78.18 21580[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primPlusNat (Succ zzz33200) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];21580 -> 22413[label="",style="solid", color="black", weight=3]; 130.29/78.18 21581[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ zzz426200)) zzz4263 zzz4264 (LT == LT)",fontsize=16,color="black",shape="box"];21581 -> 22414[label="",style="solid", color="black", weight=3]; 130.29/78.18 21582[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 False",fontsize=16,color="black",shape="box"];21582 -> 22415[label="",style="solid", color="black", weight=3]; 130.29/78.18 21583[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 False",fontsize=16,color="black",shape="box"];21583 -> 22416[label="",style="solid", color="black", weight=3]; 130.29/78.18 21584[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 False",fontsize=16,color="black",shape="box"];21584 -> 22417[label="",style="solid", color="black", weight=3]; 130.29/78.18 21585[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (Succ zzz33200) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];21585 -> 22418[label="",style="solid", color="black", weight=3]; 130.29/78.18 21586[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ zzz426200)) zzz4263 zzz4264 True",fontsize=16,color="black",shape="box"];21586 -> 22419[label="",style="solid", color="black", weight=3]; 130.29/78.18 21587[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 False",fontsize=16,color="black",shape="box"];21587 -> 22420[label="",style="solid", color="black", weight=3]; 130.29/78.18 21588[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (GT == LT)",fontsize=16,color="black",shape="box"];21588 -> 22421[label="",style="solid", color="black", weight=3]; 130.29/78.18 21589[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 False",fontsize=16,color="black",shape="box"];21589 -> 22422[label="",style="solid", color="black", weight=3]; 130.29/78.18 40402[label="zzz45010",fontsize=16,color="green",shape="box"];40403[label="zzz45020",fontsize=16,color="green",shape="box"];40404[label="FiniteMap.splitGT1 (Neg (Succ zzz4495)) zzz4496 zzz4497 zzz4498 zzz4499 (Neg (Succ zzz4500)) False",fontsize=16,color="black",shape="triangle"];40404 -> 40434[label="",style="solid", color="black", weight=3]; 130.29/78.18 40405[label="FiniteMap.splitGT1 (Neg (Succ zzz4495)) zzz4496 zzz4497 zzz4498 zzz4499 (Neg (Succ zzz4500)) True",fontsize=16,color="black",shape="box"];40405 -> 40435[label="",style="solid", color="black", weight=3]; 130.29/78.18 40406 -> 40404[label="",style="dashed", color="red", weight=0]; 130.29/78.18 40406[label="FiniteMap.splitGT1 (Neg (Succ zzz4495)) zzz4496 zzz4497 zzz4498 zzz4499 (Neg (Succ zzz4500)) False",fontsize=16,color="magenta"];40429[label="zzz45100",fontsize=16,color="green",shape="box"];40430[label="zzz45110",fontsize=16,color="green",shape="box"];40431[label="FiniteMap.splitLT1 (Neg (Succ zzz4504)) zzz4505 zzz4506 zzz4507 zzz4508 (Neg (Succ zzz4509)) True",fontsize=16,color="black",shape="box"];40431 -> 40559[label="",style="solid", color="black", weight=3]; 130.29/78.18 40432[label="FiniteMap.splitLT1 (Neg (Succ zzz4504)) zzz4505 zzz4506 zzz4507 zzz4508 (Neg (Succ zzz4509)) False",fontsize=16,color="black",shape="triangle"];40432 -> 40560[label="",style="solid", color="black", weight=3]; 130.29/78.18 40433 -> 40432[label="",style="dashed", color="red", weight=0]; 130.29/78.18 40433[label="FiniteMap.splitLT1 (Neg (Succ zzz4504)) zzz4505 zzz4506 zzz4507 zzz4508 (Neg (Succ zzz4509)) False",fontsize=16,color="magenta"];40863[label="zzz45450",fontsize=16,color="green",shape="box"];40864[label="zzz45460",fontsize=16,color="green",shape="box"];40865[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz4538)) zzz4539 zzz4540 zzz4541 zzz4542 (Neg (Succ zzz4543)) zzz4544 True",fontsize=16,color="black",shape="box"];40865 -> 40896[label="",style="solid", color="black", weight=3]; 130.29/78.18 40866[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz4538)) zzz4539 zzz4540 zzz4541 zzz4542 (Neg (Succ zzz4543)) zzz4544 False",fontsize=16,color="black",shape="triangle"];40866 -> 40897[label="",style="solid", color="black", weight=3]; 130.29/78.18 40867 -> 40866[label="",style="dashed", color="red", weight=0]; 130.29/78.18 40867[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ zzz4538)) zzz4539 zzz4540 zzz4541 zzz4542 (Neg (Succ zzz4543)) zzz4544 False",fontsize=16,color="magenta"];21663[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (primCmpNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200))) (Succ zzz34200) == LT)",fontsize=16,color="black",shape="box"];21663 -> 22718[label="",style="solid", color="black", weight=3]; 130.29/78.18 21664[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200))) Zero == LT)",fontsize=16,color="black",shape="box"];21664 -> 22719[label="",style="solid", color="black", weight=3]; 130.29/78.18 21665[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];21665 -> 22720[label="",style="solid", color="black", weight=3]; 130.29/78.18 21666[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];21666 -> 22721[label="",style="solid", color="black", weight=3]; 130.29/78.18 43856[label="zzz340",fontsize=16,color="green",shape="box"];43857[label="Zero",fontsize=16,color="green",shape="box"];43858[label="zzz3534",fontsize=16,color="green",shape="box"];43859[label="zzz343",fontsize=16,color="green",shape="box"];43860[label="zzz34200",fontsize=16,color="green",shape="box"];43861 -> 43358[label="",style="dashed", color="red", weight=0]; 130.29/78.18 43861[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz34200)",fontsize=16,color="magenta"];43861 -> 44079[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 43862[label="zzz3530",fontsize=16,color="green",shape="box"];43863[label="zzz341",fontsize=16,color="green",shape="box"];43864[label="zzz3533",fontsize=16,color="green",shape="box"];43865[label="zzz3531",fontsize=16,color="green",shape="box"];43866[label="zzz344",fontsize=16,color="green",shape="box"];43855[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg zzz4946) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="burlywood",shape="triangle"];65336[label="zzz4946/Succ zzz49460",fontsize=10,color="white",style="solid",shape="box"];43855 -> 65336[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65336 -> 44080[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65337[label="zzz4946/Zero",fontsize=10,color="white",style="solid",shape="box"];43855 -> 65337[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65337 -> 44081[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 21668[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];21668 -> 22723[label="",style="solid", color="black", weight=3]; 130.29/78.18 21669[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos zzz3420) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];21669 -> 22724[label="",style="solid", color="black", weight=3]; 130.29/78.18 21670[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpNat (Succ zzz34200) (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200))) == LT)",fontsize=16,color="black",shape="box"];21670 -> 22725[label="",style="solid", color="black", weight=3]; 130.29/78.18 21671[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpNat Zero (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200))) == LT)",fontsize=16,color="black",shape="box"];21671 -> 22726[label="",style="solid", color="black", weight=3]; 130.29/78.18 21672[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];21672 -> 22727[label="",style="solid", color="black", weight=3]; 130.29/78.18 21673 -> 44103[label="",style="dashed", color="red", weight=0]; 130.29/78.18 21673[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="magenta"];21673 -> 44104[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21673 -> 44105[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21673 -> 44106[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21673 -> 44107[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21673 -> 44108[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21673 -> 44109[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21673 -> 44110[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21673 -> 44111[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21673 -> 44112[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21673 -> 44113[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21673 -> 44114[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 21674[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];21674 -> 22729[label="",style="solid", color="black", weight=3]; 130.29/78.18 39756[label="FiniteMap.splitGT0 (Pos (Succ zzz4428)) zzz4429 zzz4430 zzz4431 zzz4432 (Pos (Succ zzz4433)) otherwise",fontsize=16,color="black",shape="box"];39756 -> 39821[label="",style="solid", color="black", weight=3]; 130.29/78.18 39757 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.18 39757[label="FiniteMap.mkVBalBranch (Pos (Succ zzz4428)) zzz4429 (FiniteMap.splitGT zzz4431 (Pos (Succ zzz4433))) zzz4432",fontsize=16,color="magenta"];39757 -> 39822[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 39757 -> 39823[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 39757 -> 39824[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 39757 -> 39825[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 38360[label="zzz4183",fontsize=16,color="green",shape="box"];38361[label="zzz4182",fontsize=16,color="green",shape="box"];38362[label="zzz4181",fontsize=16,color="green",shape="box"];18444[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 zzz332 zzz333 zzz334))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];18444 -> 20887[label="",style="solid", color="black", weight=3]; 130.29/78.18 63145[label="Pos (Succ zzz4303)",fontsize=16,color="green",shape="box"];63146 -> 4379[label="",style="dashed", color="red", weight=0]; 130.29/78.18 63146[label="FiniteMap.addToFM_C FiniteMap.addToFM0 zzz4307 (Pos (Succ zzz4308)) zzz4309",fontsize=16,color="magenta"];63146 -> 63401[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63146 -> 63402[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63146 -> 63403[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63147[label="zzz4306",fontsize=16,color="green",shape="box"];63148[label="zzz4304",fontsize=16,color="green",shape="box"];38950[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Pos (Succ zzz4303)) zzz4304 zzz4305 zzz4306 zzz4307 (Pos (Succ zzz4308)) zzz4309 True",fontsize=16,color="black",shape="box"];38950 -> 38983[label="",style="solid", color="black", weight=3]; 130.29/78.18 22348[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200)) zzz34200 == LT)",fontsize=16,color="burlywood",shape="box"];65338[label="zzz34200/Succ zzz342000",fontsize=10,color="white",style="solid",shape="box"];22348 -> 65338[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65338 -> 23419[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65339[label="zzz34200/Zero",fontsize=10,color="white",style="solid",shape="box"];22348 -> 65339[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65339 -> 23420[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 22349[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (GT == LT)",fontsize=16,color="black",shape="box"];22349 -> 23421[label="",style="solid", color="black", weight=3]; 130.29/78.18 22350[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344)",fontsize=16,color="black",shape="box"];22350 -> 23422[label="",style="solid", color="black", weight=3]; 130.29/78.18 22351[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];22351 -> 23423[label="",style="solid", color="black", weight=3]; 130.29/78.18 22352[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primMulNat (Succ (Succ (Succ Zero))) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];22352 -> 23424[label="",style="solid", color="black", weight=3]; 130.29/78.18 22353[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];22353 -> 23425[label="",style="solid", color="black", weight=3]; 130.29/78.18 22354 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.18 22354[label="FiniteMap.mkBalBranch zzz340 zzz341 (FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504) zzz343) zzz344",fontsize=16,color="magenta"];22354 -> 63153[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 22354 -> 63154[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 22354 -> 63155[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 22354 -> 63156[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 22355[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpNat zzz34200 (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200)) == LT)",fontsize=16,color="burlywood",shape="box"];65340[label="zzz34200/Succ zzz342000",fontsize=10,color="white",style="solid",shape="box"];22355 -> 65340[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65340 -> 23430[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65341[label="zzz34200/Zero",fontsize=10,color="white",style="solid",shape="box"];22355 -> 65341[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65341 -> 23431[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 22356[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];22356 -> 23432[label="",style="solid", color="black", weight=3]; 130.29/78.18 22357[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];22357 -> 23433[label="",style="solid", color="black", weight=3]; 130.29/78.18 22358[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];22358 -> 23434[label="",style="solid", color="black", weight=3]; 130.29/78.18 22359[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];22359 -> 23435[label="",style="solid", color="black", weight=3]; 130.29/78.18 22360[label="FiniteMap.splitGT2 (Pos zzz119600) zzz11961 zzz11962 zzz11963 zzz11964 (Pos Zero) (primCmpInt (Pos Zero) (Pos zzz119600) == GT)",fontsize=16,color="burlywood",shape="box"];65342[label="zzz119600/Succ zzz1196000",fontsize=10,color="white",style="solid",shape="box"];22360 -> 65342[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65342 -> 23436[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65343[label="zzz119600/Zero",fontsize=10,color="white",style="solid",shape="box"];22360 -> 65343[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65343 -> 23437[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 22361[label="FiniteMap.splitGT2 (Neg zzz119600) zzz11961 zzz11962 zzz11963 zzz11964 (Pos Zero) (primCmpInt (Pos Zero) (Neg zzz119600) == GT)",fontsize=16,color="burlywood",shape="box"];65344[label="zzz119600/Succ zzz1196000",fontsize=10,color="white",style="solid",shape="box"];22361 -> 65344[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65344 -> 23438[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65345[label="zzz119600/Zero",fontsize=10,color="white",style="solid",shape="box"];22361 -> 65345[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65345 -> 23439[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 22362[label="FiniteMap.splitLT1 (Neg (Succ zzz621000)) zzz6211 zzz6212 zzz6213 zzz6214 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ zzz621000)) == GT)",fontsize=16,color="black",shape="box"];22362 -> 23440[label="",style="solid", color="black", weight=3]; 130.29/78.18 62780[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat (Succ zzz634900) zzz634300 == LT)",fontsize=16,color="burlywood",shape="box"];65346[label="zzz634300/Succ zzz6343000",fontsize=10,color="white",style="solid",shape="box"];62780 -> 65346[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65346 -> 62788[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65347[label="zzz634300/Zero",fontsize=10,color="white",style="solid",shape="box"];62780 -> 65347[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65347 -> 62789[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 62781[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat Zero zzz634300 == LT)",fontsize=16,color="burlywood",shape="box"];65348[label="zzz634300/Succ zzz6343000",fontsize=10,color="white",style="solid",shape="box"];62781 -> 65348[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65348 -> 62790[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65349[label="zzz634300/Zero",fontsize=10,color="white",style="solid",shape="box"];62781 -> 65349[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65349 -> 62791[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 62782[label="FiniteMap.glueVBal3GlueVBal0 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 True",fontsize=16,color="black",shape="box"];62782 -> 62792[label="",style="solid", color="black", weight=3]; 130.29/78.18 63149[label="zzz47460",fontsize=16,color="green",shape="box"];63150[label="FiniteMap.glueVBal zzz47464 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034)",fontsize=16,color="burlywood",shape="box"];65350[label="zzz47464/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];63150 -> 65350[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65350 -> 63404[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65351[label="zzz47464/FiniteMap.Branch zzz474640 zzz474641 zzz474642 zzz474643 zzz474644",fontsize=10,color="white",style="solid",shape="box"];63150 -> 65351[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65351 -> 63405[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 63151[label="zzz47463",fontsize=16,color="green",shape="box"];63152[label="zzz47461",fontsize=16,color="green",shape="box"];62784[label="zzz634300",fontsize=16,color="green",shape="box"];62785[label="zzz63500",fontsize=16,color="green",shape="box"];55775[label="zzz59000",fontsize=16,color="green",shape="box"];55776[label="zzz58960",fontsize=16,color="green",shape="box"];43438[label="primMinusNat (Succ zzz482800) zzz4770",fontsize=16,color="burlywood",shape="box"];65352[label="zzz4770/Succ zzz47700",fontsize=10,color="white",style="solid",shape="box"];43438 -> 65352[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65352 -> 43682[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65353[label="zzz4770/Zero",fontsize=10,color="white",style="solid",shape="box"];43438 -> 65353[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65353 -> 43683[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 43439[label="primMinusNat Zero zzz4770",fontsize=16,color="burlywood",shape="box"];65354[label="zzz4770/Succ zzz47700",fontsize=10,color="white",style="solid",shape="box"];43439 -> 65354[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65354 -> 43684[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65355[label="zzz4770/Zero",fontsize=10,color="white",style="solid",shape="box"];43439 -> 65355[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65355 -> 43685[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 55793[label="zzz59010",fontsize=16,color="green",shape="box"];55794[label="zzz58960",fontsize=16,color="green",shape="box"];64232[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 False",fontsize=16,color="black",shape="triangle"];64232 -> 64244[label="",style="solid", color="black", weight=3]; 130.29/78.18 64233 -> 64232[label="",style="dashed", color="red", weight=0]; 130.29/78.18 64233[label="FiniteMap.mkBalBranch6MkBalBranch5 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 False",fontsize=16,color="magenta"];60765[label="FiniteMap.mkBranchUnbox zzz6234 zzz6235 zzz6232 (Pos (Succ Zero) + FiniteMap.mkBranchLeft_size zzz6234 zzz6235 zzz6232 + FiniteMap.mkBranchRight_size zzz6234 zzz6235 zzz6232)",fontsize=16,color="black",shape="box"];60765 -> 60768[label="",style="solid", color="black", weight=3]; 130.29/78.18 22413[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (Succ (Succ (primPlusNat zzz33200 zzz33200))) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];22413 -> 23501[label="",style="solid", color="black", weight=3]; 130.29/78.18 22414[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ zzz426200)) zzz4263 zzz4264 True",fontsize=16,color="black",shape="box"];22414 -> 23502[label="",style="solid", color="black", weight=3]; 130.29/78.18 22415[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 < FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264)",fontsize=16,color="black",shape="box"];22415 -> 23503[label="",style="solid", color="black", weight=3]; 130.29/78.18 22416[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 < FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264)",fontsize=16,color="black",shape="box"];22416 -> 23504[label="",style="solid", color="black", weight=3]; 130.29/78.18 22417[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 < FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264)",fontsize=16,color="black",shape="box"];22417 -> 23505[label="",style="solid", color="black", weight=3]; 130.29/78.18 22418[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (Succ (Succ (primPlusNat zzz33200 zzz33200))) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];22418 -> 23506[label="",style="solid", color="black", weight=3]; 130.29/78.18 22419 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.18 22419[label="FiniteMap.mkBalBranch zzz4260 zzz4261 (FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334) zzz4263) zzz4264",fontsize=16,color="magenta"];22419 -> 63157[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 22419 -> 63158[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 22419 -> 63159[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 22419 -> 63160[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 22420[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 < FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264)",fontsize=16,color="black",shape="box"];22420 -> 23511[label="",style="solid", color="black", weight=3]; 130.29/78.18 22421[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 False",fontsize=16,color="black",shape="box"];22421 -> 23512[label="",style="solid", color="black", weight=3]; 130.29/78.18 22422[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 < FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264)",fontsize=16,color="black",shape="box"];22422 -> 23513[label="",style="solid", color="black", weight=3]; 130.29/78.18 40434[label="FiniteMap.splitGT0 (Neg (Succ zzz4495)) zzz4496 zzz4497 zzz4498 zzz4499 (Neg (Succ zzz4500)) otherwise",fontsize=16,color="black",shape="box"];40434 -> 40561[label="",style="solid", color="black", weight=3]; 130.29/78.18 40435 -> 6244[label="",style="dashed", color="red", weight=0]; 130.29/78.18 40435[label="FiniteMap.mkVBalBranch (Neg (Succ zzz4495)) zzz4496 (FiniteMap.splitGT zzz4498 (Neg (Succ zzz4500))) zzz4499",fontsize=16,color="magenta"];40435 -> 40562[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40435 -> 40563[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40435 -> 40564[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40435 -> 40565[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40559 -> 6244[label="",style="dashed", color="red", weight=0]; 130.29/78.18 40559[label="FiniteMap.mkVBalBranch (Neg (Succ zzz4504)) zzz4505 zzz4507 (FiniteMap.splitLT zzz4508 (Neg (Succ zzz4509)))",fontsize=16,color="magenta"];40559 -> 40635[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40559 -> 40636[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40559 -> 40637[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40559 -> 40638[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40560[label="FiniteMap.splitLT0 (Neg (Succ zzz4504)) zzz4505 zzz4506 zzz4507 zzz4508 (Neg (Succ zzz4509)) otherwise",fontsize=16,color="black",shape="box"];40560 -> 40639[label="",style="solid", color="black", weight=3]; 130.29/78.18 40896 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.18 40896[label="FiniteMap.mkBalBranch (Neg (Succ zzz4538)) zzz4539 zzz4541 (FiniteMap.addToFM_C FiniteMap.addToFM0 zzz4542 (Neg (Succ zzz4543)) zzz4544)",fontsize=16,color="magenta"];40896 -> 63161[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40896 -> 63162[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40896 -> 63163[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40896 -> 63164[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40897[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Neg (Succ zzz4538)) zzz4539 zzz4540 zzz4541 zzz4542 (Neg (Succ zzz4543)) zzz4544 otherwise",fontsize=16,color="black",shape="box"];40897 -> 40914[label="",style="solid", color="black", weight=3]; 130.29/78.18 22718[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ zzz34200)) zzz343 zzz344 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200)) zzz34200 == LT)",fontsize=16,color="burlywood",shape="box"];65356[label="zzz34200/Succ zzz342000",fontsize=10,color="white",style="solid",shape="box"];22718 -> 65356[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65356 -> 23991[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65357[label="zzz34200/Zero",fontsize=10,color="white",style="solid",shape="box"];22718 -> 65357[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65357 -> 23992[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 22719[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (GT == LT)",fontsize=16,color="black",shape="box"];22719 -> 23993[label="",style="solid", color="black", weight=3]; 130.29/78.18 22720[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344)",fontsize=16,color="black",shape="box"];22720 -> 23994[label="",style="solid", color="black", weight=3]; 130.29/78.18 22721[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534)) == LT)",fontsize=16,color="black",shape="box"];22721 -> 23995[label="",style="solid", color="black", weight=3]; 130.29/78.18 44079[label="zzz34200",fontsize=16,color="green",shape="box"];43358[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz4739)",fontsize=16,color="black",shape="triangle"];43358 -> 43370[label="",style="solid", color="black", weight=3]; 130.29/78.18 44080[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg (Succ zzz49460)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];44080 -> 44326[label="",style="solid", color="black", weight=3]; 130.29/78.18 44081[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];44081 -> 44327[label="",style="solid", color="black", weight=3]; 130.29/78.18 22723[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534)) == LT)",fontsize=16,color="black",shape="box"];22723 -> 23997[label="",style="solid", color="black", weight=3]; 130.29/78.18 22724 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.18 22724[label="FiniteMap.mkBalBranch zzz340 zzz341 (FiniteMap.mkVBalBranch (Neg Zero) zzz31 (FiniteMap.Branch zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534) zzz343) zzz344",fontsize=16,color="magenta"];22724 -> 63165[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 22724 -> 63166[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 22724 -> 63167[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 22724 -> 63168[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 22725[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpNat zzz34200 (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200)) == LT)",fontsize=16,color="burlywood",shape="box"];65358[label="zzz34200/Succ zzz342000",fontsize=10,color="white",style="solid",shape="box"];22725 -> 65358[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65358 -> 24002[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65359[label="zzz34200/Zero",fontsize=10,color="white",style="solid",shape="box"];22725 -> 65359[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65359 -> 24003[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 22726[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];22726 -> 24004[label="",style="solid", color="black", weight=3]; 130.29/78.18 22727[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534)) == LT)",fontsize=16,color="black",shape="box"];22727 -> 24005[label="",style="solid", color="black", weight=3]; 130.29/78.18 44104[label="zzz340",fontsize=16,color="green",shape="box"];44105[label="Zero",fontsize=16,color="green",shape="box"];44106[label="zzz3534",fontsize=16,color="green",shape="box"];44107[label="zzz343",fontsize=16,color="green",shape="box"];44108[label="zzz34200",fontsize=16,color="green",shape="box"];44109[label="zzz3530",fontsize=16,color="green",shape="box"];44110[label="zzz341",fontsize=16,color="green",shape="box"];44111[label="zzz3533",fontsize=16,color="green",shape="box"];44112 -> 43358[label="",style="dashed", color="red", weight=0]; 130.29/78.18 44112[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz34200)",fontsize=16,color="magenta"];44112 -> 44328[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 44113[label="zzz3531",fontsize=16,color="green",shape="box"];44114[label="zzz344",fontsize=16,color="green",shape="box"];44103[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg zzz4951) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="burlywood",shape="triangle"];65360[label="zzz4951/Succ zzz49510",fontsize=10,color="white",style="solid",shape="box"];44103 -> 65360[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65360 -> 44329[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65361[label="zzz4951/Zero",fontsize=10,color="white",style="solid",shape="box"];44103 -> 65361[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65361 -> 44330[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 22729[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534)) == LT)",fontsize=16,color="black",shape="box"];22729 -> 24007[label="",style="solid", color="black", weight=3]; 130.29/78.18 39821[label="FiniteMap.splitGT0 (Pos (Succ zzz4428)) zzz4429 zzz4430 zzz4431 zzz4432 (Pos (Succ zzz4433)) True",fontsize=16,color="black",shape="box"];39821 -> 39871[label="",style="solid", color="black", weight=3]; 130.29/78.18 39822 -> 19598[label="",style="dashed", color="red", weight=0]; 130.29/78.18 39822[label="FiniteMap.splitGT zzz4431 (Pos (Succ zzz4433))",fontsize=16,color="magenta"];39822 -> 39872[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 39822 -> 39873[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 39823[label="Succ zzz4428",fontsize=16,color="green",shape="box"];39824[label="zzz4432",fontsize=16,color="green",shape="box"];39825[label="zzz4429",fontsize=16,color="green",shape="box"];20887[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz332) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 zzz332 zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="burlywood",shape="box"];65362[label="zzz332/Pos zzz3320",fontsize=10,color="white",style="solid",shape="box"];20887 -> 65362[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65362 -> 21481[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65363[label="zzz332/Neg zzz3320",fontsize=10,color="white",style="solid",shape="box"];20887 -> 65363[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65363 -> 21482[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 63401[label="Succ zzz4308",fontsize=16,color="green",shape="box"];63402[label="zzz4307",fontsize=16,color="green",shape="box"];63403[label="zzz4309",fontsize=16,color="green",shape="box"];38983[label="FiniteMap.Branch (Pos (Succ zzz4308)) (FiniteMap.addToFM0 zzz4304 zzz4309) zzz4305 zzz4306 zzz4307",fontsize=16,color="green",shape="box"];38983 -> 39009[label="",style="dashed", color="green", weight=3]; 130.29/78.18 23419[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200)) (Succ zzz342000) == LT)",fontsize=16,color="black",shape="box"];23419 -> 24472[label="",style="solid", color="black", weight=3]; 130.29/78.18 23420[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200)) Zero == LT)",fontsize=16,color="black",shape="box"];23420 -> 24473[label="",style="solid", color="black", weight=3]; 130.29/78.18 23421[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];23421 -> 24474[label="",style="solid", color="black", weight=3]; 130.29/78.18 23422[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];23422 -> 24475[label="",style="solid", color="black", weight=3]; 130.29/78.18 23423[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];23423 -> 24476[label="",style="solid", color="black", weight=3]; 130.29/78.18 23424[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ (Succ Zero)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];23424 -> 24477[label="",style="solid", color="black", weight=3]; 130.29/78.18 23425[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];23425 -> 24478[label="",style="solid", color="black", weight=3]; 130.29/78.18 63153[label="zzz340",fontsize=16,color="green",shape="box"];63154[label="zzz344",fontsize=16,color="green",shape="box"];63155 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.18 63155[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504) zzz343",fontsize=16,color="magenta"];63155 -> 63406[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63155 -> 63407[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63156[label="zzz341",fontsize=16,color="green",shape="box"];23430[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ zzz342000))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ zzz342000))) zzz343 zzz344 (primCmpNat (Succ zzz342000) (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200)) == LT)",fontsize=16,color="black",shape="box"];23430 -> 24481[label="",style="solid", color="black", weight=3]; 130.29/78.18 23431[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ Zero)) zzz343 zzz344 (primCmpNat Zero (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200)) == LT)",fontsize=16,color="black",shape="box"];23431 -> 24482[label="",style="solid", color="black", weight=3]; 130.29/78.18 23432[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];23432 -> 24483[label="",style="solid", color="black", weight=3]; 130.29/78.18 23433[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];23433 -> 24484[label="",style="solid", color="black", weight=3]; 130.29/78.18 23434[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primMulNat (Succ (Succ (Succ Zero))) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];23434 -> 24485[label="",style="solid", color="black", weight=3]; 130.29/78.18 23435[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];23435 -> 24486[label="",style="solid", color="black", weight=3]; 130.29/78.18 23436[label="FiniteMap.splitGT2 (Pos (Succ zzz1196000)) zzz11961 zzz11962 zzz11963 zzz11964 (Pos Zero) (primCmpInt (Pos Zero) (Pos (Succ zzz1196000)) == GT)",fontsize=16,color="black",shape="box"];23436 -> 24487[label="",style="solid", color="black", weight=3]; 130.29/78.18 23437[label="FiniteMap.splitGT2 (Pos Zero) zzz11961 zzz11962 zzz11963 zzz11964 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];23437 -> 24488[label="",style="solid", color="black", weight=3]; 130.29/78.18 23438[label="FiniteMap.splitGT2 (Neg (Succ zzz1196000)) zzz11961 zzz11962 zzz11963 zzz11964 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ zzz1196000)) == GT)",fontsize=16,color="black",shape="box"];23438 -> 24489[label="",style="solid", color="black", weight=3]; 130.29/78.18 23439[label="FiniteMap.splitGT2 (Neg Zero) zzz11961 zzz11962 zzz11963 zzz11964 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];23439 -> 24490[label="",style="solid", color="black", weight=3]; 130.29/78.18 23440[label="FiniteMap.splitLT1 (Neg (Succ zzz621000)) zzz6211 zzz6212 zzz6213 zzz6214 (Pos Zero) (GT == GT)",fontsize=16,color="black",shape="box"];23440 -> 24491[label="",style="solid", color="black", weight=3]; 130.29/78.18 62788[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat (Succ zzz634900) (Succ zzz6343000) == LT)",fontsize=16,color="black",shape="box"];62788 -> 62795[label="",style="solid", color="black", weight=3]; 130.29/78.18 62789[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat (Succ zzz634900) Zero == LT)",fontsize=16,color="black",shape="box"];62789 -> 62796[label="",style="solid", color="black", weight=3]; 130.29/78.18 62790[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat Zero (Succ zzz6343000) == LT)",fontsize=16,color="black",shape="box"];62790 -> 62797[label="",style="solid", color="black", weight=3]; 130.29/78.18 62791[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];62791 -> 62798[label="",style="solid", color="black", weight=3]; 130.29/78.18 62792[label="FiniteMap.glueBal (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034)",fontsize=16,color="black",shape="box"];62792 -> 62799[label="",style="solid", color="black", weight=3]; 130.29/78.18 63404[label="FiniteMap.glueVBal FiniteMap.EmptyFM (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034)",fontsize=16,color="black",shape="box"];63404 -> 63576[label="",style="solid", color="black", weight=3]; 130.29/78.18 63405[label="FiniteMap.glueVBal (FiniteMap.Branch zzz474640 zzz474641 zzz474642 zzz474643 zzz474644) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034)",fontsize=16,color="black",shape="box"];63405 -> 63577[label="",style="solid", color="black", weight=3]; 130.29/78.18 43682[label="primMinusNat (Succ zzz482800) (Succ zzz47700)",fontsize=16,color="black",shape="box"];43682 -> 45368[label="",style="solid", color="black", weight=3]; 130.29/78.18 43683[label="primMinusNat (Succ zzz482800) Zero",fontsize=16,color="black",shape="box"];43683 -> 45369[label="",style="solid", color="black", weight=3]; 130.29/78.18 43684[label="primMinusNat Zero (Succ zzz47700)",fontsize=16,color="black",shape="box"];43684 -> 45370[label="",style="solid", color="black", weight=3]; 130.29/78.18 43685[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];43685 -> 45371[label="",style="solid", color="black", weight=3]; 130.29/78.18 64244 -> 64253[label="",style="dashed", color="red", weight=0]; 130.29/78.18 64244[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (FiniteMap.mkBalBranch6Size_r zzz474034 zzz474030 zzz474031 zzz6373 > FiniteMap.sIZE_RATIO * FiniteMap.mkBalBranch6Size_l zzz474034 zzz474030 zzz474031 zzz6373)",fontsize=16,color="magenta"];64244 -> 64254[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 60768[label="Pos (Succ Zero) + FiniteMap.mkBranchLeft_size zzz6234 zzz6235 zzz6232 + FiniteMap.mkBranchRight_size zzz6234 zzz6235 zzz6232",fontsize=16,color="black",shape="box"];60768 -> 60777[label="",style="solid", color="black", weight=3]; 130.29/78.18 23501[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Pos (primPlusNat (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200))) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];23501 -> 24607[label="",style="solid", color="black", weight=3]; 130.29/78.18 23502 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.18 23502[label="FiniteMap.mkBalBranch zzz4260 zzz4261 (FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 (FiniteMap.Branch zzz330 zzz331 (Pos Zero) zzz333 zzz334) zzz4263) zzz4264",fontsize=16,color="magenta"];23502 -> 63169[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 23502 -> 63170[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 23502 -> 63171[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 23502 -> 63172[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 23503[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];23503 -> 24612[label="",style="solid", color="black", weight=3]; 130.29/78.18 23504[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];23504 -> 24613[label="",style="solid", color="black", weight=3]; 130.29/78.18 23505[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];23505 -> 24614[label="",style="solid", color="black", weight=3]; 130.29/78.18 23506[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Neg (primPlusNat (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200))) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];23506 -> 24615[label="",style="solid", color="black", weight=3]; 130.29/78.18 63157[label="zzz4260",fontsize=16,color="green",shape="box"];63158[label="zzz4264",fontsize=16,color="green",shape="box"];63159 -> 7670[label="",style="dashed", color="red", weight=0]; 130.29/78.18 63159[label="FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334) zzz4263",fontsize=16,color="magenta"];63159 -> 63408[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63159 -> 63409[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63159 -> 63410[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63160[label="zzz4261",fontsize=16,color="green",shape="box"];23511[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];23511 -> 24619[label="",style="solid", color="black", weight=3]; 130.29/78.18 23512[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 < FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264)",fontsize=16,color="black",shape="box"];23512 -> 24620[label="",style="solid", color="black", weight=3]; 130.29/78.18 23513[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];23513 -> 24621[label="",style="solid", color="black", weight=3]; 130.29/78.18 40561[label="FiniteMap.splitGT0 (Neg (Succ zzz4495)) zzz4496 zzz4497 zzz4498 zzz4499 (Neg (Succ zzz4500)) True",fontsize=16,color="black",shape="box"];40561 -> 40640[label="",style="solid", color="black", weight=3]; 130.29/78.18 40562[label="zzz4495",fontsize=16,color="green",shape="box"];40563[label="zzz4499",fontsize=16,color="green",shape="box"];40564 -> 14393[label="",style="dashed", color="red", weight=0]; 130.29/78.18 40564[label="FiniteMap.splitGT zzz4498 (Neg (Succ zzz4500))",fontsize=16,color="magenta"];40564 -> 40641[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40564 -> 40642[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40565[label="zzz4496",fontsize=16,color="green",shape="box"];40635[label="zzz4504",fontsize=16,color="green",shape="box"];40636 -> 13018[label="",style="dashed", color="red", weight=0]; 130.29/78.18 40636[label="FiniteMap.splitLT zzz4508 (Neg (Succ zzz4509))",fontsize=16,color="magenta"];40636 -> 40712[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40636 -> 40713[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40637[label="zzz4507",fontsize=16,color="green",shape="box"];40638[label="zzz4505",fontsize=16,color="green",shape="box"];40639[label="FiniteMap.splitLT0 (Neg (Succ zzz4504)) zzz4505 zzz4506 zzz4507 zzz4508 (Neg (Succ zzz4509)) True",fontsize=16,color="black",shape="box"];40639 -> 40714[label="",style="solid", color="black", weight=3]; 130.29/78.18 63161[label="Neg (Succ zzz4538)",fontsize=16,color="green",shape="box"];63162 -> 12360[label="",style="dashed", color="red", weight=0]; 130.29/78.18 63162[label="FiniteMap.addToFM_C FiniteMap.addToFM0 zzz4542 (Neg (Succ zzz4543)) zzz4544",fontsize=16,color="magenta"];63162 -> 63411[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63162 -> 63412[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63162 -> 63413[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63163[label="zzz4541",fontsize=16,color="green",shape="box"];63164[label="zzz4539",fontsize=16,color="green",shape="box"];40914[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Neg (Succ zzz4538)) zzz4539 zzz4540 zzz4541 zzz4542 (Neg (Succ zzz4543)) zzz4544 True",fontsize=16,color="black",shape="box"];40914 -> 40945[label="",style="solid", color="black", weight=3]; 130.29/78.18 23991[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200)) (Succ zzz342000) == LT)",fontsize=16,color="black",shape="box"];23991 -> 24568[label="",style="solid", color="black", weight=3]; 130.29/78.18 23992[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200)) Zero == LT)",fontsize=16,color="black",shape="box"];23992 -> 24569[label="",style="solid", color="black", weight=3]; 130.29/78.18 23993[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];23993 -> 24570[label="",style="solid", color="black", weight=3]; 130.29/78.18 23994[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];23994 -> 24571[label="",style="solid", color="black", weight=3]; 130.29/78.18 23995[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];23995 -> 24572[label="",style="solid", color="black", weight=3]; 130.29/78.18 43370 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.18 43370[label="primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz4739)) (Succ zzz4739)",fontsize=16,color="magenta"];43370 -> 43383[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 43370 -> 43384[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 44326[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg (Succ zzz49460)) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Pos Zero) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];44326 -> 44352[label="",style="solid", color="black", weight=3]; 130.29/78.18 44327[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Pos Zero) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];44327 -> 44353[label="",style="solid", color="black", weight=3]; 130.29/78.18 23997[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];23997 -> 24574[label="",style="solid", color="black", weight=3]; 130.29/78.18 63165[label="zzz340",fontsize=16,color="green",shape="box"];63166[label="zzz344",fontsize=16,color="green",shape="box"];63167 -> 7670[label="",style="dashed", color="red", weight=0]; 130.29/78.18 63167[label="FiniteMap.mkVBalBranch (Neg Zero) zzz31 (FiniteMap.Branch zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534) zzz343",fontsize=16,color="magenta"];63167 -> 63414[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63167 -> 63415[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63167 -> 63416[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63167 -> 63417[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63167 -> 63418[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63167 -> 63419[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63167 -> 63420[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63168[label="zzz341",fontsize=16,color="green",shape="box"];24002[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ zzz342000))) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ zzz342000))) zzz343 zzz344 (primCmpNat (Succ zzz342000) (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200)) == LT)",fontsize=16,color="black",shape="box"];24002 -> 24582[label="",style="solid", color="black", weight=3]; 130.29/78.18 24003[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ Zero)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ Zero)) zzz343 zzz344 (primCmpNat Zero (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200)) == LT)",fontsize=16,color="black",shape="box"];24003 -> 24583[label="",style="solid", color="black", weight=3]; 130.29/78.18 24004[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];24004 -> 24584[label="",style="solid", color="black", weight=3]; 130.29/78.18 24005[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];24005 -> 24585[label="",style="solid", color="black", weight=3]; 130.29/78.18 44328[label="zzz34200",fontsize=16,color="green",shape="box"];44329[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg (Succ zzz49510)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];44329 -> 44354[label="",style="solid", color="black", weight=3]; 130.29/78.18 44330[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];44330 -> 44355[label="",style="solid", color="black", weight=3]; 130.29/78.18 24007[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];24007 -> 24587[label="",style="solid", color="black", weight=3]; 130.29/78.18 39871[label="zzz4432",fontsize=16,color="green",shape="box"];39872[label="zzz4431",fontsize=16,color="green",shape="box"];39873[label="zzz4433",fontsize=16,color="green",shape="box"];21481[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos zzz3320) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos zzz3320) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos zzz3320)) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos zzz3320) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];21481 -> 24590[label="",style="solid", color="black", weight=3]; 130.29/78.18 21482[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg zzz3320) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg zzz3320) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg zzz3320)) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg zzz3320) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];21482 -> 24591[label="",style="solid", color="black", weight=3]; 130.29/78.18 39009 -> 13616[label="",style="dashed", color="red", weight=0]; 130.29/78.18 39009[label="FiniteMap.addToFM0 zzz4304 zzz4309",fontsize=16,color="magenta"];39009 -> 39027[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 39009 -> 39028[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24472[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (primCmpNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200) zzz342000 == LT)",fontsize=16,color="burlywood",shape="box"];65364[label="zzz250200/Succ zzz2502000",fontsize=10,color="white",style="solid",shape="box"];24472 -> 65364[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65364 -> 26023[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65365[label="zzz250200/Zero",fontsize=10,color="white",style="solid",shape="box"];24472 -> 65365[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65365 -> 26024[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 24473[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (GT == LT)",fontsize=16,color="black",shape="box"];24473 -> 26025[label="",style="solid", color="black", weight=3]; 130.29/78.18 24474[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344)",fontsize=16,color="black",shape="box"];24474 -> 26026[label="",style="solid", color="black", weight=3]; 130.29/78.18 24475[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];24475 -> 26027[label="",style="solid", color="black", weight=3]; 130.29/78.18 24476[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos 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(Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (EQ == LT)",fontsize=16,color="black",shape="box"];24478 -> 26030[label="",style="solid", color="black", weight=3]; 130.29/78.18 63406[label="FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504",fontsize=16,color="green",shape="box"];63407[label="zzz343",fontsize=16,color="green",shape="box"];24481[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ zzz342000))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ zzz342000))) zzz343 zzz344 (primCmpNat zzz342000 (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200) == LT)",fontsize=16,color="burlywood",shape="box"];65366[label="zzz342000/Succ zzz3420000",fontsize=10,color="white",style="solid",shape="box"];24481 -> 65366[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65366 -> 26031[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65367[label="zzz342000/Zero",fontsize=10,color="white",style="solid",shape="box"];24481 -> 65367[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65367 -> 26032[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 24482[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ Zero)) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];24482 -> 26033[label="",style="solid", color="black", weight=3]; 130.29/78.18 24483 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.18 24483[label="FiniteMap.mkBalBranch zzz340 zzz341 (FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504) zzz343) zzz344",fontsize=16,color="magenta"];24483 -> 63173[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24483 -> 63174[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24483 -> 63175[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24483 -> 63176[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24484[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (EQ == LT)",fontsize=16,color="black",shape="box"];24484 -> 26038[label="",style="solid", color="black", weight=3]; 130.29/78.18 24485[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ (Succ Zero)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];24485 -> 26039[label="",style="solid", color="black", weight=3]; 130.29/78.18 24486[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (EQ == LT)",fontsize=16,color="black",shape="box"];24486 -> 26040[label="",style="solid", color="black", weight=3]; 130.29/78.18 24487 -> 12107[label="",style="dashed", color="red", weight=0]; 130.29/78.18 24487[label="FiniteMap.splitGT2 (Pos (Succ zzz1196000)) zzz11961 zzz11962 zzz11963 zzz11964 (Pos Zero) (primCmpNat Zero (Succ zzz1196000) == GT)",fontsize=16,color="magenta"];24487 -> 26041[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24487 -> 26042[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24487 -> 26043[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24487 -> 26044[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24487 -> 26045[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24488 -> 4943[label="",style="dashed", color="red", weight=0]; 130.29/78.18 24488[label="FiniteMap.splitGT2 (Pos Zero) zzz11961 zzz11962 zzz11963 zzz11964 (Pos Zero) (EQ == GT)",fontsize=16,color="magenta"];24488 -> 26046[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24488 -> 26047[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24488 -> 26048[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24488 -> 26049[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24489 -> 18244[label="",style="dashed", color="red", weight=0]; 130.29/78.18 24489[label="FiniteMap.splitGT2 (Neg (Succ zzz1196000)) zzz11961 zzz11962 zzz11963 zzz11964 (Pos Zero) (GT == GT)",fontsize=16,color="magenta"];24489 -> 26050[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24489 -> 26051[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24489 -> 26052[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24489 -> 26053[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24489 -> 26054[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24490 -> 4948[label="",style="dashed", color="red", weight=0]; 130.29/78.18 24490[label="FiniteMap.splitGT2 (Neg Zero) zzz11961 zzz11962 zzz11963 zzz11964 (Pos Zero) (EQ == GT)",fontsize=16,color="magenta"];24490 -> 26055[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24490 -> 26056[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24490 -> 26057[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24490 -> 26058[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24491[label="FiniteMap.splitLT1 (Neg (Succ zzz621000)) zzz6211 zzz6212 zzz6213 zzz6214 (Pos Zero) True",fontsize=16,color="black",shape="box"];24491 -> 26059[label="",style="solid", color="black", weight=3]; 130.29/78.18 62795 -> 62767[label="",style="dashed", color="red", weight=0]; 130.29/78.18 62795[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (primCmpNat zzz634900 zzz6343000 == LT)",fontsize=16,color="magenta"];62795 -> 62804[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 62795 -> 62805[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 62796 -> 62733[label="",style="dashed", color="red", weight=0]; 130.29/78.18 62796[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (GT == LT)",fontsize=16,color="magenta"];62797 -> 62738[label="",style="dashed", color="red", weight=0]; 130.29/78.18 62797[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (LT == LT)",fontsize=16,color="magenta"];62798 -> 62755[label="",style="dashed", color="red", weight=0]; 130.29/78.18 62798[label="FiniteMap.glueVBal3GlueVBal1 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz47460 zzz47461 zzz47462 zzz47463 zzz47464 zzz474030 zzz474031 zzz474032 zzz474033 zzz474034 (EQ == LT)",fontsize=16,color="magenta"];62799[label="FiniteMap.glueBal2 (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034)",fontsize=16,color="black",shape="box"];62799 -> 62806[label="",style="solid", color="black", weight=3]; 130.29/78.18 63576[label="FiniteMap.glueVBal5 FiniteMap.EmptyFM (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034)",fontsize=16,color="black",shape="box"];63576 -> 63597[label="",style="solid", color="black", weight=3]; 130.29/78.18 63577 -> 63574[label="",style="dashed", color="red", weight=0]; 130.29/78.18 63577[label="FiniteMap.glueVBal3 (FiniteMap.Branch zzz474640 zzz474641 zzz474642 zzz474643 zzz474644) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034)",fontsize=16,color="magenta"];63577 -> 63598[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63577 -> 63599[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63577 -> 63600[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63577 -> 63601[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63577 -> 63602[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63577 -> 63603[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63577 -> 63604[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63577 -> 63605[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63577 -> 63606[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63577 -> 63607[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 45368 -> 43410[label="",style="dashed", color="red", weight=0]; 130.29/78.18 45368[label="primMinusNat zzz482800 zzz47700",fontsize=16,color="magenta"];45368 -> 46507[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 45368 -> 46508[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 45369[label="Pos (Succ zzz482800)",fontsize=16,color="green",shape="box"];45370[label="Neg (Succ zzz47700)",fontsize=16,color="green",shape="box"];45371[label="Pos Zero",fontsize=16,color="green",shape="box"];64254 -> 63793[label="",style="dashed", color="red", weight=0]; 130.29/78.18 64254[label="FiniteMap.mkBalBranch6Size_l zzz474034 zzz474030 zzz474031 zzz6373",fontsize=16,color="magenta"];64253[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (FiniteMap.mkBalBranch6Size_r zzz474034 zzz474030 zzz474031 zzz6373 > FiniteMap.sIZE_RATIO * zzz6442)",fontsize=16,color="black",shape="triangle"];64253 -> 64255[label="",style="solid", color="black", weight=3]; 130.29/78.18 60777 -> 60818[label="",style="dashed", color="red", weight=0]; 130.29/78.18 60777[label="primPlusInt (Pos (Succ Zero) + FiniteMap.mkBranchLeft_size zzz6234 zzz6235 zzz6232) (FiniteMap.mkBranchRight_size zzz6234 zzz6235 zzz6232)",fontsize=16,color="magenta"];60777 -> 60819[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24607[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Pos (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200))) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];24607 -> 26100[label="",style="solid", color="black", weight=3]; 130.29/78.18 63169[label="zzz4260",fontsize=16,color="green",shape="box"];63170[label="zzz4264",fontsize=16,color="green",shape="box"];63171 -> 7670[label="",style="dashed", color="red", weight=0]; 130.29/78.18 63171[label="FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 (FiniteMap.Branch zzz330 zzz331 (Pos Zero) zzz333 zzz334) zzz4263",fontsize=16,color="magenta"];63171 -> 63421[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63171 -> 63422[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63171 -> 63423[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63172[label="zzz4261",fontsize=16,color="green",shape="box"];24612[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];24612 -> 26104[label="",style="solid", color="black", weight=3]; 130.29/78.18 24613[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];24613 -> 26105[label="",style="solid", color="black", weight=3]; 130.29/78.18 24614[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];24614 -> 26106[label="",style="solid", color="black", weight=3]; 130.29/78.18 24615[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Neg (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200))) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];24615 -> 26107[label="",style="solid", color="black", weight=3]; 130.29/78.18 63408[label="Neg Zero",fontsize=16,color="green",shape="box"];63409[label="Succ zzz3000",fontsize=16,color="green",shape="box"];63410[label="zzz4263",fontsize=16,color="green",shape="box"];24619[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];24619 -> 26108[label="",style="solid", color="black", weight=3]; 130.29/78.18 24620[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];24620 -> 26109[label="",style="solid", color="black", weight=3]; 130.29/78.18 24621[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];24621 -> 26110[label="",style="solid", color="black", weight=3]; 130.29/78.18 40640[label="zzz4499",fontsize=16,color="green",shape="box"];40641[label="zzz4498",fontsize=16,color="green",shape="box"];40642[label="zzz4500",fontsize=16,color="green",shape="box"];40712[label="zzz4508",fontsize=16,color="green",shape="box"];40713[label="zzz4509",fontsize=16,color="green",shape="box"];40714[label="zzz4507",fontsize=16,color="green",shape="box"];63411[label="zzz4542",fontsize=16,color="green",shape="box"];63412[label="Succ zzz4543",fontsize=16,color="green",shape="box"];63413[label="zzz4544",fontsize=16,color="green",shape="box"];40945[label="FiniteMap.Branch (Neg (Succ zzz4543)) (FiniteMap.addToFM0 zzz4539 zzz4544) zzz4540 zzz4541 zzz4542",fontsize=16,color="green",shape="box"];40945 -> 40953[label="",style="dashed", color="green", weight=3]; 130.29/78.18 24568[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (primCmpNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200) zzz342000 == LT)",fontsize=16,color="burlywood",shape="box"];65368[label="zzz353200/Succ zzz3532000",fontsize=10,color="white",style="solid",shape="box"];24568 -> 65368[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65368 -> 26428[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65369[label="zzz353200/Zero",fontsize=10,color="white",style="solid",shape="box"];24568 -> 65369[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65369 -> 26429[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 24569[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (GT == LT)",fontsize=16,color="black",shape="box"];24569 -> 26430[label="",style="solid", color="black", weight=3]; 130.29/78.18 24570[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344)",fontsize=16,color="black",shape="box"];24570 -> 26431[label="",style="solid", color="black", weight=3]; 130.29/78.18 24571[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];24571 -> 26432[label="",style="solid", color="black", weight=3]; 130.29/78.18 24572[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (EQ == LT)",fontsize=16,color="black",shape="box"];24572 -> 26433[label="",style="solid", color="black", weight=3]; 130.29/78.18 43383[label="Succ zzz4739",fontsize=16,color="green",shape="box"];44352[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg (Succ zzz49460)) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];44352 -> 44378[label="",style="solid", color="black", weight=3]; 130.29/78.18 44353[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];44353 -> 44379[label="",style="solid", color="black", weight=3]; 130.29/78.18 24574[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (EQ == LT)",fontsize=16,color="black",shape="box"];24574 -> 26435[label="",style="solid", color="black", weight=3]; 130.29/78.18 63414[label="Neg (Succ zzz353200)",fontsize=16,color="green",shape="box"];63415[label="Zero",fontsize=16,color="green",shape="box"];63416[label="zzz3534",fontsize=16,color="green",shape="box"];63417[label="zzz343",fontsize=16,color="green",shape="box"];63418[label="zzz3530",fontsize=16,color="green",shape="box"];63419[label="zzz3533",fontsize=16,color="green",shape="box"];63420[label="zzz3531",fontsize=16,color="green",shape="box"];24582[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ zzz342000))) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ zzz342000))) zzz343 zzz344 (primCmpNat zzz342000 (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200) == LT)",fontsize=16,color="burlywood",shape="box"];65370[label="zzz342000/Succ zzz3420000",fontsize=10,color="white",style="solid",shape="box"];24582 -> 65370[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65370 -> 26436[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65371[label="zzz342000/Zero",fontsize=10,color="white",style="solid",shape="box"];24582 -> 65371[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65371 -> 26437[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 24583[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ Zero)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ Zero)) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];24583 -> 26438[label="",style="solid", color="black", weight=3]; 130.29/78.18 24584 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.18 24584[label="FiniteMap.mkBalBranch zzz340 zzz341 (FiniteMap.mkVBalBranch (Neg Zero) zzz31 (FiniteMap.Branch zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534) zzz343) zzz344",fontsize=16,color="magenta"];24584 -> 63177[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24584 -> 63178[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24584 -> 63179[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24584 -> 63180[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 24585[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (EQ == LT)",fontsize=16,color="black",shape="box"];24585 -> 26443[label="",style="solid", color="black", weight=3]; 130.29/78.18 44354[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg (Succ zzz49510)) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];44354 -> 44380[label="",style="solid", color="black", weight=3]; 130.29/78.18 44355[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];44355 -> 44381[label="",style="solid", color="black", weight=3]; 130.29/78.18 24587[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (EQ == LT)",fontsize=16,color="black",shape="box"];24587 -> 26445[label="",style="solid", color="black", weight=3]; 130.29/78.18 24590[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos zzz3320) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos zzz3320) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz3320)) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos zzz3320) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="burlywood",shape="box"];65372[label="zzz3320/Succ zzz33200",fontsize=10,color="white",style="solid",shape="box"];24590 -> 65372[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65372 -> 26615[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65373[label="zzz3320/Zero",fontsize=10,color="white",style="solid",shape="box"];24590 -> 65373[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65373 -> 26616[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 24591[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg zzz3320) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg zzz3320) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz3320)) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg zzz3320) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="burlywood",shape="box"];65374[label="zzz3320/Succ zzz33200",fontsize=10,color="white",style="solid",shape="box"];24591 -> 65374[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65374 -> 26617[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65375[label="zzz3320/Zero",fontsize=10,color="white",style="solid",shape="box"];24591 -> 65375[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65375 -> 26618[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 39027[label="zzz4304",fontsize=16,color="green",shape="box"];39028[label="zzz4309",fontsize=16,color="green",shape="box"];26023[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (primCmpNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000)) zzz342000 == LT)",fontsize=16,color="black",shape="box"];26023 -> 26665[label="",style="solid", color="black", weight=3]; 130.29/78.18 26024[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (primCmpNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) Zero) zzz342000 == LT)",fontsize=16,color="black",shape="box"];26024 -> 26666[label="",style="solid", color="black", weight=3]; 130.29/78.18 26025[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];26025 -> 26667[label="",style="solid", color="black", weight=3]; 130.29/78.18 26026[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];26026 -> 26668[label="",style="solid", color="black", weight=3]; 130.29/78.18 26027[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];26027 -> 26669[label="",style="solid", color="black", weight=3]; 130.29/78.18 26028[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];26028 -> 26670[label="",style="solid", color="black", weight=3]; 130.29/78.18 26029[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat Zero (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];26029 -> 26671[label="",style="solid", color="black", weight=3]; 130.29/78.18 26030[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];26030 -> 26672[label="",style="solid", color="black", weight=3]; 130.29/78.18 26031[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (primCmpNat (Succ zzz3420000) (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200) == LT)",fontsize=16,color="burlywood",shape="box"];65376[label="zzz250200/Succ zzz2502000",fontsize=10,color="white",style="solid",shape="box"];26031 -> 65376[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65376 -> 26673[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65377[label="zzz250200/Zero",fontsize=10,color="white",style="solid",shape="box"];26031 -> 65377[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65377 -> 26674[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 26032[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (primCmpNat Zero (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz250200 zzz250200)) zzz250200)) zzz250200)) zzz250200) == LT)",fontsize=16,color="burlywood",shape="box"];65378[label="zzz250200/Succ zzz2502000",fontsize=10,color="white",style="solid",shape="box"];26032 -> 65378[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65378 -> 26675[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65379[label="zzz250200/Zero",fontsize=10,color="white",style="solid",shape="box"];26032 -> 65379[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65379 -> 26676[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 26033[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ Zero)) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];26033 -> 26677[label="",style="solid", color="black", weight=3]; 130.29/78.18 63173[label="zzz340",fontsize=16,color="green",shape="box"];63174[label="zzz344",fontsize=16,color="green",shape="box"];63175 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.18 63175[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504) zzz343",fontsize=16,color="magenta"];63175 -> 63424[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63175 -> 63425[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63176[label="zzz341",fontsize=16,color="green",shape="box"];26038[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];26038 -> 26680[label="",style="solid", color="black", weight=3]; 130.29/78.18 26039[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ Zero) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];26039 -> 26681[label="",style="solid", color="black", weight=3]; 130.29/78.18 26040[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];26040 -> 26682[label="",style="solid", color="black", weight=3]; 130.29/78.18 26041[label="zzz11961",fontsize=16,color="green",shape="box"];26042[label="zzz11964",fontsize=16,color="green",shape="box"];26043[label="zzz11962",fontsize=16,color="green",shape="box"];26044[label="zzz1196000",fontsize=16,color="green",shape="box"];26045[label="zzz11963",fontsize=16,color="green",shape="box"];26046[label="zzz11962",fontsize=16,color="green",shape="box"];26047[label="zzz11964",fontsize=16,color="green",shape="box"];26048[label="zzz11963",fontsize=16,color="green",shape="box"];26049[label="zzz11961",fontsize=16,color="green",shape="box"];26050[label="zzz11962",fontsize=16,color="green",shape="box"];26051[label="zzz11963",fontsize=16,color="green",shape="box"];26052[label="zzz1196000",fontsize=16,color="green",shape="box"];26053[label="zzz11964",fontsize=16,color="green",shape="box"];26054[label="zzz11961",fontsize=16,color="green",shape="box"];26055[label="zzz11962",fontsize=16,color="green",shape="box"];26056[label="zzz11964",fontsize=16,color="green",shape="box"];26057[label="zzz11963",fontsize=16,color="green",shape="box"];26058[label="zzz11961",fontsize=16,color="green",shape="box"];26059 -> 6244[label="",style="dashed", color="red", weight=0]; 130.29/78.18 26059[label="FiniteMap.mkVBalBranch (Neg (Succ zzz621000)) zzz6211 zzz6213 (FiniteMap.splitLT zzz6214 (Pos Zero))",fontsize=16,color="magenta"];26059 -> 26683[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 26059 -> 26684[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 26059 -> 26685[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 26059 -> 26686[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 62804[label="zzz634900",fontsize=16,color="green",shape="box"];62805[label="zzz6343000",fontsize=16,color="green",shape="box"];62806 -> 62818[label="",style="dashed", color="red", weight=0]; 130.29/78.18 62806[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.sizeFM (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) > FiniteMap.sizeFM (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464))",fontsize=16,color="magenta"];62806 -> 62819[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 62806 -> 62820[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63597[label="FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034",fontsize=16,color="green",shape="box"];63598[label="zzz474030",fontsize=16,color="green",shape="box"];63599[label="zzz474033",fontsize=16,color="green",shape="box"];63600[label="zzz474031",fontsize=16,color="green",shape="box"];63601[label="zzz474032",fontsize=16,color="green",shape="box"];63602[label="zzz474640",fontsize=16,color="green",shape="box"];63603[label="zzz474642",fontsize=16,color="green",shape="box"];63604[label="zzz474643",fontsize=16,color="green",shape="box"];63605[label="zzz474644",fontsize=16,color="green",shape="box"];63606[label="zzz474034",fontsize=16,color="green",shape="box"];63607[label="zzz474641",fontsize=16,color="green",shape="box"];46507[label="zzz482800",fontsize=16,color="green",shape="box"];46508[label="zzz47700",fontsize=16,color="green",shape="box"];64255[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (compare (FiniteMap.mkBalBranch6Size_r zzz474034 zzz474030 zzz474031 zzz6373) (FiniteMap.sIZE_RATIO * zzz6442) == GT)",fontsize=16,color="black",shape="box"];64255 -> 64262[label="",style="solid", color="black", weight=3]; 130.29/78.18 60819[label="Pos (Succ Zero) + FiniteMap.mkBranchLeft_size zzz6234 zzz6235 zzz6232",fontsize=16,color="black",shape="box"];60819 -> 60821[label="",style="solid", color="black", weight=3]; 130.29/78.18 60818[label="primPlusInt zzz6242 (FiniteMap.mkBranchRight_size zzz6234 zzz6235 zzz6232)",fontsize=16,color="burlywood",shape="triangle"];65380[label="zzz6242/Pos zzz62420",fontsize=10,color="white",style="solid",shape="box"];60818 -> 65380[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65380 -> 60822[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65381[label="zzz6242/Neg zzz62420",fontsize=10,color="white",style="solid",shape="box"];60818 -> 65381[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65381 -> 60823[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 26100[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];26100 -> 26724[label="",style="solid", color="black", weight=3]; 130.29/78.18 63421[label="Pos Zero",fontsize=16,color="green",shape="box"];63422[label="Succ zzz3000",fontsize=16,color="green",shape="box"];63423[label="zzz4263",fontsize=16,color="green",shape="box"];26104[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];26104 -> 26725[label="",style="solid", color="black", weight=3]; 130.29/78.18 26105[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];26105 -> 26726[label="",style="solid", color="black", weight=3]; 130.29/78.18 26106[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];26106 -> 26727[label="",style="solid", color="black", weight=3]; 130.29/78.18 26107[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];26107 -> 26728[label="",style="solid", color="black", weight=3]; 130.29/78.18 26108[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];26108 -> 26729[label="",style="solid", color="black", weight=3]; 130.29/78.18 26109[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];26109 -> 26730[label="",style="solid", color="black", weight=3]; 130.29/78.18 26110[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];26110 -> 26731[label="",style="solid", color="black", weight=3]; 130.29/78.18 40953 -> 13616[label="",style="dashed", color="red", weight=0]; 130.29/78.18 40953[label="FiniteMap.addToFM0 zzz4539 zzz4544",fontsize=16,color="magenta"];40953 -> 40974[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 40953 -> 40975[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 26428[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ (Succ zzz3532000))) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ (Succ zzz3532000))) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (primCmpNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000))) (Succ zzz3532000))) (Succ zzz3532000)) zzz342000 == LT)",fontsize=16,color="black",shape="box"];26428 -> 27429[label="",style="solid", color="black", weight=3]; 130.29/78.18 26429[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ Zero)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ Zero)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (primCmpNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) Zero) zzz342000 == LT)",fontsize=16,color="black",shape="box"];26429 -> 27430[label="",style="solid", color="black", weight=3]; 130.29/78.18 26430[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];26430 -> 27431[label="",style="solid", color="black", weight=3]; 130.29/78.18 26431[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];26431 -> 27432[label="",style="solid", color="black", weight=3]; 130.29/78.18 26432[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];26432 -> 27433[label="",style="solid", color="black", weight=3]; 130.29/78.18 26433[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];26433 -> 27434[label="",style="solid", color="black", weight=3]; 130.29/78.18 44378[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (LT == LT)",fontsize=16,color="black",shape="box"];44378 -> 44413[label="",style="solid", color="black", weight=3]; 130.29/78.18 44379[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (EQ == LT)",fontsize=16,color="black",shape="box"];44379 -> 44414[label="",style="solid", color="black", weight=3]; 130.29/78.18 26435[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];26435 -> 27436[label="",style="solid", color="black", weight=3]; 130.29/78.18 26436[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (primCmpNat (Succ zzz3420000) (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200) == LT)",fontsize=16,color="burlywood",shape="box"];65382[label="zzz353200/Succ zzz3532000",fontsize=10,color="white",style="solid",shape="box"];26436 -> 65382[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65382 -> 27437[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65383[label="zzz353200/Zero",fontsize=10,color="white",style="solid",shape="box"];26436 -> 65383[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65383 -> 27438[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 26437[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (primCmpNat Zero (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz353200 zzz353200)) zzz353200)) zzz353200)) zzz353200) == LT)",fontsize=16,color="burlywood",shape="box"];65384[label="zzz353200/Succ zzz3532000",fontsize=10,color="white",style="solid",shape="box"];26437 -> 65384[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65384 -> 27439[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65385[label="zzz353200/Zero",fontsize=10,color="white",style="solid",shape="box"];26437 -> 65385[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65385 -> 27440[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 26438[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ Zero)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ Zero)) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];26438 -> 27441[label="",style="solid", color="black", weight=3]; 130.29/78.18 63177[label="zzz340",fontsize=16,color="green",shape="box"];63178[label="zzz344",fontsize=16,color="green",shape="box"];63179 -> 7670[label="",style="dashed", color="red", weight=0]; 130.29/78.18 63179[label="FiniteMap.mkVBalBranch (Neg Zero) zzz31 (FiniteMap.Branch zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534) zzz343",fontsize=16,color="magenta"];63179 -> 63426[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63179 -> 63427[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63179 -> 63428[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63179 -> 63429[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63179 -> 63430[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63179 -> 63431[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63179 -> 63432[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63180[label="zzz341",fontsize=16,color="green",shape="box"];26443[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];26443 -> 27449[label="",style="solid", color="black", weight=3]; 130.29/78.18 44380[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg (Succ zzz49510)) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];44380 -> 44415[label="",style="solid", color="black", weight=3]; 130.29/78.18 44381[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];44381 -> 44416[label="",style="solid", color="black", weight=3]; 130.29/78.18 26445[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];26445 -> 27451[label="",style="solid", color="black", weight=3]; 130.29/78.18 26615[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];26615 -> 28192[label="",style="solid", color="black", weight=3]; 130.29/78.18 26616[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];26616 -> 28193[label="",style="solid", color="black", weight=3]; 130.29/78.18 26617[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];26617 -> 28194[label="",style="solid", color="black", weight=3]; 130.29/78.18 26618[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];26618 -> 28195[label="",style="solid", color="black", weight=3]; 130.29/78.18 26665[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (primCmpNat (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000)) zzz2502000))) zzz342000 == LT)",fontsize=16,color="burlywood",shape="box"];65386[label="zzz342000/Succ zzz3420000",fontsize=10,color="white",style="solid",shape="box"];26665 -> 65386[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65386 -> 28246[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65387[label="zzz342000/Zero",fontsize=10,color="white",style="solid",shape="box"];26665 -> 65387[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65387 -> 28247[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 26666[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) zzz342000 == LT)",fontsize=16,color="burlywood",shape="box"];65388[label="zzz342000/Succ zzz3420000",fontsize=10,color="white",style="solid",shape="box"];26666 -> 65388[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65388 -> 28248[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65389[label="zzz342000/Zero",fontsize=10,color="white",style="solid",shape="box"];26666 -> 65389[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65389 -> 28249[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 26667[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344)",fontsize=16,color="black",shape="box"];26667 -> 28250[label="",style="solid", color="black", weight=3]; 130.29/78.18 26668[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];26668 -> 28251[label="",style="solid", color="black", weight=3]; 130.29/78.18 26669[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];26669 -> 28252[label="",style="solid", color="black", weight=3]; 130.29/78.18 26670[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 otherwise",fontsize=16,color="black",shape="box"];26670 -> 28253[label="",style="solid", color="black", weight=3]; 130.29/78.18 26671[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat Zero (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];26671 -> 28254[label="",style="solid", color="black", weight=3]; 130.29/78.18 26672[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 otherwise",fontsize=16,color="black",shape="box"];26672 -> 28255[label="",style="solid", color="black", weight=3]; 130.29/78.18 26673[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (primCmpNat (Succ zzz3420000) (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000)) == LT)",fontsize=16,color="black",shape="box"];26673 -> 28256[label="",style="solid", color="black", weight=3]; 130.29/78.18 26674[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (primCmpNat (Succ zzz3420000) (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) Zero) == LT)",fontsize=16,color="black",shape="box"];26674 -> 28257[label="",style="solid", color="black", weight=3]; 130.29/78.18 26675[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (primCmpNat Zero (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000)) == LT)",fontsize=16,color="black",shape="box"];26675 -> 28258[label="",style="solid", color="black", weight=3]; 130.29/78.18 26676[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (primCmpNat Zero (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) Zero) == LT)",fontsize=16,color="black",shape="box"];26676 -> 28259[label="",style="solid", color="black", weight=3]; 130.29/78.18 26677 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.18 26677[label="FiniteMap.mkBalBranch zzz340 zzz341 (FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504) zzz343) zzz344",fontsize=16,color="magenta"];26677 -> 63181[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 26677 -> 63182[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 26677 -> 63183[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 26677 -> 63184[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63424[label="FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504",fontsize=16,color="green",shape="box"];63425[label="zzz343",fontsize=16,color="green",shape="box"];26680[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 otherwise",fontsize=16,color="black",shape="box"];26680 -> 28264[label="",style="solid", color="black", weight=3]; 130.29/78.18 26681[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat Zero (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];26681 -> 28265[label="",style="solid", color="black", weight=3]; 130.29/78.18 26682[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 otherwise",fontsize=16,color="black",shape="box"];26682 -> 28266[label="",style="solid", color="black", weight=3]; 130.29/78.18 26683[label="zzz621000",fontsize=16,color="green",shape="box"];26684 -> 12322[label="",style="dashed", color="red", weight=0]; 130.29/78.18 26684[label="FiniteMap.splitLT zzz6214 (Pos Zero)",fontsize=16,color="magenta"];26684 -> 28267[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 26685[label="zzz6213",fontsize=16,color="green",shape="box"];26686[label="zzz6211",fontsize=16,color="green",shape="box"];62819 -> 54589[label="",style="dashed", color="red", weight=0]; 130.29/78.18 62819[label="FiniteMap.sizeFM (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464)",fontsize=16,color="magenta"];62819 -> 62834[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 62820 -> 54589[label="",style="dashed", color="red", weight=0]; 130.29/78.18 62820[label="FiniteMap.sizeFM (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034)",fontsize=16,color="magenta"];62820 -> 62835[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 62818[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (zzz6355 > zzz6354)",fontsize=16,color="black",shape="triangle"];62818 -> 62836[label="",style="solid", color="black", weight=3]; 130.29/78.18 64262 -> 64264[label="",style="dashed", color="red", weight=0]; 130.29/78.18 64262[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (FiniteMap.mkBalBranch6Size_r zzz474034 zzz474030 zzz474031 zzz6373) (FiniteMap.sIZE_RATIO * zzz6442) == GT)",fontsize=16,color="magenta"];64262 -> 64265[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 60821 -> 55581[label="",style="dashed", color="red", weight=0]; 130.29/78.18 60821[label="primPlusInt (Pos (Succ Zero)) (FiniteMap.mkBranchLeft_size zzz6234 zzz6235 zzz6232)",fontsize=16,color="magenta"];60821 -> 60826[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 60821 -> 60827[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 60822[label="primPlusInt (Pos zzz62420) (FiniteMap.mkBranchRight_size zzz6234 zzz6235 zzz6232)",fontsize=16,color="black",shape="box"];60822 -> 60828[label="",style="solid", color="black", weight=3]; 130.29/78.18 60823[label="primPlusInt (Neg zzz62420) (FiniteMap.mkBranchRight_size zzz6234 zzz6235 zzz6232)",fontsize=16,color="black",shape="box"];60823 -> 60829[label="",style="solid", color="black", weight=3]; 130.29/78.18 26724[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)))) (FiniteMap.sizeFM (FiniteMap.Branch zzz4260 zzz4261 zzz4262 zzz4263 zzz4264)) == LT)",fontsize=16,color="black",shape="box"];26724 -> 28494[label="",style="solid", color="black", weight=3]; 130.29/78.18 26725[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];26725 -> 28495[label="",style="solid", color="black", weight=3]; 130.29/78.18 26726[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];26726 -> 28496[label="",style="solid", color="black", weight=3]; 130.29/78.18 26727[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];26727 -> 28497[label="",style="solid", color="black", weight=3]; 130.29/78.18 26728[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)))) (FiniteMap.sizeFM (FiniteMap.Branch zzz4260 zzz4261 zzz4262 zzz4263 zzz4264)) == LT)",fontsize=16,color="black",shape="box"];26728 -> 28498[label="",style="solid", color="black", weight=3]; 130.29/78.18 26729[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];26729 -> 28499[label="",style="solid", color="black", weight=3]; 130.29/78.18 26730[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];26730 -> 28500[label="",style="solid", color="black", weight=3]; 130.29/78.18 26731[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];26731 -> 28501[label="",style="solid", color="black", weight=3]; 130.29/78.18 40974[label="zzz4539",fontsize=16,color="green",shape="box"];40975[label="zzz4544",fontsize=16,color="green",shape="box"];27429 -> 44629[label="",style="dashed", color="red", weight=0]; 130.29/78.18 27429[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ (Succ zzz3532000))) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ (Succ zzz3532000))) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (primCmpNat (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000))) (Succ zzz3532000)) zzz3532000))) zzz342000 == LT)",fontsize=16,color="magenta"];27429 -> 44630[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27429 -> 44631[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27429 -> 44632[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27429 -> 44633[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27429 -> 44634[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27429 -> 44635[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27429 -> 44636[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27429 -> 44637[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27429 -> 44638[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27429 -> 44639[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27429 -> 44640[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27429 -> 44641[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27429 -> 44642[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27429 -> 44643[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27430 -> 45509[label="",style="dashed", color="red", weight=0]; 130.29/78.18 27430[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Pos (Succ Zero)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ Zero)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ (Succ zzz342000))) zzz343 zzz344 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) zzz342000 == LT)",fontsize=16,color="magenta"];27430 -> 45510[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27430 -> 45511[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27430 -> 45512[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27430 -> 45513[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27430 -> 45514[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27430 -> 45515[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27430 -> 45516[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27430 -> 45517[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27430 -> 45518[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27430 -> 45519[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27430 -> 45520[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27430 -> 45521[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27430 -> 45522[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27431[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344)",fontsize=16,color="black",shape="box"];27431 -> 28698[label="",style="solid", color="black", weight=3]; 130.29/78.18 27432[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];27432 -> 28699[label="",style="solid", color="black", weight=3]; 130.29/78.18 27433[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];27433 -> 28700[label="",style="solid", color="black", weight=3]; 130.29/78.18 27434[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 otherwise",fontsize=16,color="black",shape="box"];27434 -> 28701[label="",style="solid", color="black", weight=3]; 130.29/78.18 44413[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 True",fontsize=16,color="black",shape="box"];44413 -> 44442[label="",style="solid", color="black", weight=3]; 130.29/78.18 44414[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 False",fontsize=16,color="black",shape="box"];44414 -> 44443[label="",style="solid", color="black", weight=3]; 130.29/78.18 27436[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 otherwise",fontsize=16,color="black",shape="box"];27436 -> 28703[label="",style="solid", color="black", weight=3]; 130.29/78.18 27437[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ (Succ zzz3532000))) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ (Succ zzz3532000))) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (primCmpNat (Succ zzz3420000) (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000))) (Succ zzz3532000))) (Succ zzz3532000)) == LT)",fontsize=16,color="black",shape="box"];27437 -> 28704[label="",style="solid", color="black", weight=3]; 130.29/78.18 27438[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ Zero)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ Zero)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (primCmpNat (Succ zzz3420000) (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) Zero) == LT)",fontsize=16,color="black",shape="box"];27438 -> 28705[label="",style="solid", color="black", weight=3]; 130.29/78.18 27439[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ (Succ zzz3532000))) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ (Succ zzz3532000))) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (primCmpNat Zero (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000))) (Succ zzz3532000))) (Succ zzz3532000)) == LT)",fontsize=16,color="black",shape="box"];27439 -> 28706[label="",style="solid", color="black", weight=3]; 130.29/78.18 27440[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ Zero)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ Zero)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (primCmpNat Zero (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) Zero) == LT)",fontsize=16,color="black",shape="box"];27440 -> 28707[label="",style="solid", color="black", weight=3]; 130.29/78.18 27441 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.18 27441[label="FiniteMap.mkBalBranch zzz340 zzz341 (FiniteMap.mkVBalBranch (Neg Zero) zzz31 (FiniteMap.Branch zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534) zzz343) zzz344",fontsize=16,color="magenta"];27441 -> 63185[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27441 -> 63186[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27441 -> 63187[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 27441 -> 63188[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63426[label="Neg (Succ zzz353200)",fontsize=16,color="green",shape="box"];63427[label="Zero",fontsize=16,color="green",shape="box"];63428[label="zzz3534",fontsize=16,color="green",shape="box"];63429[label="zzz343",fontsize=16,color="green",shape="box"];63430[label="zzz3530",fontsize=16,color="green",shape="box"];63431[label="zzz3533",fontsize=16,color="green",shape="box"];63432[label="zzz3531",fontsize=16,color="green",shape="box"];27449[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 otherwise",fontsize=16,color="black",shape="box"];27449 -> 28712[label="",style="solid", color="black", weight=3]; 130.29/78.18 44415[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpNat Zero (Succ zzz49510) == LT)",fontsize=16,color="black",shape="box"];44415 -> 44444[label="",style="solid", color="black", weight=3]; 130.29/78.18 44416[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (EQ == LT)",fontsize=16,color="black",shape="box"];44416 -> 44445[label="",style="solid", color="black", weight=3]; 130.29/78.18 27451[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 otherwise",fontsize=16,color="black",shape="box"];27451 -> 28714[label="",style="solid", color="black", weight=3]; 130.29/78.18 28192[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Pos (primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];28192 -> 28754[label="",style="solid", color="black", weight=3]; 130.29/78.18 28193[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];28193 -> 28755[label="",style="solid", color="black", weight=3]; 130.29/78.18 28194[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Neg (primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];28194 -> 28756[label="",style="solid", color="black", weight=3]; 130.29/78.18 28195[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];28195 -> 28757[label="",style="solid", color="black", weight=3]; 130.29/78.18 28246[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (primCmpNat (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000)) zzz2502000))) (Succ zzz3420000) == LT)",fontsize=16,color="black",shape="box"];28246 -> 28813[label="",style="solid", color="black", weight=3]; 130.29/78.18 28247[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpNat (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000)) zzz2502000))) Zero == LT)",fontsize=16,color="black",shape="box"];28247 -> 28814[label="",style="solid", color="black", weight=3]; 130.29/78.18 28248[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) (Succ zzz3420000) == LT)",fontsize=16,color="black",shape="box"];28248 -> 28815[label="",style="solid", color="black", weight=3]; 130.29/78.18 28249[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) Zero == LT)",fontsize=16,color="black",shape="box"];28249 -> 28816[label="",style="solid", color="black", weight=3]; 130.29/78.18 28250[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];28250 -> 28817[label="",style="solid", color="black", weight=3]; 130.29/78.18 28251[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];28251 -> 28818[label="",style="solid", color="black", weight=3]; 130.29/78.18 28252[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Neg zzz3420) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];28252 -> 28819[label="",style="solid", color="black", weight=3]; 130.29/78.18 28253[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];28253 -> 28820[label="",style="solid", color="black", weight=3]; 130.29/78.18 28254[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (Succ zzz34200) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];28254 -> 28821[label="",style="solid", color="black", weight=3]; 130.29/78.18 28255[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];28255 -> 28822[label="",style="solid", color="black", weight=3]; 130.29/78.18 28256[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (primCmpNat (Succ zzz3420000) (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000)) zzz2502000))) == LT)",fontsize=16,color="black",shape="box"];28256 -> 28823[label="",style="solid", color="black", weight=3]; 130.29/78.18 28257[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (primCmpNat (Succ zzz3420000) (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) == LT)",fontsize=16,color="black",shape="box"];28257 -> 28824[label="",style="solid", color="black", weight=3]; 130.29/78.18 28258[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (primCmpNat Zero (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000)) zzz2502000))) == LT)",fontsize=16,color="black",shape="box"];28258 -> 28825[label="",style="solid", color="black", weight=3]; 130.29/78.18 28259[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (primCmpNat Zero (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) == LT)",fontsize=16,color="black",shape="box"];28259 -> 28826[label="",style="solid", color="black", weight=3]; 130.29/78.18 63181[label="zzz340",fontsize=16,color="green",shape="box"];63182[label="zzz344",fontsize=16,color="green",shape="box"];63183 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.18 63183[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 zzz2504) zzz343",fontsize=16,color="magenta"];63183 -> 63433[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63183 -> 63434[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63184[label="zzz341",fontsize=16,color="green",shape="box"];28264[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];28264 -> 28829[label="",style="solid", color="black", weight=3]; 130.29/78.18 28265[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat Zero (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];28265 -> 28830[label="",style="solid", color="black", weight=3]; 130.29/78.18 28266[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];28266 -> 28831[label="",style="solid", color="black", weight=3]; 130.29/78.18 28267[label="zzz6214",fontsize=16,color="green",shape="box"];62834[label="FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464",fontsize=16,color="green",shape="box"];62835[label="FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034",fontsize=16,color="green",shape="box"];62836[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (compare zzz6355 zzz6354 == GT)",fontsize=16,color="black",shape="box"];62836 -> 62840[label="",style="solid", color="black", weight=3]; 130.29/78.18 64265[label="FiniteMap.mkBalBranch6Size_r zzz474034 zzz474030 zzz474031 zzz6373",fontsize=16,color="black",shape="triangle"];64265 -> 64267[label="",style="solid", color="black", weight=3]; 130.29/78.18 64264[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt zzz6443 (FiniteMap.sIZE_RATIO * zzz6442) == GT)",fontsize=16,color="burlywood",shape="triangle"];65390[label="zzz6443/Pos zzz64430",fontsize=10,color="white",style="solid",shape="box"];64264 -> 65390[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65390 -> 64268[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65391[label="zzz6443/Neg zzz64430",fontsize=10,color="white",style="solid",shape="box"];64264 -> 65391[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65391 -> 64269[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 60826[label="Succ Zero",fontsize=16,color="green",shape="box"];60827[label="FiniteMap.mkBranchLeft_size zzz6234 zzz6235 zzz6232",fontsize=16,color="black",shape="box"];60827 -> 60832[label="",style="solid", color="black", weight=3]; 130.29/78.18 60828 -> 55581[label="",style="dashed", color="red", weight=0]; 130.29/78.18 60828[label="primPlusInt (Pos zzz62420) (FiniteMap.sizeFM zzz6235)",fontsize=16,color="magenta"];60828 -> 60833[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 60828 -> 60834[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 60829 -> 55610[label="",style="dashed", color="red", weight=0]; 130.29/78.18 60829[label="primPlusInt (Neg zzz62420) (FiniteMap.sizeFM zzz6235)",fontsize=16,color="magenta"];60829 -> 60835[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 60829 -> 60836[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28494[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)))) zzz4262 == LT)",fontsize=16,color="burlywood",shape="box"];65392[label="zzz4262/Pos zzz42620",fontsize=10,color="white",style="solid",shape="box"];28494 -> 65392[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65392 -> 28855[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65393[label="zzz4262/Neg zzz42620",fontsize=10,color="white",style="solid",shape="box"];28494 -> 65393[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65393 -> 28856[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 28495[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];28495 -> 28857[label="",style="solid", color="black", weight=3]; 130.29/78.18 28496[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];28496 -> 28858[label="",style="solid", color="black", weight=3]; 130.29/78.18 28497[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];28497 -> 28859[label="",style="solid", color="black", weight=3]; 130.29/78.18 28498[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 zzz4262 zzz4263 zzz4264 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)))) zzz4262 == LT)",fontsize=16,color="burlywood",shape="box"];65394[label="zzz4262/Pos zzz42620",fontsize=10,color="white",style="solid",shape="box"];28498 -> 65394[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65394 -> 28860[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65395[label="zzz4262/Neg zzz42620",fontsize=10,color="white",style="solid",shape="box"];28498 -> 65395[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65395 -> 28861[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 28499[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];28499 -> 28862[label="",style="solid", color="black", weight=3]; 130.29/78.18 28500[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];28500 -> 28863[label="",style="solid", color="black", weight=3]; 130.29/78.18 28501[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];28501 -> 28864[label="",style="solid", color="black", weight=3]; 130.29/78.18 44630[label="zzz3532000",fontsize=16,color="green",shape="box"];44631[label="zzz31",fontsize=16,color="green",shape="box"];44632[label="Succ zzz342000",fontsize=16,color="green",shape="box"];44633[label="zzz344",fontsize=16,color="green",shape="box"];44634[label="zzz3534",fontsize=16,color="green",shape="box"];44635[label="zzz341",fontsize=16,color="green",shape="box"];44636[label="zzz3533",fontsize=16,color="green",shape="box"];44637[label="zzz343",fontsize=16,color="green",shape="box"];44638[label="Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000))) (Succ zzz3532000)) zzz3532000))",fontsize=16,color="green",shape="box"];44638 -> 44742[label="",style="dashed", color="green", weight=3]; 130.29/78.18 44639[label="zzz340",fontsize=16,color="green",shape="box"];44640[label="zzz342000",fontsize=16,color="green",shape="box"];44641[label="zzz3530",fontsize=16,color="green",shape="box"];44642[label="zzz3531",fontsize=16,color="green",shape="box"];44643[label="Zero",fontsize=16,color="green",shape="box"];44629[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpNat zzz5005 zzz5006 == LT)",fontsize=16,color="burlywood",shape="triangle"];65396[label="zzz5005/Succ zzz50050",fontsize=10,color="white",style="solid",shape="box"];44629 -> 65396[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65396 -> 44743[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65397[label="zzz5005/Zero",fontsize=10,color="white",style="solid",shape="box"];44629 -> 65397[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65397 -> 44744[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 45510[label="zzz344",fontsize=16,color="green",shape="box"];45511[label="zzz3533",fontsize=16,color="green",shape="box"];45512[label="zzz3534",fontsize=16,color="green",shape="box"];45513[label="Succ zzz342000",fontsize=16,color="green",shape="box"];45514[label="zzz3531",fontsize=16,color="green",shape="box"];45515[label="Zero",fontsize=16,color="green",shape="box"];45516[label="zzz340",fontsize=16,color="green",shape="box"];45517[label="zzz341",fontsize=16,color="green",shape="box"];45518[label="zzz343",fontsize=16,color="green",shape="box"];45519[label="zzz342000",fontsize=16,color="green",shape="box"];45520[label="zzz31",fontsize=16,color="green",shape="box"];45521[label="Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)",fontsize=16,color="green",shape="box"];45521 -> 45653[label="",style="dashed", color="green", weight=3]; 130.29/78.18 45522[label="zzz3530",fontsize=16,color="green",shape="box"];45509[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpNat zzz5101 zzz5102 == LT)",fontsize=16,color="burlywood",shape="triangle"];65398[label="zzz5101/Succ zzz51010",fontsize=10,color="white",style="solid",shape="box"];45509 -> 65398[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65398 -> 45654[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65399[label="zzz5101/Zero",fontsize=10,color="white",style="solid",shape="box"];45509 -> 65399[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65399 -> 45655[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 28698[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];28698 -> 29089[label="",style="solid", color="black", weight=3]; 130.29/78.18 28699[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];28699 -> 29090[label="",style="solid", color="black", weight=3]; 130.29/78.18 28700[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Neg zzz3420) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];28700 -> 29091[label="",style="solid", color="black", weight=3]; 130.29/78.18 28701[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];28701 -> 29092[label="",style="solid", color="black", weight=3]; 130.29/78.18 44442 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.18 44442[label="FiniteMap.mkBalBranch zzz330 zzz331 zzz333 (FiniteMap.mkVBalBranch (Neg zzz300) zzz31 zzz334 (FiniteMap.Branch zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234))",fontsize=16,color="magenta"];44442 -> 63189[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 44442 -> 63190[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 44442 -> 63191[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 44442 -> 63192[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 44443[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 otherwise",fontsize=16,color="black",shape="box"];44443 -> 44512[label="",style="solid", color="black", weight=3]; 130.29/78.18 28703[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];28703 -> 29094[label="",style="solid", color="black", weight=3]; 130.29/78.18 28704 -> 46205[label="",style="dashed", color="red", weight=0]; 130.29/78.18 28704[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ (Succ zzz3532000))) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ (Succ zzz3532000))) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (primCmpNat (Succ zzz3420000) (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000))) (Succ zzz3532000)) zzz3532000))) == LT)",fontsize=16,color="magenta"];28704 -> 46206[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28704 -> 46207[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28704 -> 46208[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28704 -> 46209[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28704 -> 46210[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28704 -> 46211[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28704 -> 46212[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28704 -> 46213[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28704 -> 46214[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28704 -> 46215[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28704 -> 46216[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28704 -> 46217[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28704 -> 46218[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28704 -> 46219[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28705 -> 47219[label="",style="dashed", color="red", weight=0]; 130.29/78.18 28705[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ Zero)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ Zero)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (primCmpNat (Succ zzz3420000) (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) == LT)",fontsize=16,color="magenta"];28705 -> 47220[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28705 -> 47221[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28705 -> 47222[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28705 -> 47223[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28705 -> 47224[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28705 -> 47225[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28705 -> 47226[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28705 -> 47227[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28705 -> 47228[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28705 -> 47229[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28705 -> 47230[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28705 -> 47231[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28705 -> 47232[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28706 -> 46205[label="",style="dashed", color="red", weight=0]; 130.29/78.18 28706[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ (Succ zzz3532000))) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ (Succ zzz3532000))) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (primCmpNat Zero (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000))) (Succ zzz3532000)) zzz3532000))) == LT)",fontsize=16,color="magenta"];28706 -> 46220[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28706 -> 46221[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28706 -> 46222[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28706 -> 46223[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28706 -> 46224[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28706 -> 46225[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28706 -> 46226[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28706 -> 46227[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28706 -> 46228[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28706 -> 46229[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28706 -> 46230[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28706 -> 46231[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28706 -> 46232[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28706 -> 46233[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28707 -> 47219[label="",style="dashed", color="red", weight=0]; 130.29/78.18 28707[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3530 zzz3531 (Neg (Succ Zero)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg (Succ Zero)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (primCmpNat Zero (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) == LT)",fontsize=16,color="magenta"];28707 -> 47233[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28707 -> 47234[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28707 -> 47235[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28707 -> 47236[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28707 -> 47237[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28707 -> 47238[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28707 -> 47239[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28707 -> 47240[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28707 -> 47241[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28707 -> 47242[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28707 -> 47243[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28707 -> 47244[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28707 -> 47245[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63185[label="zzz340",fontsize=16,color="green",shape="box"];63186[label="zzz344",fontsize=16,color="green",shape="box"];63187 -> 7670[label="",style="dashed", color="red", weight=0]; 130.29/78.18 63187[label="FiniteMap.mkVBalBranch (Neg Zero) zzz31 (FiniteMap.Branch zzz3530 zzz3531 (Neg (Succ zzz353200)) zzz3533 zzz3534) zzz343",fontsize=16,color="magenta"];63187 -> 63435[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63187 -> 63436[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63187 -> 63437[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63187 -> 63438[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63187 -> 63439[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63187 -> 63440[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63187 -> 63441[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63188[label="zzz341",fontsize=16,color="green",shape="box"];28712[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];28712 -> 29106[label="",style="solid", color="black", weight=3]; 130.29/78.18 44444[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (LT == LT)",fontsize=16,color="black",shape="box"];44444 -> 44513[label="",style="solid", color="black", weight=3]; 130.29/78.18 44445[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 False",fontsize=16,color="black",shape="box"];44445 -> 44514[label="",style="solid", color="black", weight=3]; 130.29/78.18 28714[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];28714 -> 29108[label="",style="solid", color="black", weight=3]; 130.29/78.18 28754[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Pos (primPlusNat (primPlusNat (primMulNat (Succ (Succ (Succ Zero))) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];28754 -> 29137[label="",style="solid", color="black", weight=3]; 130.29/78.18 28755[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz5230 zzz5231 zzz5232 zzz5233 zzz5234)) == LT)",fontsize=16,color="black",shape="box"];28755 -> 29138[label="",style="solid", color="black", weight=3]; 130.29/78.18 28756[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Neg (primPlusNat (primPlusNat (primMulNat (Succ (Succ (Succ Zero))) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];28756 -> 29139[label="",style="solid", color="black", weight=3]; 130.29/78.18 28757[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz5230 zzz5231 zzz5232 zzz5233 zzz5234)) == LT)",fontsize=16,color="black",shape="box"];28757 -> 29140[label="",style="solid", color="black", weight=3]; 130.29/78.18 28813[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (primCmpNat (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000)) zzz2502000)) zzz3420000 == LT)",fontsize=16,color="burlywood",shape="box"];65400[label="zzz3420000/Succ zzz34200000",fontsize=10,color="white",style="solid",shape="box"];28813 -> 65400[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65400 -> 29180[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65401[label="zzz3420000/Zero",fontsize=10,color="white",style="solid",shape="box"];28813 -> 65401[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65401 -> 29181[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 28814[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (GT == LT)",fontsize=16,color="black",shape="box"];28814 -> 29182[label="",style="solid", color="black", weight=3]; 130.29/78.18 28815[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (primCmpNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero) zzz3420000 == LT)",fontsize=16,color="black",shape="box"];28815 -> 29183[label="",style="solid", color="black", weight=3]; 130.29/78.18 28816[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (GT == LT)",fontsize=16,color="black",shape="box"];28816 -> 29184[label="",style="solid", color="black", weight=3]; 130.29/78.18 28817[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];28817 -> 29185[label="",style="solid", color="black", weight=3]; 130.29/78.18 28818[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];28818 -> 29186[label="",style="solid", color="black", weight=3]; 130.29/78.18 28819[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg zzz3420)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];28819 -> 29187[label="",style="solid", color="black", weight=3]; 130.29/78.18 28820 -> 60457[label="",style="dashed", color="red", weight=0]; 130.29/78.18 28820[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504) (FiniteMap.Branch zzz340 zzz341 (Pos Zero) zzz343 zzz344)",fontsize=16,color="magenta"];28820 -> 60463[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28820 -> 60464[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28820 -> 60465[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28820 -> 60466[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28820 -> 60467[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28821[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (Succ (Succ (primPlusNat zzz34200 zzz34200))) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];28821 -> 29228[label="",style="solid", color="black", weight=3]; 130.29/78.18 28822 -> 60457[label="",style="dashed", color="red", weight=0]; 130.29/78.18 28822[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504) (FiniteMap.Branch zzz340 zzz341 (Neg Zero) zzz343 zzz344)",fontsize=16,color="magenta"];28822 -> 60468[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28822 -> 60469[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28822 -> 60470[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28822 -> 60471[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28822 -> 60472[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28823[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (primCmpNat zzz3420000 (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000)) zzz2502000)) == LT)",fontsize=16,color="burlywood",shape="box"];65402[label="zzz3420000/Succ zzz34200000",fontsize=10,color="white",style="solid",shape="box"];28823 -> 65402[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65402 -> 29266[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65403[label="zzz3420000/Zero",fontsize=10,color="white",style="solid",shape="box"];28823 -> 65403[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65403 -> 29267[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 28824[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (primCmpNat zzz3420000 (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero) == LT)",fontsize=16,color="burlywood",shape="box"];65404[label="zzz3420000/Succ zzz34200000",fontsize=10,color="white",style="solid",shape="box"];28824 -> 65404[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65404 -> 29268[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65405[label="zzz3420000/Zero",fontsize=10,color="white",style="solid",shape="box"];28824 -> 65405[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65405 -> 29269[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 28825[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];28825 -> 29270[label="",style="solid", color="black", weight=3]; 130.29/78.18 28826[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];28826 -> 29271[label="",style="solid", color="black", weight=3]; 130.29/78.18 63433[label="FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ zzz250200)) zzz2503 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130.29/78.18 28831 -> 60479[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28831 -> 60480[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28831 -> 60481[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28831 -> 60482[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 62840[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt zzz6355 zzz6354 == GT)",fontsize=16,color="burlywood",shape="box"];65406[label="zzz6355/Pos zzz63550",fontsize=10,color="white",style="solid",shape="box"];62840 -> 65406[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65406 -> 62858[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65407[label="zzz6355/Neg zzz63550",fontsize=10,color="white",style="solid",shape="box"];62840 -> 65407[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65407 -> 62859[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 64267 -> 54589[label="",style="dashed", color="red", weight=0]; 130.29/78.18 64267[label="FiniteMap.sizeFM zzz474034",fontsize=16,color="magenta"];64267 -> 64270[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 64268[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos zzz64430) (FiniteMap.sIZE_RATIO * zzz6442) == GT)",fontsize=16,color="burlywood",shape="box"];65408[label="zzz64430/Succ zzz644300",fontsize=10,color="white",style="solid",shape="box"];64268 -> 65408[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65408 -> 64271[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65409[label="zzz64430/Zero",fontsize=10,color="white",style="solid",shape="box"];64268 -> 65409[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65409 -> 64272[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 64269[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg zzz64430) (FiniteMap.sIZE_RATIO * zzz6442) == GT)",fontsize=16,color="burlywood",shape="box"];65410[label="zzz64430/Succ zzz644300",fontsize=10,color="white",style="solid",shape="box"];64269 -> 65410[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65410 -> 64273[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65411[label="zzz64430/Zero",fontsize=10,color="white",style="solid",shape="box"];64269 -> 65411[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65411 -> 64274[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 60832 -> 54589[label="",style="dashed", color="red", weight=0]; 130.29/78.18 60832[label="FiniteMap.sizeFM zzz6234",fontsize=16,color="magenta"];60832 -> 60839[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 60833[label="zzz62420",fontsize=16,color="green",shape="box"];60834 -> 54589[label="",style="dashed", color="red", weight=0]; 130.29/78.18 60834[label="FiniteMap.sizeFM zzz6235",fontsize=16,color="magenta"];60834 -> 60840[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 60835[label="zzz62420",fontsize=16,color="green",shape="box"];60836 -> 54589[label="",style="dashed", color="red", weight=0]; 130.29/78.18 60836[label="FiniteMap.sizeFM zzz6235",fontsize=16,color="magenta"];60836 -> 60841[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 28855[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos zzz42620) zzz4263 zzz4264 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)))) (Pos zzz42620) == LT)",fontsize=16,color="black",shape="box"];28855 -> 29352[label="",style="solid", color="black", weight=3]; 130.29/78.18 28856[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)))) (Neg zzz42620) == LT)",fontsize=16,color="black",shape="box"];28856 -> 29353[label="",style="solid", color="black", weight=3]; 130.29/78.18 28857[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];28857 -> 29354[label="",style="solid", color="black", weight=3]; 130.29/78.18 28858[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg (Succ zzz426200))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];28858 -> 29355[label="",style="solid", color="black", weight=3]; 130.29/78.18 28859[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];28859 -> 29356[label="",style="solid", color="black", weight=3]; 130.29/78.18 28860[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos zzz42620) zzz4263 zzz4264 (primCmpInt (Neg (Succ (Succ (primPlusNat 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zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];28862 -> 29359[label="",style="solid", color="black", weight=3]; 130.29/78.18 28863[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];28863 -> 29360[label="",style="solid", color="black", weight=3]; 130.29/78.18 28864[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];28864 -> 29361[label="",style="solid", color="black", weight=3]; 130.29/78.18 44742 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.18 44742[label="primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000))) (Succ zzz3532000)) zzz3532000",fontsize=16,color="magenta"];44742 -> 44758[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 44742 -> 44759[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 44743[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpNat (Succ zzz50050) zzz5006 == LT)",fontsize=16,color="burlywood",shape="box"];65412[label="zzz5006/Succ zzz50060",fontsize=10,color="white",style="solid",shape="box"];44743 -> 65412[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65412 -> 44760[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65413[label="zzz5006/Zero",fontsize=10,color="white",style="solid",shape="box"];44743 -> 65413[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65413 -> 44761[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 44744[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpNat Zero zzz5006 == LT)",fontsize=16,color="burlywood",shape="box"];65414[label="zzz5006/Succ zzz50060",fontsize=10,color="white",style="solid",shape="box"];44744 -> 65414[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65414 -> 44762[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65415[label="zzz5006/Zero",fontsize=10,color="white",style="solid",shape="box"];44744 -> 65415[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65415 -> 44763[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 45653 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.18 45653[label="primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero",fontsize=16,color="magenta"];45653 -> 45667[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 45653 -> 45668[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 45654[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpNat (Succ zzz51010) zzz5102 == LT)",fontsize=16,color="burlywood",shape="box"];65416[label="zzz5102/Succ zzz51020",fontsize=10,color="white",style="solid",shape="box"];45654 -> 65416[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65416 -> 45669[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65417[label="zzz5102/Zero",fontsize=10,color="white",style="solid",shape="box"];45654 -> 65417[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65417 -> 45670[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 45655[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpNat Zero zzz5102 == LT)",fontsize=16,color="burlywood",shape="box"];65418[label="zzz5102/Succ zzz51020",fontsize=10,color="white",style="solid",shape="box"];45655 -> 65418[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65418 -> 45671[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65419[label="zzz5102/Zero",fontsize=10,color="white",style="solid",shape="box"];45655 -> 65419[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65419 -> 45672[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 29089[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];29089 -> 29907[label="",style="solid", color="black", weight=3]; 130.29/78.18 29090[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];29090 -> 29908[label="",style="solid", color="black", weight=3]; 130.29/78.18 29091[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg zzz3420)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];29091 -> 29909[label="",style="solid", color="black", weight=3]; 130.29/78.18 29092 -> 60457[label="",style="dashed", color="red", weight=0]; 130.29/78.18 29092[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Neg Zero) zzz31 (FiniteMap.Branch zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534) (FiniteMap.Branch zzz340 zzz341 (Pos Zero) zzz343 zzz344)",fontsize=16,color="magenta"];29092 -> 60493[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29092 -> 60494[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29092 -> 60495[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29092 -> 60496[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29092 -> 60497[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 63189[label="zzz330",fontsize=16,color="green",shape="box"];63190[label="FiniteMap.mkVBalBranch (Neg zzz300) zzz31 zzz334 (FiniteMap.Branch zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234)",fontsize=16,color="burlywood",shape="triangle"];65420[label="zzz334/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];63190 -> 65420[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65420 -> 63442[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65421[label="zzz334/FiniteMap.Branch zzz3340 zzz3341 zzz3342 zzz3343 zzz3344",fontsize=10,color="white",style="solid",shape="box"];63190 -> 65421[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65421 -> 63443[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 63191[label="zzz333",fontsize=16,color="green",shape="box"];63192[label="zzz331",fontsize=16,color="green",shape="box"];44512[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 True",fontsize=16,color="black",shape="box"];44512 -> 44558[label="",style="solid", color="black", weight=3]; 130.29/78.18 29094 -> 60457[label="",style="dashed", color="red", weight=0]; 130.29/78.18 29094[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Neg Zero) zzz31 (FiniteMap.Branch zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534) (FiniteMap.Branch zzz340 zzz341 (Neg Zero) zzz343 zzz344)",fontsize=16,color="magenta"];29094 -> 60498[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29094 -> 60499[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29094 -> 60500[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29094 -> 60501[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29094 -> 60502[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 46206[label="zzz341",fontsize=16,color="green",shape="box"];46207[label="zzz3534",fontsize=16,color="green",shape="box"];46208[label="zzz344",fontsize=16,color="green",shape="box"];46209[label="Zero",fontsize=16,color="green",shape="box"];46210[label="zzz31",fontsize=16,color="green",shape="box"];46211[label="zzz3530",fontsize=16,color="green",shape="box"];46212[label="zzz3533",fontsize=16,color="green",shape="box"];46213[label="zzz340",fontsize=16,color="green",shape="box"];46214[label="Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000))) (Succ zzz3532000)) zzz3532000))",fontsize=16,color="green",shape="box"];46214 -> 46374[label="",style="dashed", color="green", weight=3]; 130.29/78.18 46215[label="Succ zzz3420000",fontsize=16,color="green",shape="box"];46216[label="zzz3531",fontsize=16,color="green",shape="box"];46217[label="zzz343",fontsize=16,color="green",shape="box"];46218[label="zzz3532000",fontsize=16,color="green",shape="box"];46219[label="Succ (Succ zzz3420000)",fontsize=16,color="green",shape="box"];46205[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpNat zzz5142 zzz5143 == LT)",fontsize=16,color="burlywood",shape="triangle"];65422[label="zzz5142/Succ zzz51420",fontsize=10,color="white",style="solid",shape="box"];46205 -> 65422[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65422 -> 46375[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65423[label="zzz5142/Zero",fontsize=10,color="white",style="solid",shape="box"];46205 -> 65423[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65423 -> 46376[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 47220[label="Succ (Succ zzz3420000)",fontsize=16,color="green",shape="box"];47221[label="Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)",fontsize=16,color="green",shape="box"];47221 -> 47415[label="",style="dashed", color="green", weight=3]; 130.29/78.18 47222[label="zzz3530",fontsize=16,color="green",shape="box"];47223[label="zzz344",fontsize=16,color="green",shape="box"];47224[label="Zero",fontsize=16,color="green",shape="box"];47225[label="zzz343",fontsize=16,color="green",shape="box"];47226[label="zzz31",fontsize=16,color="green",shape="box"];47227[label="zzz3533",fontsize=16,color="green",shape="box"];47228[label="zzz341",fontsize=16,color="green",shape="box"];47229[label="zzz3534",fontsize=16,color="green",shape="box"];47230[label="Succ zzz3420000",fontsize=16,color="green",shape="box"];47231[label="zzz3531",fontsize=16,color="green",shape="box"];47232[label="zzz340",fontsize=16,color="green",shape="box"];47219[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpNat zzz5258 zzz5259 == LT)",fontsize=16,color="burlywood",shape="triangle"];65424[label="zzz5258/Succ zzz52580",fontsize=10,color="white",style="solid",shape="box"];47219 -> 65424[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65424 -> 47416[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65425[label="zzz5258/Zero",fontsize=10,color="white",style="solid",shape="box"];47219 -> 65425[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65425 -> 47417[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 46220[label="zzz341",fontsize=16,color="green",shape="box"];46221[label="zzz3534",fontsize=16,color="green",shape="box"];46222[label="zzz344",fontsize=16,color="green",shape="box"];46223[label="Zero",fontsize=16,color="green",shape="box"];46224[label="zzz31",fontsize=16,color="green",shape="box"];46225[label="zzz3530",fontsize=16,color="green",shape="box"];46226[label="zzz3533",fontsize=16,color="green",shape="box"];46227[label="zzz340",fontsize=16,color="green",shape="box"];46228[label="Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000))) (Succ zzz3532000)) zzz3532000))",fontsize=16,color="green",shape="box"];46228 -> 46377[label="",style="dashed", color="green", weight=3]; 130.29/78.18 46229[label="Zero",fontsize=16,color="green",shape="box"];46230[label="zzz3531",fontsize=16,color="green",shape="box"];46231[label="zzz343",fontsize=16,color="green",shape="box"];46232[label="zzz3532000",fontsize=16,color="green",shape="box"];46233[label="Succ Zero",fontsize=16,color="green",shape="box"];47233[label="Succ Zero",fontsize=16,color="green",shape="box"];47234[label="Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)",fontsize=16,color="green",shape="box"];47234 -> 47418[label="",style="dashed", color="green", weight=3]; 130.29/78.18 47235[label="zzz3530",fontsize=16,color="green",shape="box"];47236[label="zzz344",fontsize=16,color="green",shape="box"];47237[label="Zero",fontsize=16,color="green",shape="box"];47238[label="zzz343",fontsize=16,color="green",shape="box"];47239[label="zzz31",fontsize=16,color="green",shape="box"];47240[label="zzz3533",fontsize=16,color="green",shape="box"];47241[label="zzz341",fontsize=16,color="green",shape="box"];47242[label="zzz3534",fontsize=16,color="green",shape="box"];47243[label="Zero",fontsize=16,color="green",shape="box"];47244[label="zzz3531",fontsize=16,color="green",shape="box"];47245[label="zzz340",fontsize=16,color="green",shape="box"];63435[label="Neg (Succ zzz353200)",fontsize=16,color="green",shape="box"];63436[label="Zero",fontsize=16,color="green",shape="box"];63437[label="zzz3534",fontsize=16,color="green",shape="box"];63438[label="zzz343",fontsize=16,color="green",shape="box"];63439[label="zzz3530",fontsize=16,color="green",shape="box"];63440[label="zzz3533",fontsize=16,color="green",shape="box"];63441[label="zzz3531",fontsize=16,color="green",shape="box"];29106 -> 60457[label="",style="dashed", color="red", weight=0]; 130.29/78.18 29106[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Neg Zero) zzz31 (FiniteMap.Branch zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534) (FiniteMap.Branch zzz340 zzz341 (Pos Zero) zzz343 zzz344)",fontsize=16,color="magenta"];29106 -> 60503[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29106 -> 60504[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29106 -> 60505[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29106 -> 60506[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29106 -> 60507[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 44513[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 True",fontsize=16,color="black",shape="box"];44513 -> 44559[label="",style="solid", color="black", weight=3]; 130.29/78.18 44514[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 otherwise",fontsize=16,color="black",shape="box"];44514 -> 44560[label="",style="solid", color="black", weight=3]; 130.29/78.18 29108 -> 60457[label="",style="dashed", color="red", weight=0]; 130.29/78.18 29108[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Neg Zero) zzz31 (FiniteMap.Branch zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534) (FiniteMap.Branch zzz340 zzz341 (Neg Zero) zzz343 zzz344)",fontsize=16,color="magenta"];29108 -> 60508[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29108 -> 60509[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29108 -> 60510[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29108 -> 60511[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29108 -> 60512[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29137[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ (Succ Zero)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];29137 -> 30642[label="",style="solid", color="black", weight=3]; 130.29/78.18 29138[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Pos Zero) zzz5232 == LT)",fontsize=16,color="burlywood",shape="box"];65426[label="zzz5232/Pos zzz52320",fontsize=10,color="white",style="solid",shape="box"];29138 -> 65426[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65426 -> 30643[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65427[label="zzz5232/Neg zzz52320",fontsize=10,color="white",style="solid",shape="box"];29138 -> 65427[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65427 -> 30644[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 29139[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ (Succ Zero)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];29139 -> 30645[label="",style="solid", color="black", weight=3]; 130.29/78.18 29140[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Neg Zero) zzz5232 == LT)",fontsize=16,color="burlywood",shape="box"];65428[label="zzz5232/Pos zzz52320",fontsize=10,color="white",style="solid",shape="box"];29140 -> 65428[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65428 -> 30646[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65429[label="zzz5232/Neg zzz52320",fontsize=10,color="white",style="solid",shape="box"];29140 -> 65429[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65429 -> 30647[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 29180[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (primCmpNat (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000)) zzz2502000)) (Succ zzz34200000) == LT)",fontsize=16,color="black",shape="box"];29180 -> 30698[label="",style="solid", color="black", weight=3]; 130.29/78.18 29181[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpNat (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000)) zzz2502000)) Zero == LT)",fontsize=16,color="black",shape="box"];29181 -> 30699[label="",style="solid", color="black", weight=3]; 130.29/78.18 29182[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];29182 -> 30700[label="",style="solid", color="black", weight=3]; 130.29/78.18 29183[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ zzz3420000)))) zzz343 zzz344 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) zzz3420000 == LT)",fontsize=16,color="burlywood",shape="box"];65430[label="zzz3420000/Succ zzz34200000",fontsize=10,color="white",style="solid",shape="box"];29183 -> 65430[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65430 -> 30701[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65431[label="zzz3420000/Zero",fontsize=10,color="white",style="solid",shape="box"];29183 -> 65431[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65431 -> 30702[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 29184[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];29184 -> 30703[label="",style="solid", color="black", weight=3]; 130.29/78.18 29185[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];29185 -> 30704[label="",style="solid", color="black", weight=3]; 130.29/78.18 29186[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Pos Zero) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];29186 -> 30705[label="",style="solid", color="black", weight=3]; 130.29/78.18 29187[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz3420)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344) == LT)",fontsize=16,color="burlywood",shape="box"];65432[label="zzz3420/Succ zzz34200",fontsize=10,color="white",style="solid",shape="box"];29187 -> 65432[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65432 -> 30706[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65433[label="zzz3420/Zero",fontsize=10,color="white",style="solid",shape="box"];29187 -> 65433[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65433 -> 30707[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 60463[label="zzz31",fontsize=16,color="green",shape="box"];60464[label="Pos zzz300",fontsize=16,color="green",shape="box"];60465[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];60466[label="FiniteMap.Branch zzz340 zzz341 (Pos Zero) zzz343 zzz344",fontsize=16,color="green",shape="box"];60467[label="FiniteMap.Branch zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504",fontsize=16,color="green",shape="box"];29228[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat zzz34200 zzz34200)) zzz34200))) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];29228 -> 30709[label="",style="solid", color="black", weight=3]; 130.29/78.18 60468[label="zzz31",fontsize=16,color="green",shape="box"];60469[label="Pos zzz300",fontsize=16,color="green",shape="box"];60470[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];60471[label="FiniteMap.Branch zzz340 zzz341 (Neg Zero) zzz343 zzz344",fontsize=16,color="green",shape="box"];60472[label="FiniteMap.Branch zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504",fontsize=16,color="green",shape="box"];29266[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (primCmpNat (Succ zzz34200000) (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000)) zzz2502000)) == LT)",fontsize=16,color="black",shape="box"];29266 -> 30711[label="",style="solid", color="black", weight=3]; 130.29/78.18 29267[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpNat Zero (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000)) zzz2502000)) == LT)",fontsize=16,color="black",shape="box"];29267 -> 30712[label="",style="solid", color="black", weight=3]; 130.29/78.18 29268[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (primCmpNat (Succ zzz34200000) (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero) == LT)",fontsize=16,color="black",shape="box"];29268 -> 30713[label="",style="solid", color="black", weight=3]; 130.29/78.18 29269[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpNat Zero (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero) == LT)",fontsize=16,color="black",shape="box"];29269 -> 30714[label="",style="solid", color="black", weight=3]; 130.29/78.18 29270[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];29270 -> 30715[label="",style="solid", color="black", weight=3]; 130.29/78.18 29271[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ Zero))) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];29271 -> 30716[label="",style="solid", color="black", weight=3]; 130.29/78.18 60473[label="zzz31",fontsize=16,color="green",shape="box"];60474[label="Pos zzz300",fontsize=16,color="green",shape="box"];60475[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];60476[label="FiniteMap.Branch zzz340 zzz341 (Pos Zero) zzz343 zzz344",fontsize=16,color="green",shape="box"];60477[label="FiniteMap.Branch zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504",fontsize=16,color="green",shape="box"];29297[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (Succ (Succ (primPlusNat zzz34200 zzz34200))) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];29297 -> 30718[label="",style="solid", color="black", weight=3]; 130.29/78.18 60478[label="zzz31",fontsize=16,color="green",shape="box"];60479[label="Pos zzz300",fontsize=16,color="green",shape="box"];60480[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];60481[label="FiniteMap.Branch zzz340 zzz341 (Neg Zero) zzz343 zzz344",fontsize=16,color="green",shape="box"];60482[label="FiniteMap.Branch zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504",fontsize=16,color="green",shape="box"];62858[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Pos zzz63550) zzz6354 == GT)",fontsize=16,color="burlywood",shape="box"];65434[label="zzz63550/Succ zzz635500",fontsize=10,color="white",style="solid",shape="box"];62858 -> 65434[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65434 -> 62865[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65435[label="zzz63550/Zero",fontsize=10,color="white",style="solid",shape="box"];62858 -> 65435[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65435 -> 62866[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 62859[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Neg zzz63550) zzz6354 == GT)",fontsize=16,color="burlywood",shape="box"];65436[label="zzz63550/Succ zzz635500",fontsize=10,color="white",style="solid",shape="box"];62859 -> 65436[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65436 -> 62867[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65437[label="zzz63550/Zero",fontsize=10,color="white",style="solid",shape="box"];62859 -> 65437[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65437 -> 62868[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 64270[label="zzz474034",fontsize=16,color="green",shape="box"];64271[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos (Succ zzz644300)) (FiniteMap.sIZE_RATIO * zzz6442) == GT)",fontsize=16,color="black",shape="box"];64271 -> 64275[label="",style="solid", color="black", weight=3]; 130.29/78.18 64272[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (FiniteMap.sIZE_RATIO * zzz6442) == GT)",fontsize=16,color="black",shape="box"];64272 -> 64276[label="",style="solid", color="black", weight=3]; 130.29/78.18 64273[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg (Succ zzz644300)) (FiniteMap.sIZE_RATIO * zzz6442) == GT)",fontsize=16,color="black",shape="box"];64273 -> 64277[label="",style="solid", color="black", weight=3]; 130.29/78.18 64274[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (FiniteMap.sIZE_RATIO * zzz6442) == GT)",fontsize=16,color="black",shape="box"];64274 -> 64278[label="",style="solid", color="black", weight=3]; 130.29/78.18 60839[label="zzz6234",fontsize=16,color="green",shape="box"];60840[label="zzz6235",fontsize=16,color="green",shape="box"];60841[label="zzz6235",fontsize=16,color="green",shape="box"];29352[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos zzz42620) zzz4263 zzz4264 (primCmpNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200))) zzz42620 == LT)",fontsize=16,color="burlywood",shape="box"];65438[label="zzz42620/Succ zzz426200",fontsize=10,color="white",style="solid",shape="box"];29352 -> 65438[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65438 -> 30746[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65439[label="zzz42620/Zero",fontsize=10,color="white",style="solid",shape="box"];29352 -> 65439[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65439 -> 30747[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 29353[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (GT == LT)",fontsize=16,color="black",shape="box"];29353 -> 30748[label="",style="solid", color="black", weight=3]; 130.29/78.18 29354[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];29354 -> 30749[label="",style="solid", color="black", weight=3]; 130.29/78.18 29355 -> 43855[label="",style="dashed", color="red", weight=0]; 130.29/78.18 29355[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz426200))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) == LT)",fontsize=16,color="magenta"];29355 -> 43955[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29355 -> 43956[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29355 -> 43957[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29355 -> 43958[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29355 -> 43959[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29355 -> 43960[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29355 -> 43961[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 29356[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];29356 -> 30751[label="",style="solid", color="black", weight=3]; 130.29/78.18 29357[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos zzz42620) zzz4263 zzz4264 (LT == LT)",fontsize=16,color="black",shape="box"];29357 -> 30752[label="",style="solid", color="black", weight=3]; 130.29/78.18 29358[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (primCmpNat zzz42620 (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200))) == LT)",fontsize=16,color="burlywood",shape="box"];65440[label="zzz42620/Succ zzz426200",fontsize=10,color="white",style="solid",shape="box"];29358 -> 65440[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65440 -> 30753[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65441[label="zzz42620/Zero",fontsize=10,color="white",style="solid",shape="box"];29358 -> 65441[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65441 -> 30754[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 29359[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];29359 -> 30755[label="",style="solid", color="black", weight=3]; 130.29/78.18 29360[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg (Succ zzz426200))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];29360 -> 30756[label="",style="solid", color="black", weight=3]; 130.29/78.18 29361[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];29361 -> 30757[label="",style="solid", color="black", weight=3]; 130.29/78.18 44758[label="zzz3532000",fontsize=16,color="green",shape="box"];44759 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.18 44759[label="primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000))) (Succ zzz3532000)",fontsize=16,color="magenta"];44759 -> 44816[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 44759 -> 44817[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 44760[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpNat (Succ zzz50050) (Succ zzz50060) == LT)",fontsize=16,color="black",shape="box"];44760 -> 44818[label="",style="solid", color="black", weight=3]; 130.29/78.18 44761[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpNat (Succ zzz50050) Zero == LT)",fontsize=16,color="black",shape="box"];44761 -> 44819[label="",style="solid", color="black", weight=3]; 130.29/78.18 44762[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpNat Zero (Succ zzz50060) == LT)",fontsize=16,color="black",shape="box"];44762 -> 44820[label="",style="solid", color="black", weight=3]; 130.29/78.18 44763[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];44763 -> 44821[label="",style="solid", color="black", weight=3]; 130.29/78.18 45667[label="Zero",fontsize=16,color="green",shape="box"];45668[label="Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)",fontsize=16,color="green",shape="box"];45668 -> 45716[label="",style="dashed", color="green", weight=3]; 130.29/78.18 45669[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpNat (Succ zzz51010) (Succ zzz51020) == LT)",fontsize=16,color="black",shape="box"];45669 -> 45717[label="",style="solid", color="black", weight=3]; 130.29/78.18 45670[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpNat (Succ zzz51010) Zero == LT)",fontsize=16,color="black",shape="box"];45670 -> 45718[label="",style="solid", color="black", weight=3]; 130.29/78.18 45671[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpNat Zero (Succ zzz51020) == LT)",fontsize=16,color="black",shape="box"];45671 -> 45719[label="",style="solid", color="black", weight=3]; 130.29/78.18 45672[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];45672 -> 45720[label="",style="solid", color="black", weight=3]; 130.29/78.18 29907[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];29907 -> 31097[label="",style="solid", color="black", weight=3]; 130.29/78.18 29908[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Pos Zero) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];29908 -> 31098[label="",style="solid", color="black", weight=3]; 130.29/78.18 29909[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz3420)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg zzz3420) zzz343 zzz344) == LT)",fontsize=16,color="burlywood",shape="box"];65442[label="zzz3420/Succ zzz34200",fontsize=10,color="white",style="solid",shape="box"];29909 -> 65442[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65442 -> 31099[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65443[label="zzz3420/Zero",fontsize=10,color="white",style="solid",shape="box"];29909 -> 65443[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65443 -> 31100[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 60493[label="zzz31",fontsize=16,color="green",shape="box"];60494[label="Neg Zero",fontsize=16,color="green",shape="box"];60495[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];60496[label="FiniteMap.Branch zzz340 zzz341 (Pos Zero) zzz343 zzz344",fontsize=16,color="green",shape="box"];60497[label="FiniteMap.Branch zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534",fontsize=16,color="green",shape="box"];63442[label="FiniteMap.mkVBalBranch (Neg zzz300) zzz31 FiniteMap.EmptyFM (FiniteMap.Branch zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];63442 -> 63578[label="",style="solid", color="black", weight=3]; 130.29/78.18 63443[label="FiniteMap.mkVBalBranch (Neg zzz300) zzz31 (FiniteMap.Branch zzz3340 zzz3341 zzz3342 zzz3343 zzz3344) (FiniteMap.Branch zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];63443 -> 63579[label="",style="solid", color="black", weight=3]; 130.29/78.18 44558 -> 60457[label="",style="dashed", color="red", weight=0]; 130.29/78.18 44558[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 (Pos Zero) zzz333 zzz334) (FiniteMap.Branch zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234)",fontsize=16,color="magenta"];44558 -> 60538[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 44558 -> 60539[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 44558 -> 60540[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 44558 -> 60541[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 44558 -> 60542[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 60498[label="zzz31",fontsize=16,color="green",shape="box"];60499[label="Neg Zero",fontsize=16,color="green",shape="box"];60500[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];60501[label="FiniteMap.Branch zzz340 zzz341 (Neg Zero) zzz343 zzz344",fontsize=16,color="green",shape="box"];60502[label="FiniteMap.Branch zzz3530 zzz3531 (Pos Zero) zzz3533 zzz3534",fontsize=16,color="green",shape="box"];46374 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.18 46374[label="primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000))) (Succ zzz3532000)) zzz3532000",fontsize=16,color="magenta"];46374 -> 46582[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 46374 -> 46583[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 46375[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpNat (Succ zzz51420) zzz5143 == LT)",fontsize=16,color="burlywood",shape="box"];65444[label="zzz5143/Succ zzz51430",fontsize=10,color="white",style="solid",shape="box"];46375 -> 65444[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65444 -> 46584[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65445[label="zzz5143/Zero",fontsize=10,color="white",style="solid",shape="box"];46375 -> 65445[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65445 -> 46585[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 46376[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpNat Zero zzz5143 == LT)",fontsize=16,color="burlywood",shape="box"];65446[label="zzz5143/Succ zzz51430",fontsize=10,color="white",style="solid",shape="box"];46376 -> 65446[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65446 -> 46586[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65447[label="zzz5143/Zero",fontsize=10,color="white",style="solid",shape="box"];46376 -> 65447[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65447 -> 46587[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 47415 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.18 47415[label="primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero",fontsize=16,color="magenta"];47415 -> 47555[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 47415 -> 47556[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 47416[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpNat (Succ zzz52580) zzz5259 == LT)",fontsize=16,color="burlywood",shape="box"];65448[label="zzz5259/Succ zzz52590",fontsize=10,color="white",style="solid",shape="box"];47416 -> 65448[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65448 -> 47557[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65449[label="zzz5259/Zero",fontsize=10,color="white",style="solid",shape="box"];47416 -> 65449[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65449 -> 47558[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 47417[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpNat Zero zzz5259 == LT)",fontsize=16,color="burlywood",shape="box"];65450[label="zzz5259/Succ zzz52590",fontsize=10,color="white",style="solid",shape="box"];47417 -> 65450[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65450 -> 47559[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65451[label="zzz5259/Zero",fontsize=10,color="white",style="solid",shape="box"];47417 -> 65451[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65451 -> 47560[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 46377 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.18 46377[label="primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000))) (Succ zzz3532000)) zzz3532000",fontsize=16,color="magenta"];46377 -> 46588[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 46377 -> 46589[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 47418 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.18 47418[label="primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero",fontsize=16,color="magenta"];47418 -> 47561[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 47418 -> 47562[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 60503[label="zzz31",fontsize=16,color="green",shape="box"];60504[label="Neg Zero",fontsize=16,color="green",shape="box"];60505[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];60506[label="FiniteMap.Branch zzz340 zzz341 (Pos Zero) zzz343 zzz344",fontsize=16,color="green",shape="box"];60507[label="FiniteMap.Branch zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534",fontsize=16,color="green",shape="box"];44559 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.18 44559[label="FiniteMap.mkBalBranch zzz330 zzz331 zzz333 (FiniteMap.mkVBalBranch (Neg zzz300) zzz31 zzz334 (FiniteMap.Branch zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234))",fontsize=16,color="magenta"];44559 -> 63193[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 44559 -> 63194[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 44559 -> 63195[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 44559 -> 63196[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 44560[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 True",fontsize=16,color="black",shape="box"];44560 -> 44613[label="",style="solid", color="black", weight=3]; 130.29/78.18 60508[label="zzz31",fontsize=16,color="green",shape="box"];60509[label="Neg Zero",fontsize=16,color="green",shape="box"];60510[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];60511[label="FiniteMap.Branch zzz340 zzz341 (Neg Zero) zzz343 zzz344",fontsize=16,color="green",shape="box"];60512[label="FiniteMap.Branch zzz3530 zzz3531 (Neg Zero) zzz3533 zzz3534",fontsize=16,color="green",shape="box"];30642[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ Zero) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];30642 -> 31274[label="",style="solid", color="black", weight=3]; 130.29/78.18 30643[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos zzz52320) zzz5233 zzz5234 (primCmpInt (Pos Zero) (Pos zzz52320) == LT)",fontsize=16,color="burlywood",shape="box"];65452[label="zzz52320/Succ zzz523200",fontsize=10,color="white",style="solid",shape="box"];30643 -> 65452[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65452 -> 31275[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65453[label="zzz52320/Zero",fontsize=10,color="white",style="solid",shape="box"];30643 -> 65453[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65453 -> 31276[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 30644[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (primCmpInt (Pos Zero) (Neg zzz52320) == LT)",fontsize=16,color="burlywood",shape="box"];65454[label="zzz52320/Succ zzz523200",fontsize=10,color="white",style="solid",shape="box"];30644 -> 65454[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65454 -> 31277[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65455[label="zzz52320/Zero",fontsize=10,color="white",style="solid",shape="box"];30644 -> 65455[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65455 -> 31278[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 30645[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ Zero) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];30645 -> 31279[label="",style="solid", color="black", weight=3]; 130.29/78.18 30646[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos zzz52320) zzz5233 zzz5234 (primCmpInt (Neg Zero) (Pos zzz52320) == LT)",fontsize=16,color="burlywood",shape="box"];65456[label="zzz52320/Succ zzz523200",fontsize=10,color="white",style="solid",shape="box"];30646 -> 65456[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65456 -> 31280[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65457[label="zzz52320/Zero",fontsize=10,color="white",style="solid",shape="box"];30646 -> 65457[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65457 -> 31281[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 30647[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (primCmpInt (Neg Zero) (Neg zzz52320) == LT)",fontsize=16,color="burlywood",shape="box"];65458[label="zzz52320/Succ zzz523200",fontsize=10,color="white",style="solid",shape="box"];30647 -> 65458[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65458 -> 31282[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65459[label="zzz52320/Zero",fontsize=10,color="white",style="solid",shape="box"];30647 -> 65459[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65459 -> 31283[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 30698[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (primCmpNat (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000)) zzz2502000) zzz34200000 == LT)",fontsize=16,color="black",shape="box"];30698 -> 31363[label="",style="solid", color="black", weight=3]; 130.29/78.18 30699[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (GT == LT)",fontsize=16,color="black",shape="box"];30699 -> 31364[label="",style="solid", color="black", weight=3]; 130.29/78.18 30700[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344)",fontsize=16,color="black",shape="box"];30700 -> 31365[label="",style="solid", color="black", weight=3]; 130.29/78.18 30701[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) (Succ zzz34200000) == LT)",fontsize=16,color="black",shape="box"];30701 -> 31366[label="",style="solid", color="black", weight=3]; 130.29/78.18 30702[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero == LT)",fontsize=16,color="black",shape="box"];30702 -> 31367[label="",style="solid", color="black", weight=3]; 130.29/78.18 30703[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344)",fontsize=16,color="black",shape="box"];30703 -> 31368[label="",style="solid", color="black", weight=3]; 130.29/78.18 30704[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];30704 -> 31369[label="",style="solid", color="black", weight=3]; 130.29/78.18 30705[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos Zero)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];30705 -> 31370[label="",style="solid", color="black", weight=3]; 130.29/78.18 30706[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];30706 -> 31371[label="",style="solid", color="black", weight=3]; 130.29/78.18 30707[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];30707 -> 31372[label="",style="solid", color="black", weight=3]; 130.29/78.18 30709[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz34200 zzz34200)) zzz34200)) zzz34200))) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];30709 -> 31374[label="",style="solid", color="black", weight=3]; 130.29/78.18 30711[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (primCmpNat zzz34200000 (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000)) zzz2502000) == LT)",fontsize=16,color="burlywood",shape="box"];65460[label="zzz34200000/Succ zzz342000000",fontsize=10,color="white",style="solid",shape="box"];30711 -> 65460[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65460 -> 31376[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 65461[label="zzz34200000/Zero",fontsize=10,color="white",style="solid",shape="box"];30711 -> 65461[label="",style="solid", color="burlywood", weight=9]; 130.29/78.18 65461 -> 31377[label="",style="solid", color="burlywood", weight=3]; 130.29/78.18 30712[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ Zero)))) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];30712 -> 31378[label="",style="solid", color="black", weight=3]; 130.29/78.18 30713[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (primCmpNat (Succ zzz34200000) (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) == LT)",fontsize=16,color="black",shape="box"];30713 -> 31379[label="",style="solid", color="black", weight=3]; 130.29/78.18 30714[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpNat Zero (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) == LT)",fontsize=16,color="black",shape="box"];30714 -> 31380[label="",style="solid", color="black", weight=3]; 130.29/78.18 30715 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.18 30715[label="FiniteMap.mkBalBranch zzz340 zzz341 (FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504) zzz343) zzz344",fontsize=16,color="magenta"];30715 -> 63197[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 30715 -> 63198[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 30715 -> 63199[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 30715 -> 63200[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 30716 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.18 30716[label="FiniteMap.mkBalBranch zzz340 zzz341 (FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504) zzz343) zzz344",fontsize=16,color="magenta"];30716 -> 63201[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 30716 -> 63202[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 30716 -> 63203[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 30716 -> 63204[label="",style="dashed", color="magenta", weight=3]; 130.29/78.18 30718[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat zzz34200 zzz34200)) zzz34200))) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];30718 -> 31390[label="",style="solid", color="black", weight=3]; 130.29/78.19 62865[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Pos (Succ zzz635500)) zzz6354 == GT)",fontsize=16,color="burlywood",shape="box"];65462[label="zzz6354/Pos zzz63540",fontsize=10,color="white",style="solid",shape="box"];62865 -> 65462[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65462 -> 62873[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 65463[label="zzz6354/Neg zzz63540",fontsize=10,color="white",style="solid",shape="box"];62865 -> 65463[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65463 -> 62874[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 62866[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Pos Zero) zzz6354 == GT)",fontsize=16,color="burlywood",shape="box"];65464[label="zzz6354/Pos zzz63540",fontsize=10,color="white",style="solid",shape="box"];62866 -> 65464[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65464 -> 62875[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 65465[label="zzz6354/Neg zzz63540",fontsize=10,color="white",style="solid",shape="box"];62866 -> 65465[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65465 -> 62876[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 62867[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Neg (Succ zzz635500)) zzz6354 == GT)",fontsize=16,color="burlywood",shape="box"];65466[label="zzz6354/Pos zzz63540",fontsize=10,color="white",style="solid",shape="box"];62867 -> 65466[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65466 -> 62877[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 65467[label="zzz6354/Neg zzz63540",fontsize=10,color="white",style="solid",shape="box"];62867 -> 65467[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65467 -> 62878[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 62868[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Neg Zero) zzz6354 == GT)",fontsize=16,color="burlywood",shape="box"];65468[label="zzz6354/Pos zzz63540",fontsize=10,color="white",style="solid",shape="box"];62868 -> 65468[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65468 -> 62879[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 65469[label="zzz6354/Neg zzz63540",fontsize=10,color="white",style="solid",shape="box"];62868 -> 65469[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65469 -> 62880[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 64275[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos (Succ zzz644300)) (primMulInt FiniteMap.sIZE_RATIO zzz6442) == GT)",fontsize=16,color="black",shape="box"];64275 -> 64279[label="",style="solid", color="black", weight=3]; 130.29/78.19 64276[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (primMulInt FiniteMap.sIZE_RATIO zzz6442) == GT)",fontsize=16,color="black",shape="box"];64276 -> 64280[label="",style="solid", color="black", weight=3]; 130.29/78.19 64277[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg (Succ zzz644300)) (primMulInt FiniteMap.sIZE_RATIO zzz6442) == GT)",fontsize=16,color="black",shape="box"];64277 -> 64281[label="",style="solid", color="black", weight=3]; 130.29/78.19 64278[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (primMulInt FiniteMap.sIZE_RATIO zzz6442) == GT)",fontsize=16,color="black",shape="box"];64278 -> 64282[label="",style="solid", color="black", weight=3]; 130.29/78.19 30746[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ zzz426200)) zzz4263 zzz4264 (primCmpNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200))) (Succ zzz426200) == LT)",fontsize=16,color="black",shape="box"];30746 -> 31457[label="",style="solid", color="black", weight=3]; 130.29/78.19 30747[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200))) Zero == LT)",fontsize=16,color="black",shape="box"];30747 -> 31458[label="",style="solid", color="black", weight=3]; 130.29/78.19 30748[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 False",fontsize=16,color="black",shape="box"];30748 -> 31459[label="",style="solid", color="black", weight=3]; 130.29/78.19 30749[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (Pos 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Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];30751 -> 31462[label="",style="solid", color="black", weight=3]; 130.29/78.19 30752[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos zzz42620) zzz4263 zzz4264 True",fontsize=16,color="black",shape="box"];30752 -> 31463[label="",style="solid", color="black", weight=3]; 130.29/78.19 30753[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (primCmpNat (Succ zzz426200) (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200))) == LT)",fontsize=16,color="black",shape="box"];30753 -> 31464[label="",style="solid", color="black", weight=3]; 130.29/78.19 30754[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpNat Zero (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200))) == LT)",fontsize=16,color="black",shape="box"];30754 -> 31465[label="",style="solid", color="black", weight=3]; 130.29/78.19 30755[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];30755 -> 31466[label="",style="solid", color="black", weight=3]; 130.29/78.19 30756 -> 44103[label="",style="dashed", color="red", weight=0]; 130.29/78.19 30756[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz426200))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) == LT)",fontsize=16,color="magenta"];30756 -> 44203[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 30756 -> 44204[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 30756 -> 44205[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 30756 -> 44206[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 30756 -> 44207[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 30756 -> 44208[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 30756 -> 44209[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 30757[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];30757 -> 31468[label="",style="solid", color="black", weight=3]; 130.29/78.19 44816[label="Succ zzz3532000",fontsize=16,color="green",shape="box"];44817[label="Succ (primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000))",fontsize=16,color="green",shape="box"];44817 -> 44882[label="",style="dashed", color="green", weight=3]; 130.29/78.19 44818 -> 44629[label="",style="dashed", color="red", weight=0]; 130.29/78.19 44818[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpNat zzz50050 zzz50060 == LT)",fontsize=16,color="magenta"];44818 -> 44883[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 44818 -> 44884[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 44819[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (GT == LT)",fontsize=16,color="black",shape="box"];44819 -> 44885[label="",style="solid", color="black", weight=3]; 130.29/78.19 44820[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (LT == LT)",fontsize=16,color="black",shape="box"];44820 -> 44886[label="",style="solid", color="black", weight=3]; 130.29/78.19 44821[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (EQ == LT)",fontsize=16,color="black",shape="box"];44821 -> 44887[label="",style="solid", color="black", weight=3]; 130.29/78.19 45716 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.19 45716[label="primPlusNat (Succ (primPlusNat Zero Zero)) Zero",fontsize=16,color="magenta"];45716 -> 45763[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 45716 -> 45764[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 45717 -> 45509[label="",style="dashed", color="red", weight=0]; 130.29/78.19 45717[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 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45768[label="",style="solid", color="black", weight=3]; 130.29/78.19 45720[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (EQ == LT)",fontsize=16,color="black",shape="box"];45720 -> 45769[label="",style="solid", color="black", weight=3]; 130.29/78.19 31097[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31097 -> 31581[label="",style="solid", color="black", weight=3]; 130.29/78.19 31098[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos Zero)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31098 -> 31582[label="",style="solid", color="black", weight=3]; 130.29/78.19 31099[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31099 -> 31583[label="",style="solid", color="black", weight=3]; 130.29/78.19 31100[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31100 -> 31584[label="",style="solid", color="black", weight=3]; 130.29/78.19 63578[label="FiniteMap.mkVBalBranch5 (Neg zzz300) zzz31 FiniteMap.EmptyFM (FiniteMap.Branch zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];63578 -> 63608[label="",style="solid", color="black", weight=3]; 130.29/78.19 63579 -> 11068[label="",style="dashed", color="red", weight=0]; 130.29/78.19 63579[label="FiniteMap.mkVBalBranch3 (Neg zzz300) zzz31 (FiniteMap.Branch zzz3340 zzz3341 zzz3342 zzz3343 zzz3344) (FiniteMap.Branch zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234)",fontsize=16,color="magenta"];63579 -> 63609[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 63579 -> 63610[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 63579 -> 63611[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 63579 -> 63612[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 63579 -> 63613[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 63579 -> 63614[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 60538[label="zzz31",fontsize=16,color="green",shape="box"];60539[label="Neg zzz300",fontsize=16,color="green",shape="box"];60540[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];60541[label="FiniteMap.Branch zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234",fontsize=16,color="green",shape="box"];60542[label="FiniteMap.Branch zzz330 zzz331 (Pos Zero) zzz333 zzz334",fontsize=16,color="green",shape="box"];46582[label="zzz3532000",fontsize=16,color="green",shape="box"];46583 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.19 46583[label="primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000))) (Succ zzz3532000)",fontsize=16,color="magenta"];46583 -> 46653[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 46583 -> 46654[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 46584[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpNat (Succ zzz51420) (Succ zzz51430) == LT)",fontsize=16,color="black",shape="box"];46584 -> 46655[label="",style="solid", color="black", weight=3]; 130.29/78.19 46585[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpNat (Succ zzz51420) Zero == LT)",fontsize=16,color="black",shape="box"];46585 -> 46656[label="",style="solid", color="black", weight=3]; 130.29/78.19 46586[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpNat Zero (Succ zzz51430) == LT)",fontsize=16,color="black",shape="box"];46586 -> 46657[label="",style="solid", color="black", weight=3]; 130.29/78.19 46587[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];46587 -> 46658[label="",style="solid", color="black", weight=3]; 130.29/78.19 47555[label="Zero",fontsize=16,color="green",shape="box"];47556[label="Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)",fontsize=16,color="green",shape="box"];47556 -> 47653[label="",style="dashed", color="green", weight=3]; 130.29/78.19 47557[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpNat (Succ zzz52580) (Succ zzz52590) == LT)",fontsize=16,color="black",shape="box"];47557 -> 47654[label="",style="solid", color="black", weight=3]; 130.29/78.19 47558[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpNat (Succ zzz52580) Zero == LT)",fontsize=16,color="black",shape="box"];47558 -> 47655[label="",style="solid", color="black", weight=3]; 130.29/78.19 47559[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpNat Zero (Succ zzz52590) == LT)",fontsize=16,color="black",shape="box"];47559 -> 47656[label="",style="solid", color="black", weight=3]; 130.29/78.19 47560[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];47560 -> 47657[label="",style="solid", color="black", weight=3]; 130.29/78.19 46588[label="zzz3532000",fontsize=16,color="green",shape="box"];46589 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.19 46589[label="primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000))) (Succ zzz3532000)",fontsize=16,color="magenta"];46589 -> 46659[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 46589 -> 46660[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 47561[label="Zero",fontsize=16,color="green",shape="box"];47562[label="Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)",fontsize=16,color="green",shape="box"];47562 -> 47658[label="",style="dashed", color="green", weight=3]; 130.29/78.19 63193[label="zzz330",fontsize=16,color="green",shape="box"];63194 -> 63190[label="",style="dashed", color="red", weight=0]; 130.29/78.19 63194[label="FiniteMap.mkVBalBranch (Neg zzz300) zzz31 zzz334 (FiniteMap.Branch zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234)",fontsize=16,color="magenta"];63195[label="zzz333",fontsize=16,color="green",shape="box"];63196[label="zzz331",fontsize=16,color="green",shape="box"];44613 -> 60457[label="",style="dashed", color="red", weight=0]; 130.29/78.19 44613[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334) (FiniteMap.Branch zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234)",fontsize=16,color="magenta"];44613 -> 60563[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 44613 -> 60564[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 44613 -> 60565[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 44613 -> 60566[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 44613 -> 60567[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 31274[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat Zero (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];31274 -> 31645[label="",style="solid", color="black", weight=3]; 130.29/78.19 31275[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Pos Zero) (Pos (Succ zzz523200)) == LT)",fontsize=16,color="black",shape="box"];31275 -> 31646[label="",style="solid", color="black", weight=3]; 130.29/78.19 31276[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];31276 -> 31647[label="",style="solid", color="black", weight=3]; 130.29/78.19 31277[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Pos Zero) (Neg (Succ zzz523200)) == LT)",fontsize=16,color="black",shape="box"];31277 -> 31648[label="",style="solid", color="black", weight=3]; 130.29/78.19 31278[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];31278 -> 31649[label="",style="solid", color="black", weight=3]; 130.29/78.19 31279[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat Zero (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];31279 -> 31650[label="",style="solid", color="black", weight=3]; 130.29/78.19 31280[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg Zero) (Pos (Succ zzz523200)) == LT)",fontsize=16,color="black",shape="box"];31280 -> 31651[label="",style="solid", color="black", weight=3]; 130.29/78.19 31281[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];31281 -> 31652[label="",style="solid", color="black", weight=3]; 130.29/78.19 31282[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg Zero) (Neg (Succ zzz523200)) == LT)",fontsize=16,color="black",shape="box"];31282 -> 31653[label="",style="solid", color="black", weight=3]; 130.29/78.19 31283[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];31283 -> 31654[label="",style="solid", color="black", weight=3]; 130.29/78.19 31363[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (primCmpNat (primPlusNat (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000)) zzz2502000))) zzz2502000) zzz34200000 == LT)",fontsize=16,color="burlywood",shape="box"];65470[label="zzz2502000/Succ zzz25020000",fontsize=10,color="white",style="solid",shape="box"];31363 -> 65470[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65470 -> 31966[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 65471[label="zzz2502000/Zero",fontsize=10,color="white",style="solid",shape="box"];31363 -> 65471[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65471 -> 31967[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 31364[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];31364 -> 31968[label="",style="solid", color="black", weight=3]; 130.29/78.19 31365[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31365 -> 31969[label="",style="solid", color="black", weight=3]; 130.29/78.19 31366[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (primCmpNat (primPlusNat (Succ (primPlusNat Zero Zero)) Zero) zzz34200000 == LT)",fontsize=16,color="black",shape="box"];31366 -> 31970[label="",style="solid", color="black", weight=3]; 130.29/78.19 31367[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (GT == LT)",fontsize=16,color="black",shape="box"];31367 -> 31971[label="",style="solid", color="black", weight=3]; 130.29/78.19 31368[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31368 -> 31972[label="",style="solid", color="black", weight=3]; 130.29/78.19 31369[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31369 -> 31973[label="",style="solid", color="black", weight=3]; 130.29/78.19 31370[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31370 -> 31974[label="",style="solid", color="black", weight=3]; 130.29/78.19 31371[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31371 -> 31975[label="",style="solid", color="black", weight=3]; 130.29/78.19 31372[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31372 -> 31976[label="",style="solid", color="black", weight=3]; 130.29/78.19 31374[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz34200 zzz34200)) zzz34200)) zzz34200)) zzz34200)))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31374 -> 31978[label="",style="solid", color="black", weight=3]; 130.29/78.19 31376[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (primCmpNat (Succ zzz342000000) (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000)) zzz2502000) == LT)",fontsize=16,color="black",shape="box"];31376 -> 31980[label="",style="solid", color="black", weight=3]; 130.29/78.19 31377[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpNat Zero (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000))) (Succ zzz2502000)) zzz2502000) == LT)",fontsize=16,color="black",shape="box"];31377 -> 31981[label="",style="solid", color="black", weight=3]; 130.29/78.19 31378[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ Zero)))) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];31378 -> 31982[label="",style="solid", color="black", weight=3]; 130.29/78.19 31379[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (primCmpNat zzz34200000 (primPlusNat (Succ (primPlusNat Zero Zero)) Zero) == LT)",fontsize=16,color="burlywood",shape="box"];65472[label="zzz34200000/Succ zzz342000000",fontsize=10,color="white",style="solid",shape="box"];31379 -> 65472[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65472 -> 31983[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 65473[label="zzz34200000/Zero",fontsize=10,color="white",style="solid",shape="box"];31379 -> 65473[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65473 -> 31984[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 31380[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ Zero)))) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];31380 -> 31985[label="",style="solid", color="black", weight=3]; 130.29/78.19 63197[label="zzz340",fontsize=16,color="green",shape="box"];63198[label="zzz344",fontsize=16,color="green",shape="box"];63199 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.19 63199[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504) zzz343",fontsize=16,color="magenta"];63199 -> 63444[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 63199 -> 63445[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 63200[label="zzz341",fontsize=16,color="green",shape="box"];63201[label="zzz340",fontsize=16,color="green",shape="box"];63202[label="zzz344",fontsize=16,color="green",shape="box"];63203 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.19 63203[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504) zzz343",fontsize=16,color="magenta"];63203 -> 63446[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 63203 -> 63447[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 63204[label="zzz341",fontsize=16,color="green",shape="box"];31390[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz34200 zzz34200)) zzz34200)) zzz34200))) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31390 -> 31991[label="",style="solid", color="black", weight=3]; 130.29/78.19 62873[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Pos (Succ zzz635500)) (Pos zzz63540) == GT)",fontsize=16,color="black",shape="box"];62873 -> 62885[label="",style="solid", color="black", weight=3]; 130.29/78.19 62874[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Pos (Succ zzz635500)) (Neg zzz63540) == GT)",fontsize=16,color="black",shape="box"];62874 -> 62886[label="",style="solid", color="black", weight=3]; 130.29/78.19 62875[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Pos Zero) (Pos zzz63540) == GT)",fontsize=16,color="burlywood",shape="box"];65474[label="zzz63540/Succ zzz635400",fontsize=10,color="white",style="solid",shape="box"];62875 -> 65474[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65474 -> 62887[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 65475[label="zzz63540/Zero",fontsize=10,color="white",style="solid",shape="box"];62875 -> 65475[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65475 -> 62888[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 62876[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Pos Zero) (Neg zzz63540) == GT)",fontsize=16,color="burlywood",shape="box"];65476[label="zzz63540/Succ zzz635400",fontsize=10,color="white",style="solid",shape="box"];62876 -> 65476[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65476 -> 62889[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 65477[label="zzz63540/Zero",fontsize=10,color="white",style="solid",shape="box"];62876 -> 65477[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65477 -> 62890[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 62877[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Neg (Succ zzz635500)) (Pos zzz63540) == GT)",fontsize=16,color="black",shape="box"];62877 -> 62891[label="",style="solid", color="black", weight=3]; 130.29/78.19 62878[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Neg (Succ zzz635500)) (Neg zzz63540) == GT)",fontsize=16,color="black",shape="box"];62878 -> 62892[label="",style="solid", color="black", weight=3]; 130.29/78.19 62879[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Neg Zero) (Pos zzz63540) == GT)",fontsize=16,color="burlywood",shape="box"];65478[label="zzz63540/Succ zzz635400",fontsize=10,color="white",style="solid",shape="box"];62879 -> 65478[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65478 -> 62893[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 65479[label="zzz63540/Zero",fontsize=10,color="white",style="solid",shape="box"];62879 -> 65479[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65479 -> 62894[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 62880[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Neg Zero) (Neg zzz63540) == GT)",fontsize=16,color="burlywood",shape="box"];65480[label="zzz63540/Succ zzz635400",fontsize=10,color="white",style="solid",shape="box"];62880 -> 65480[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65480 -> 62895[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 65481[label="zzz63540/Zero",fontsize=10,color="white",style="solid",shape="box"];62880 -> 65481[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65481 -> 62896[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 64279[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos (Succ zzz644300)) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz6442) == GT)",fontsize=16,color="burlywood",shape="box"];65482[label="zzz6442/Pos zzz64420",fontsize=10,color="white",style="solid",shape="box"];64279 -> 65482[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65482 -> 64283[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 65483[label="zzz6442/Neg zzz64420",fontsize=10,color="white",style="solid",shape="box"];64279 -> 65483[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65483 -> 64284[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 64280[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz6442) == GT)",fontsize=16,color="burlywood",shape="box"];65484[label="zzz6442/Pos zzz64420",fontsize=10,color="white",style="solid",shape="box"];64280 -> 65484[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65484 -> 64285[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 65485[label="zzz6442/Neg zzz64420",fontsize=10,color="white",style="solid",shape="box"];64280 -> 65485[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65485 -> 64286[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 64281[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg (Succ zzz644300)) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz6442) == GT)",fontsize=16,color="burlywood",shape="box"];65486[label="zzz6442/Pos zzz64420",fontsize=10,color="white",style="solid",shape="box"];64281 -> 65486[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65486 -> 64287[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 65487[label="zzz6442/Neg zzz64420",fontsize=10,color="white",style="solid",shape="box"];64281 -> 65487[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65487 -> 64288[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 64282[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz6442) == GT)",fontsize=16,color="burlywood",shape="box"];65488[label="zzz6442/Pos zzz64420",fontsize=10,color="white",style="solid",shape="box"];64282 -> 65488[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65488 -> 64289[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 65489[label="zzz6442/Neg zzz64420",fontsize=10,color="white",style="solid",shape="box"];64282 -> 65489[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65489 -> 64290[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 31457[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ zzz426200)) zzz4263 zzz4264 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)) zzz426200 == LT)",fontsize=16,color="burlywood",shape="box"];65490[label="zzz426200/Succ zzz4262000",fontsize=10,color="white",style="solid",shape="box"];31457 -> 65490[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65490 -> 32099[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 65491[label="zzz426200/Zero",fontsize=10,color="white",style="solid",shape="box"];31457 -> 65491[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65491 -> 32100[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 31458[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (GT == LT)",fontsize=16,color="black",shape="box"];31458 -> 32101[label="",style="solid", color="black", weight=3]; 130.29/78.19 31459[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 < FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264)",fontsize=16,color="black",shape="box"];31459 -> 32102[label="",style="solid", color="black", weight=3]; 130.29/78.19 31460[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Pos Zero) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];31460 -> 32103[label="",style="solid", color="black", weight=3]; 130.29/78.19 44089[label="zzz426200",fontsize=16,color="green",shape="box"];31462[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Pos Zero) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];31462 -> 32105[label="",style="solid", color="black", weight=3]; 130.29/78.19 31463 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.19 31463[label="FiniteMap.mkBalBranch zzz4260 zzz4261 (FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334) zzz4263) zzz4264",fontsize=16,color="magenta"];31463 -> 63205[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 31463 -> 63206[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 31463 -> 63207[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 31463 -> 63208[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 31464[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (primCmpNat zzz426200 (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)) == LT)",fontsize=16,color="burlywood",shape="box"];65492[label="zzz426200/Succ zzz4262000",fontsize=10,color="white",style="solid",shape="box"];31464 -> 65492[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65492 -> 32110[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 65493[label="zzz426200/Zero",fontsize=10,color="white",style="solid",shape="box"];31464 -> 65493[label="",style="solid", color="burlywood", weight=9]; 130.29/78.19 65493 -> 32111[label="",style="solid", color="burlywood", weight=3]; 130.29/78.19 31465[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (LT == LT)",fontsize=16,color="black",shape="box"];31465 -> 32112[label="",style="solid", color="black", weight=3]; 130.29/78.19 31466[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];31466 -> 32113[label="",style="solid", color="black", weight=3]; 130.29/78.19 44203[label="zzz4260",fontsize=16,color="green",shape="box"];44204[label="Succ zzz3000",fontsize=16,color="green",shape="box"];44205[label="zzz4263",fontsize=16,color="green",shape="box"];44206[label="zzz426200",fontsize=16,color="green",shape="box"];44207[label="zzz4261",fontsize=16,color="green",shape="box"];44208 -> 43358[label="",style="dashed", color="red", weight=0]; 130.29/78.19 44208[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz426200)",fontsize=16,color="magenta"];44208 -> 44342[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 44209[label="zzz4264",fontsize=16,color="green",shape="box"];31468[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];31468 -> 32115[label="",style="solid", color="black", weight=3]; 130.29/78.19 44882 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.19 44882[label="primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000)",fontsize=16,color="magenta"];44882 -> 44915[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 44882 -> 44916[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 44883[label="zzz50050",fontsize=16,color="green",shape="box"];44884[label="zzz50060",fontsize=16,color="green",shape="box"];44885[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 False",fontsize=16,color="black",shape="triangle"];44885 -> 44917[label="",style="solid", color="black", weight=3]; 130.29/78.19 44886[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 True",fontsize=16,color="black",shape="box"];44886 -> 44918[label="",style="solid", color="black", weight=3]; 130.29/78.19 44887 -> 44885[label="",style="dashed", color="red", weight=0]; 130.29/78.19 44887[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 False",fontsize=16,color="magenta"];45763[label="Zero",fontsize=16,color="green",shape="box"];45764[label="Succ (primPlusNat Zero Zero)",fontsize=16,color="green",shape="box"];45764 -> 45962[label="",style="dashed", color="green", weight=3]; 130.29/78.19 45765[label="zzz51020",fontsize=16,color="green",shape="box"];45766[label="zzz51010",fontsize=16,color="green",shape="box"];45767[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 False",fontsize=16,color="black",shape="triangle"];45767 -> 45963[label="",style="solid", color="black", weight=3]; 130.29/78.19 45768[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 True",fontsize=16,color="black",shape="box"];45768 -> 45964[label="",style="solid", color="black", weight=3]; 130.29/78.19 45769 -> 45767[label="",style="dashed", color="red", weight=0]; 130.29/78.19 45769[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 False",fontsize=16,color="magenta"];31581[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31581 -> 32352[label="",style="solid", color="black", weight=3]; 130.29/78.19 31582[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31582 -> 32353[label="",style="solid", color="black", weight=3]; 130.29/78.19 31583 -> 49578[label="",style="dashed", color="red", weight=0]; 130.29/78.19 31583[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="magenta"];31583 -> 49579[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 31583 -> 49580[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 31583 -> 49581[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 31583 -> 49582[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 31583 -> 49583[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 31583 -> 49584[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 31583 -> 49585[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 31583 -> 49586[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 31583 -> 49587[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 31583 -> 49588[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 31583 -> 49589[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 31583 -> 49590[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 31584[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31584 -> 32355[label="",style="solid", color="black", weight=3]; 130.29/78.19 63608 -> 12428[label="",style="dashed", color="red", weight=0]; 130.29/78.19 63608[label="FiniteMap.addToFM (FiniteMap.Branch zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) (Neg zzz300) zzz31",fontsize=16,color="magenta"];63608 -> 63662[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 63608 -> 63663[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 63608 -> 63664[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 63608 -> 63665[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 63608 -> 63666[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 63609[label="zzz3342",fontsize=16,color="green",shape="box"];63610[label="zzz3344",fontsize=16,color="green",shape="box"];63611[label="Neg (Succ 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46746[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 46655 -> 46747[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 46656[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (GT == LT)",fontsize=16,color="black",shape="box"];46656 -> 46748[label="",style="solid", color="black", weight=3]; 130.29/78.19 46657[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (LT == LT)",fontsize=16,color="black",shape="box"];46657 -> 46749[label="",style="solid", color="black", weight=3]; 130.29/78.19 46658[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (EQ == LT)",fontsize=16,color="black",shape="box"];46658 -> 46750[label="",style="solid", color="black", weight=3]; 130.29/78.19 47653 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.19 47653[label="primPlusNat (Succ (primPlusNat Zero Zero)) Zero",fontsize=16,color="magenta"];47653 -> 47747[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 47653 -> 47748[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 47654 -> 47219[label="",style="dashed", color="red", weight=0]; 130.29/78.19 47654[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpNat zzz52580 zzz52590 == LT)",fontsize=16,color="magenta"];47654 -> 47749[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 47654 -> 47750[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 47655[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (GT == LT)",fontsize=16,color="black",shape="box"];47655 -> 47751[label="",style="solid", color="black", weight=3]; 130.29/78.19 47656[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (LT == LT)",fontsize=16,color="black",shape="box"];47656 -> 47752[label="",style="solid", color="black", weight=3]; 130.29/78.19 47657[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (EQ == LT)",fontsize=16,color="black",shape="box"];47657 -> 47753[label="",style="solid", color="black", weight=3]; 130.29/78.19 46659[label="Succ zzz3532000",fontsize=16,color="green",shape="box"];46660[label="Succ (primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000))",fontsize=16,color="green",shape="box"];46660 -> 46751[label="",style="dashed", color="green", weight=3]; 130.29/78.19 47658 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.19 47658[label="primPlusNat (Succ (primPlusNat Zero Zero)) Zero",fontsize=16,color="magenta"];47658 -> 47754[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 47658 -> 47755[label="",style="dashed", color="magenta", weight=3]; 130.29/78.19 60563[label="zzz31",fontsize=16,color="green",shape="box"];60564[label="Neg zzz300",fontsize=16,color="green",shape="box"];60565[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];60566[label="FiniteMap.Branch zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234",fontsize=16,color="green",shape="box"];60567[label="FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334",fontsize=16,color="green",shape="box"];31645[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat Zero (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];31645 -> 32573[label="",style="solid", color="black", weight=3]; 130.29/78.20 31646[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ zzz523200)) zzz5233 zzz5234 (primCmpNat Zero (Succ zzz523200) == LT)",fontsize=16,color="black",shape="box"];31646 -> 32574[label="",style="solid", color="black", weight=3]; 130.29/78.20 31647[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (EQ == LT)",fontsize=16,color="black",shape="box"];31647 -> 32575[label="",style="solid", color="black", weight=3]; 130.29/78.20 31648[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (GT == LT)",fontsize=16,color="black",shape="box"];31648 -> 32576[label="",style="solid", color="black", weight=3]; 130.29/78.20 31649[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (EQ == LT)",fontsize=16,color="black",shape="box"];31649 -> 32577[label="",style="solid", color="black", weight=3]; 130.29/78.20 31650[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat Zero (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];31650 -> 32578[label="",style="solid", color="black", weight=3]; 130.29/78.20 31651[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ zzz523200)) zzz5233 zzz5234 (LT == LT)",fontsize=16,color="black",shape="box"];31651 -> 32579[label="",style="solid", color="black", weight=3]; 130.29/78.20 31652[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (EQ == LT)",fontsize=16,color="black",shape="box"];31652 -> 32580[label="",style="solid", color="black", weight=3]; 130.29/78.20 31653[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpNat (Succ zzz523200) Zero == LT)",fontsize=16,color="black",shape="box"];31653 -> 32581[label="",style="solid", color="black", weight=3]; 130.29/78.20 31654[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (EQ == LT)",fontsize=16,color="black",shape="box"];31654 -> 32582[label="",style="solid", color="black", weight=3]; 130.29/78.20 31966[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ (Succ (Succ zzz25020000)))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ (Succ zzz25020000)))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (primCmpNat (primPlusNat (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ zzz25020000)) (Succ (Succ zzz25020000)))) (Succ (Succ zzz25020000))) (Succ zzz25020000)))) (Succ zzz25020000)) zzz34200000 == LT)",fontsize=16,color="black",shape="box"];31966 -> 32583[label="",style="solid", color="black", weight=3]; 130.29/78.20 31967[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ (Succ Zero))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ Zero))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (primCmpNat (primPlusNat (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ Zero) (Succ Zero))) (Succ Zero)) Zero))) Zero) zzz34200000 == LT)",fontsize=16,color="black",shape="box"];31967 -> 32584[label="",style="solid", color="black", weight=3]; 130.29/78.20 31968[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344)",fontsize=16,color="black",shape="box"];31968 -> 32585[label="",style="solid", color="black", weight=3]; 130.29/78.20 31969[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31969 -> 32586[label="",style="solid", color="black", weight=3]; 130.29/78.20 31970[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (primCmpNat (Succ (primPlusNat Zero Zero)) zzz34200000 == LT)",fontsize=16,color="burlywood",shape="box"];65494[label="zzz34200000/Succ zzz342000000",fontsize=10,color="white",style="solid",shape="box"];31970 -> 65494[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65494 -> 32587[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65495[label="zzz34200000/Zero",fontsize=10,color="white",style="solid",shape="box"];31970 -> 65495[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65495 -> 32588[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 31971[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];31971 -> 32589[label="",style="solid", color="black", weight=3]; 130.29/78.20 31972[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31972 -> 32590[label="",style="solid", color="black", weight=3]; 130.29/78.20 31973[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos (Succ Zero))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31973 -> 32591[label="",style="solid", color="black", weight=3]; 130.29/78.20 31974[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31974 -> 32592[label="",style="solid", color="black", weight=3]; 130.29/78.20 31975[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primMulNat (Succ (Succ (Succ Zero))) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31975 -> 32593[label="",style="solid", color="black", weight=3]; 130.29/78.20 31976[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];31976 -> 32594[label="",style="solid", color="black", weight=3]; 130.29/78.20 31978[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz34200 zzz34200)) zzz34200)) zzz34200)) zzz34200)))) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];31978 -> 32596[label="",style="solid", color="black", weight=3]; 130.29/78.20 31980[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (primCmpNat (Succ zzz342000000) (primPlusNat (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000)) zzz2502000))) zzz2502000) == LT)",fontsize=16,color="burlywood",shape="box"];65496[label="zzz2502000/Succ zzz25020000",fontsize=10,color="white",style="solid",shape="box"];31980 -> 65496[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65496 -> 32598[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65497[label="zzz2502000/Zero",fontsize=10,color="white",style="solid",shape="box"];31980 -> 65497[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65497 -> 32599[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 31981[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpNat Zero (primPlusNat (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ zzz2502000) (Succ zzz2502000))) (Succ zzz2502000)) zzz2502000))) zzz2502000) == LT)",fontsize=16,color="burlywood",shape="box"];65498[label="zzz2502000/Succ zzz25020000",fontsize=10,color="white",style="solid",shape="box"];31981 -> 65498[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65498 -> 32600[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65499[label="zzz2502000/Zero",fontsize=10,color="white",style="solid",shape="box"];31981 -> 65499[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65499 -> 32601[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 31982 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.20 31982[label="FiniteMap.mkBalBranch zzz340 zzz341 (FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504) zzz343) zzz344",fontsize=16,color="magenta"];31982 -> 63209[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 31982 -> 63210[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 31982 -> 63211[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 31982 -> 63212[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 31983[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (primCmpNat (Succ zzz342000000) (primPlusNat (Succ (primPlusNat Zero Zero)) Zero) == LT)",fontsize=16,color="black",shape="box"];31983 -> 32606[label="",style="solid", color="black", weight=3]; 130.29/78.20 31984[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpNat Zero (primPlusNat (Succ (primPlusNat Zero Zero)) Zero) == LT)",fontsize=16,color="black",shape="box"];31984 -> 32607[label="",style="solid", color="black", weight=3]; 130.29/78.20 31985[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ Zero)))) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];31985 -> 32608[label="",style="solid", color="black", weight=3]; 130.29/78.20 63444[label="FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504",fontsize=16,color="green",shape="box"];63445[label="zzz343",fontsize=16,color="green",shape="box"];63446[label="FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504",fontsize=16,color="green",shape="box"];63447[label="zzz343",fontsize=16,color="green",shape="box"];31991[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz34200 zzz34200)) zzz34200)) zzz34200)) zzz34200)))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];31991 -> 32610[label="",style="solid", color="black", weight=3]; 130.29/78.20 62885[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpNat (Succ zzz635500) zzz63540 == GT)",fontsize=16,color="burlywood",shape="triangle"];65500[label="zzz63540/Succ zzz635400",fontsize=10,color="white",style="solid",shape="box"];62885 -> 65500[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65500 -> 62905[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65501[label="zzz63540/Zero",fontsize=10,color="white",style="solid",shape="box"];62885 -> 65501[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65501 -> 62906[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 62886[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (GT == GT)",fontsize=16,color="black",shape="triangle"];62886 -> 62907[label="",style="solid", color="black", weight=3]; 130.29/78.20 62887[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Pos Zero) (Pos (Succ zzz635400)) == GT)",fontsize=16,color="black",shape="box"];62887 -> 62908[label="",style="solid", color="black", weight=3]; 130.29/78.20 62888[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];62888 -> 62909[label="",style="solid", color="black", weight=3]; 130.29/78.20 62889[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Pos Zero) (Neg (Succ zzz635400)) == GT)",fontsize=16,color="black",shape="box"];62889 -> 62910[label="",style="solid", color="black", weight=3]; 130.29/78.20 62890[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Pos Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];62890 -> 62911[label="",style="solid", color="black", weight=3]; 130.29/78.20 62891[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (LT == GT)",fontsize=16,color="black",shape="triangle"];62891 -> 62912[label="",style="solid", color="black", weight=3]; 130.29/78.20 62892[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpNat zzz63540 (Succ zzz635500) == GT)",fontsize=16,color="burlywood",shape="triangle"];65502[label="zzz63540/Succ zzz635400",fontsize=10,color="white",style="solid",shape="box"];62892 -> 65502[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65502 -> 62913[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65503[label="zzz63540/Zero",fontsize=10,color="white",style="solid",shape="box"];62892 -> 65503[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65503 -> 62914[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 62893[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Neg Zero) (Pos (Succ zzz635400)) == GT)",fontsize=16,color="black",shape="box"];62893 -> 62915[label="",style="solid", color="black", weight=3]; 130.29/78.20 62894[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Neg Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];62894 -> 62916[label="",style="solid", color="black", weight=3]; 130.29/78.20 62895[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Neg Zero) (Neg (Succ zzz635400)) == GT)",fontsize=16,color="black",shape="box"];62895 -> 62917[label="",style="solid", color="black", weight=3]; 130.29/78.20 62896[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpInt (Neg Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];62896 -> 62918[label="",style="solid", color="black", weight=3]; 130.29/78.20 64283[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos (Succ zzz644300)) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos zzz64420)) == GT)",fontsize=16,color="black",shape="box"];64283 -> 64291[label="",style="solid", color="black", weight=3]; 130.29/78.20 64284[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos (Succ zzz644300)) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg zzz64420)) == GT)",fontsize=16,color="black",shape="box"];64284 -> 64292[label="",style="solid", color="black", weight=3]; 130.29/78.20 64285[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos zzz64420)) == GT)",fontsize=16,color="black",shape="box"];64285 -> 64293[label="",style="solid", color="black", weight=3]; 130.29/78.20 64286[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg zzz64420)) == GT)",fontsize=16,color="black",shape="box"];64286 -> 64294[label="",style="solid", color="black", weight=3]; 130.29/78.20 64287[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg (Succ zzz644300)) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos zzz64420)) == GT)",fontsize=16,color="black",shape="box"];64287 -> 64295[label="",style="solid", color="black", weight=3]; 130.29/78.20 64288[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg (Succ zzz644300)) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg zzz64420)) == GT)",fontsize=16,color="black",shape="box"];64288 -> 64296[label="",style="solid", color="black", weight=3]; 130.29/78.20 64289[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos zzz64420)) == GT)",fontsize=16,color="black",shape="box"];64289 -> 64297[label="",style="solid", color="black", weight=3]; 130.29/78.20 64290[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg zzz64420)) == GT)",fontsize=16,color="black",shape="box"];64290 -> 64298[label="",style="solid", color="black", weight=3]; 130.29/78.20 32099[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ (Succ zzz4262000))) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ (Succ zzz4262000))) zzz4263 zzz4264 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)) (Succ zzz4262000) == LT)",fontsize=16,color="black",shape="box"];32099 -> 32645[label="",style="solid", color="black", weight=3]; 130.29/78.20 32100[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)) Zero == LT)",fontsize=16,color="black",shape="box"];32100 -> 32646[label="",style="solid", color="black", weight=3]; 130.29/78.20 32101[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 False",fontsize=16,color="black",shape="box"];32101 -> 32647[label="",style="solid", color="black", weight=3]; 130.29/78.20 32102[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];32102 -> 32648[label="",style="solid", color="black", weight=3]; 130.29/78.20 32103[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];32103 -> 32649[label="",style="solid", color="black", weight=3]; 130.29/78.20 32105[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];32105 -> 32651[label="",style="solid", color="black", weight=3]; 130.29/78.20 63205[label="zzz4260",fontsize=16,color="green",shape="box"];63206[label="zzz4264",fontsize=16,color="green",shape="box"];63207 -> 7670[label="",style="dashed", color="red", weight=0]; 130.29/78.20 63207[label="FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334) zzz4263",fontsize=16,color="magenta"];63207 -> 63448[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63207 -> 63449[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63207 -> 63450[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63208[label="zzz4261",fontsize=16,color="green",shape="box"];32110[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ zzz4262000))) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ zzz4262000))) zzz4263 zzz4264 (primCmpNat (Succ zzz4262000) (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)) == LT)",fontsize=16,color="black",shape="box"];32110 -> 32655[label="",style="solid", color="black", weight=3]; 130.29/78.20 32111[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ Zero)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ Zero)) zzz4263 zzz4264 (primCmpNat Zero (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)) == LT)",fontsize=16,color="black",shape="box"];32111 -> 32656[label="",style="solid", color="black", weight=3]; 130.29/78.20 32112[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 True",fontsize=16,color="black",shape="box"];32112 -> 32657[label="",style="solid", color="black", weight=3]; 130.29/78.20 32113[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];32113 -> 32658[label="",style="solid", color="black", weight=3]; 130.29/78.20 44342[label="zzz426200",fontsize=16,color="green",shape="box"];32115[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];32115 -> 32660[label="",style="solid", color="black", weight=3]; 130.29/78.20 44915[label="Succ zzz3532000",fontsize=16,color="green",shape="box"];44916[label="Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))",fontsize=16,color="green",shape="box"];44916 -> 45028[label="",style="dashed", color="green", weight=3]; 130.29/78.20 44917[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 < FiniteMap.mkVBalBranch3Size_l zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002)",fontsize=16,color="black",shape="box"];44917 -> 45029[label="",style="solid", color="black", weight=3]; 130.29/78.20 44918 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.20 44918[label="FiniteMap.mkBalBranch zzz4998 zzz4999 (FiniteMap.mkVBalBranch (Neg zzz5003) zzz5004 (FiniteMap.Branch zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997) zzz5001) zzz5002",fontsize=16,color="magenta"];44918 -> 63213[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 44918 -> 63214[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 44918 -> 63215[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 44918 -> 63216[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 45962 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.20 45962[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];45962 -> 46049[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 45962 -> 46050[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 45963[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 < FiniteMap.mkVBalBranch3Size_l zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098)",fontsize=16,color="black",shape="box"];45963 -> 46051[label="",style="solid", color="black", weight=3]; 130.29/78.20 45964 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.20 45964[label="FiniteMap.mkBalBranch zzz5094 zzz5095 (FiniteMap.mkVBalBranch (Neg zzz5099) zzz5100 (FiniteMap.Branch zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093) zzz5097) zzz5098",fontsize=16,color="magenta"];45964 -> 63217[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 45964 -> 63218[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 45964 -> 63219[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 45964 -> 63220[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32352[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos (Succ Zero))) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];32352 -> 33560[label="",style="solid", color="black", weight=3]; 130.29/78.20 32353[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];32353 -> 33561[label="",style="solid", color="black", weight=3]; 130.29/78.20 49579[label="Zero",fontsize=16,color="green",shape="box"];49580[label="zzz3534",fontsize=16,color="green",shape="box"];49581[label="zzz343",fontsize=16,color="green",shape="box"];49582[label="zzz341",fontsize=16,color="green",shape="box"];49583[label="zzz3531",fontsize=16,color="green",shape="box"];49584[label="zzz344",fontsize=16,color="green",shape="box"];49585[label="zzz340",fontsize=16,color="green",shape="box"];49586 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.20 49586[label="primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz34200)) (Succ zzz34200)",fontsize=16,color="magenta"];49586 -> 49726[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 49586 -> 49727[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 49587[label="zzz34200",fontsize=16,color="green",shape="box"];49588[label="zzz353200",fontsize=16,color="green",shape="box"];49589[label="zzz3530",fontsize=16,color="green",shape="box"];49590[label="zzz3533",fontsize=16,color="green",shape="box"];49578[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg zzz5460) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="burlywood",shape="triangle"];65504[label="zzz5460/Succ zzz54600",fontsize=10,color="white",style="solid",shape="box"];49578 -> 65504[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65504 -> 49728[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65505[label="zzz5460/Zero",fontsize=10,color="white",style="solid",shape="box"];49578 -> 65505[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65505 -> 49729[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 32355[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534)) == LT)",fontsize=16,color="black",shape="box"];32355 -> 33563[label="",style="solid", color="black", weight=3]; 130.29/78.20 63662[label="Neg (Succ zzz523200)",fontsize=16,color="green",shape="box"];63663[label="zzz5234",fontsize=16,color="green",shape="box"];63664[label="zzz5230",fontsize=16,color="green",shape="box"];63665[label="zzz5233",fontsize=16,color="green",shape="box"];63666[label="zzz5231",fontsize=16,color="green",shape="box"];46745 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.20 46745[label="primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000)",fontsize=16,color="magenta"];46745 -> 46851[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 46745 -> 46852[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 46746[label="zzz51430",fontsize=16,color="green",shape="box"];46747[label="zzz51420",fontsize=16,color="green",shape="box"];46748[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 False",fontsize=16,color="black",shape="triangle"];46748 -> 46853[label="",style="solid", color="black", weight=3]; 130.29/78.20 46749[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 True",fontsize=16,color="black",shape="box"];46749 -> 46854[label="",style="solid", color="black", weight=3]; 130.29/78.20 46750 -> 46748[label="",style="dashed", color="red", weight=0]; 130.29/78.20 46750[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 False",fontsize=16,color="magenta"];47747[label="Zero",fontsize=16,color="green",shape="box"];47748[label="Succ (primPlusNat Zero Zero)",fontsize=16,color="green",shape="box"];47748 -> 47853[label="",style="dashed", color="green", weight=3]; 130.29/78.20 47749[label="zzz52590",fontsize=16,color="green",shape="box"];47750[label="zzz52580",fontsize=16,color="green",shape="box"];47751[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 False",fontsize=16,color="black",shape="triangle"];47751 -> 47854[label="",style="solid", color="black", weight=3]; 130.29/78.20 47752[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 True",fontsize=16,color="black",shape="box"];47752 -> 47855[label="",style="solid", color="black", weight=3]; 130.29/78.20 47753 -> 47751[label="",style="dashed", color="red", weight=0]; 130.29/78.20 47753[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 False",fontsize=16,color="magenta"];46751 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.20 46751[label="primPlusNat (Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))) (Succ zzz3532000)",fontsize=16,color="magenta"];46751 -> 46855[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 46751 -> 46856[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 47754[label="Zero",fontsize=16,color="green",shape="box"];47755[label="Succ (primPlusNat Zero Zero)",fontsize=16,color="green",shape="box"];47755 -> 47856[label="",style="dashed", color="green", weight=3]; 130.29/78.20 32573[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (primPlusNat (Succ zzz33200) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];32573 -> 34005[label="",style="solid", color="black", weight=3]; 130.29/78.20 32574[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ zzz523200)) zzz5233 zzz5234 (LT == LT)",fontsize=16,color="black",shape="box"];32574 -> 34006[label="",style="solid", color="black", weight=3]; 130.29/78.20 32575[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 False",fontsize=16,color="black",shape="box"];32575 -> 34007[label="",style="solid", color="black", weight=3]; 130.29/78.20 32576[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 False",fontsize=16,color="black",shape="box"];32576 -> 34008[label="",style="solid", color="black", weight=3]; 130.29/78.20 32577[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 False",fontsize=16,color="black",shape="box"];32577 -> 34009[label="",style="solid", color="black", weight=3]; 130.29/78.20 32578[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (Succ zzz33200) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];32578 -> 34010[label="",style="solid", color="black", weight=3]; 130.29/78.20 32579[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ zzz523200)) zzz5233 zzz5234 True",fontsize=16,color="black",shape="box"];32579 -> 34011[label="",style="solid", color="black", weight=3]; 130.29/78.20 32580[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 False",fontsize=16,color="black",shape="box"];32580 -> 34012[label="",style="solid", color="black", weight=3]; 130.29/78.20 32581[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (GT == LT)",fontsize=16,color="black",shape="box"];32581 -> 34013[label="",style="solid", color="black", weight=3]; 130.29/78.20 32582[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 False",fontsize=16,color="black",shape="box"];32582 -> 34014[label="",style="solid", color="black", weight=3]; 130.29/78.20 32583 -> 41690[label="",style="dashed", color="red", weight=0]; 130.29/78.20 32583[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ (Succ (Succ zzz25020000)))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ (Succ zzz25020000)))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (primCmpNat (Succ (Succ (primPlusNat (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ zzz25020000)) (Succ (Succ zzz25020000)))) (Succ (Succ zzz25020000))) (Succ zzz25020000))) zzz25020000))) zzz34200000 == LT)",fontsize=16,color="magenta"];32583 -> 41691[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32583 -> 41692[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32583 -> 41693[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32583 -> 41694[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32583 -> 41695[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32583 -> 41696[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32583 -> 41697[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32583 -> 41698[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32583 -> 41699[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32583 -> 41700[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32583 -> 41701[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32583 -> 41702[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32583 -> 41703[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32583 -> 41704[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32584 -> 39527[label="",style="dashed", color="red", weight=0]; 130.29/78.20 32584[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ (Succ Zero))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ Zero))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ zzz34200000))))) zzz343 zzz344 (primCmpNat (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ Zero) (Succ Zero))) (Succ Zero)) Zero))) zzz34200000 == LT)",fontsize=16,color="magenta"];32584 -> 39528[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32584 -> 39529[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32584 -> 39530[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32584 -> 39531[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32584 -> 39532[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32584 -> 39533[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32584 -> 39534[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32584 -> 39535[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32584 -> 39536[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32584 -> 39537[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32584 -> 39538[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32584 -> 39539[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32584 -> 39540[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32585[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];32585 -> 34053[label="",style="solid", color="black", weight=3]; 130.29/78.20 32586[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];32586 -> 34054[label="",style="solid", color="black", weight=3]; 130.29/78.20 32587[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (primCmpNat (Succ (primPlusNat Zero Zero)) (Succ zzz342000000) == LT)",fontsize=16,color="black",shape="box"];32587 -> 34055[label="",style="solid", color="black", weight=3]; 130.29/78.20 32588[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpNat (Succ (primPlusNat Zero Zero)) Zero == LT)",fontsize=16,color="black",shape="box"];32588 -> 34056[label="",style="solid", color="black", weight=3]; 130.29/78.20 32589[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344)",fontsize=16,color="black",shape="box"];32589 -> 34057[label="",style="solid", color="black", weight=3]; 130.29/78.20 32590[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];32590 -> 34058[label="",style="solid", color="black", weight=3]; 130.29/78.20 32591 -> 39576[label="",style="dashed", color="red", weight=0]; 130.29/78.20 32591[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ Zero))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) == LT)",fontsize=16,color="magenta"];32591 -> 39577[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32592[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];32592 -> 34060[label="",style="solid", color="black", weight=3]; 130.29/78.20 32593[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ (Succ Zero)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];32593 -> 34061[label="",style="solid", color="black", weight=3]; 130.29/78.20 32594[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (Pos (Succ zzz250200)) == LT)",fontsize=16,color="black",shape="box"];32594 -> 34062[label="",style="solid", color="black", weight=3]; 130.29/78.20 32596[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz34200 zzz34200)) zzz34200)) zzz34200)) zzz34200)))) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];32596 -> 34064[label="",style="solid", color="black", weight=3]; 130.29/78.20 32598[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ (Succ zzz25020000)))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ (Succ zzz25020000)))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (primCmpNat (Succ zzz342000000) (primPlusNat (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ zzz25020000)) (Succ (Succ zzz25020000)))) (Succ (Succ zzz25020000))) (Succ zzz25020000)))) (Succ zzz25020000)) == LT)",fontsize=16,color="black",shape="box"];32598 -> 34066[label="",style="solid", color="black", weight=3]; 130.29/78.20 32599[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ Zero))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ Zero))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (primCmpNat (Succ zzz342000000) (primPlusNat (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ Zero) (Succ Zero))) (Succ Zero)) Zero))) Zero) == LT)",fontsize=16,color="black",shape="box"];32599 -> 34067[label="",style="solid", color="black", weight=3]; 130.29/78.20 32600[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ (Succ zzz25020000)))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ (Succ zzz25020000)))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpNat Zero (primPlusNat (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ zzz25020000)) (Succ (Succ zzz25020000)))) (Succ (Succ zzz25020000))) (Succ zzz25020000)))) (Succ zzz25020000)) == LT)",fontsize=16,color="black",shape="box"];32600 -> 34068[label="",style="solid", color="black", weight=3]; 130.29/78.20 32601[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ Zero))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ Zero))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpNat Zero (primPlusNat (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ Zero) (Succ Zero))) (Succ Zero)) Zero))) Zero) == LT)",fontsize=16,color="black",shape="box"];32601 -> 34069[label="",style="solid", color="black", weight=3]; 130.29/78.20 63209[label="zzz340",fontsize=16,color="green",shape="box"];63210[label="zzz344",fontsize=16,color="green",shape="box"];63211 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.20 63211[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504) zzz343",fontsize=16,color="magenta"];63211 -> 63451[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63211 -> 63452[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63212[label="zzz341",fontsize=16,color="green",shape="box"];32606[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (primCmpNat (Succ zzz342000000) (Succ (primPlusNat Zero Zero)) == LT)",fontsize=16,color="black",shape="box"];32606 -> 34072[label="",style="solid", color="black", weight=3]; 130.29/78.20 32607[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpNat Zero (Succ (primPlusNat Zero Zero)) == LT)",fontsize=16,color="black",shape="box"];32607 -> 34073[label="",style="solid", color="black", weight=3]; 130.29/78.20 32608 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.20 32608[label="FiniteMap.mkBalBranch zzz340 zzz341 (FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504) zzz343) zzz344",fontsize=16,color="magenta"];32608 -> 63221[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32608 -> 63222[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32608 -> 63223[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32608 -> 63224[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32610[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz34200 zzz34200)) zzz34200)) zzz34200)) zzz34200)))) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];32610 -> 34079[label="",style="solid", color="black", weight=3]; 130.29/78.20 62905[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpNat (Succ zzz635500) (Succ zzz635400) == GT)",fontsize=16,color="black",shape="box"];62905 -> 62927[label="",style="solid", color="black", weight=3]; 130.29/78.20 62906[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 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zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpNat Zero (Succ zzz635400) == GT)",fontsize=16,color="magenta"];62908 -> 62930[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 62908 -> 62931[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 62909[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (EQ == GT)",fontsize=16,color="black",shape="triangle"];62909 -> 62932[label="",style="solid", color="black", weight=3]; 130.29/78.20 62910 -> 62886[label="",style="dashed", color="red", weight=0]; 130.29/78.20 62910[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 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130.29/78.20 62913[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpNat (Succ zzz635400) (Succ zzz635500) == GT)",fontsize=16,color="black",shape="box"];62913 -> 62934[label="",style="solid", color="black", weight=3]; 130.29/78.20 62914[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpNat Zero (Succ zzz635500) == GT)",fontsize=16,color="black",shape="box"];62914 -> 62935[label="",style="solid", color="black", weight=3]; 130.29/78.20 62915 -> 62891[label="",style="dashed", color="red", weight=0]; 130.29/78.20 62915[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (LT == GT)",fontsize=16,color="magenta"];62916 -> 62909[label="",style="dashed", color="red", weight=0]; 130.29/78.20 62916[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (EQ == GT)",fontsize=16,color="magenta"];62917 -> 62885[label="",style="dashed", color="red", weight=0]; 130.29/78.20 62917[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpNat (Succ zzz635400) Zero == GT)",fontsize=16,color="magenta"];62917 -> 62936[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 62917 -> 62937[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 62918 -> 62909[label="",style="dashed", color="red", weight=0]; 130.29/78.20 62918[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (EQ == GT)",fontsize=16,color="magenta"];64291 -> 64299[label="",style="dashed", color="red", weight=0]; 130.29/78.20 64291[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos (Succ zzz644300)) (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64420)) == GT)",fontsize=16,color="magenta"];64291 -> 64300[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 64292 -> 64301[label="",style="dashed", color="red", weight=0]; 130.29/78.20 64292[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos (Succ zzz644300)) (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64420)) == GT)",fontsize=16,color="magenta"];64292 -> 64302[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 64293 -> 64303[label="",style="dashed", color="red", weight=0]; 130.29/78.20 64293[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64420)) == GT)",fontsize=16,color="magenta"];64293 -> 64304[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 64294 -> 64305[label="",style="dashed", color="red", weight=0]; 130.29/78.20 64294[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64420)) == GT)",fontsize=16,color="magenta"];64294 -> 64306[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 64295 -> 64307[label="",style="dashed", color="red", weight=0]; 130.29/78.20 64295[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg (Succ zzz644300)) (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64420)) == GT)",fontsize=16,color="magenta"];64295 -> 64308[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 64296 -> 64309[label="",style="dashed", color="red", weight=0]; 130.29/78.20 64296[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg (Succ zzz644300)) (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64420)) == GT)",fontsize=16,color="magenta"];64296 -> 64310[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 64297 -> 64311[label="",style="dashed", color="red", weight=0]; 130.29/78.20 64297[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64420)) == GT)",fontsize=16,color="magenta"];64297 -> 64312[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 64298 -> 64313[label="",style="dashed", color="red", weight=0]; 130.29/78.20 64298[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64420)) == GT)",fontsize=16,color="magenta"];64298 -> 64314[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32645[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ (Succ zzz4262000))) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ (Succ zzz4262000))) zzz4263 zzz4264 (primCmpNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200) zzz4262000 == LT)",fontsize=16,color="burlywood",shape="box"];65506[label="zzz33200/Succ zzz332000",fontsize=10,color="white",style="solid",shape="box"];32645 -> 65506[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65506 -> 34144[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65507[label="zzz33200/Zero",fontsize=10,color="white",style="solid",shape="box"];32645 -> 65507[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65507 -> 34145[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 32646[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (GT == LT)",fontsize=16,color="black",shape="box"];32646 -> 34146[label="",style="solid", color="black", weight=3]; 130.29/78.20 32647[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 < FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264)",fontsize=16,color="black",shape="box"];32647 -> 34147[label="",style="solid", color="black", weight=3]; 130.29/78.20 32648[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];32648 -> 34148[label="",style="solid", color="black", weight=3]; 130.29/78.20 32649[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (EQ == LT)",fontsize=16,color="black",shape="box"];32649 -> 34149[label="",style="solid", color="black", weight=3]; 130.29/78.20 32651[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (EQ == LT)",fontsize=16,color="black",shape="box"];32651 -> 34151[label="",style="solid", color="black", weight=3]; 130.29/78.20 63448[label="Neg (Succ zzz33200)",fontsize=16,color="green",shape="box"];63449[label="Succ zzz3000",fontsize=16,color="green",shape="box"];63450[label="zzz4263",fontsize=16,color="green",shape="box"];32655[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ zzz4262000))) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ zzz4262000))) zzz4263 zzz4264 (primCmpNat zzz4262000 (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200) == LT)",fontsize=16,color="burlywood",shape="box"];65508[label="zzz4262000/Succ zzz42620000",fontsize=10,color="white",style="solid",shape="box"];32655 -> 65508[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65508 -> 34152[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65509[label="zzz4262000/Zero",fontsize=10,color="white",style="solid",shape="box"];32655 -> 65509[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65509 -> 34153[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 32656[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ Zero)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ Zero)) zzz4263 zzz4264 (LT == LT)",fontsize=16,color="black",shape="box"];32656 -> 34154[label="",style="solid", color="black", weight=3]; 130.29/78.20 32657 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.20 32657[label="FiniteMap.mkBalBranch zzz4260 zzz4261 (FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334) zzz4263) zzz4264",fontsize=16,color="magenta"];32657 -> 63225[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32657 -> 63226[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32657 -> 63227[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32657 -> 63228[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 32658[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (EQ == LT)",fontsize=16,color="black",shape="box"];32658 -> 34159[label="",style="solid", color="black", weight=3]; 130.29/78.20 32660[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (EQ == LT)",fontsize=16,color="black",shape="box"];32660 -> 34161[label="",style="solid", color="black", weight=3]; 130.29/78.20 45028 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.20 45028[label="primPlusNat (Succ zzz3532000) (Succ zzz3532000)",fontsize=16,color="magenta"];45028 -> 45096[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 45028 -> 45097[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 45029[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002) (FiniteMap.mkVBalBranch3Size_l zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002) == LT)",fontsize=16,color="black",shape="box"];45029 -> 45098[label="",style="solid", color="black", weight=3]; 130.29/78.20 63213[label="zzz4998",fontsize=16,color="green",shape="box"];63214[label="zzz5002",fontsize=16,color="green",shape="box"];63215 -> 7670[label="",style="dashed", color="red", weight=0]; 130.29/78.20 63215[label="FiniteMap.mkVBalBranch (Neg zzz5003) zzz5004 (FiniteMap.Branch zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997) zzz5001",fontsize=16,color="magenta"];63215 -> 63453[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63215 -> 63454[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63215 -> 63455[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63215 -> 63456[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63215 -> 63457[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63215 -> 63458[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63215 -> 63459[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63215 -> 63460[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63216[label="zzz4999",fontsize=16,color="green",shape="box"];46049[label="Zero",fontsize=16,color="green",shape="box"];46050[label="Zero",fontsize=16,color="green",shape="box"];46051[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098) (FiniteMap.mkVBalBranch3Size_l zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098) == LT)",fontsize=16,color="black",shape="box"];46051 -> 46147[label="",style="solid", color="black", weight=3]; 130.29/78.20 63217[label="zzz5094",fontsize=16,color="green",shape="box"];63218[label="zzz5098",fontsize=16,color="green",shape="box"];63219 -> 7670[label="",style="dashed", color="red", weight=0]; 130.29/78.20 63219[label="FiniteMap.mkVBalBranch (Neg zzz5099) zzz5100 (FiniteMap.Branch zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093) zzz5097",fontsize=16,color="magenta"];63219 -> 63461[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63219 -> 63462[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63219 -> 63463[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63219 -> 63464[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63219 -> 63465[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63219 -> 63466[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63219 -> 63467[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63219 -> 63468[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63220[label="zzz5095",fontsize=16,color="green",shape="box"];33560 -> 50854[label="",style="dashed", color="red", weight=0]; 130.29/78.20 33560[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ Zero))) (FiniteMap.mkVBalBranch3Size_l zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) == LT)",fontsize=16,color="magenta"];33560 -> 50855[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 33560 -> 50856[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 33560 -> 50857[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 33560 -> 50858[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 33560 -> 50859[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 33560 -> 50860[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 33560 -> 50861[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 33560 -> 50862[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 33560 -> 50863[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 33560 -> 50864[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 33560 -> 50865[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 33561[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534)) == LT)",fontsize=16,color="black",shape="box"];33561 -> 34499[label="",style="solid", color="black", weight=3]; 130.29/78.20 49726[label="Succ zzz34200",fontsize=16,color="green",shape="box"];49727 -> 43384[label="",style="dashed", color="red", weight=0]; 130.29/78.20 49727[label="primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz34200)",fontsize=16,color="magenta"];49727 -> 49755[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 49728[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg (Succ zzz54600)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];49728 -> 49756[label="",style="solid", color="black", weight=3]; 130.29/78.20 49729[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];49729 -> 49757[label="",style="solid", color="black", weight=3]; 130.29/78.20 33563[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (primCmpInt (Neg Zero) (Pos (Succ zzz353200)) == LT)",fontsize=16,color="black",shape="box"];33563 -> 34501[label="",style="solid", color="black", weight=3]; 130.29/78.20 46851[label="Succ zzz3532000",fontsize=16,color="green",shape="box"];46852[label="Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))",fontsize=16,color="green",shape="box"];46852 -> 46873[label="",style="dashed", color="green", weight=3]; 130.29/78.20 46853[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 < FiniteMap.mkVBalBranch3Size_l zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139)",fontsize=16,color="black",shape="box"];46853 -> 46874[label="",style="solid", color="black", weight=3]; 130.29/78.20 46854 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.20 46854[label="FiniteMap.mkBalBranch zzz5135 zzz5136 (FiniteMap.mkVBalBranch (Neg zzz5140) zzz5141 (FiniteMap.Branch zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134) zzz5138) zzz5139",fontsize=16,color="magenta"];46854 -> 63229[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 46854 -> 63230[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 46854 -> 63231[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 46854 -> 63232[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 47853 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.20 47853[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];47853 -> 47969[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 47853 -> 47970[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 47854[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 < FiniteMap.mkVBalBranch3Size_l zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255)",fontsize=16,color="black",shape="box"];47854 -> 47971[label="",style="solid", color="black", weight=3]; 130.29/78.20 47855 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.20 47855[label="FiniteMap.mkBalBranch zzz5251 zzz5252 (FiniteMap.mkVBalBranch (Neg zzz5256) zzz5257 (FiniteMap.Branch zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250) zzz5254) zzz5255",fontsize=16,color="magenta"];47855 -> 63233[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 47855 -> 63234[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 47855 -> 63235[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 47855 -> 63236[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 46855[label="Succ zzz3532000",fontsize=16,color="green",shape="box"];46856[label="Succ (primPlusNat (Succ zzz3532000) (Succ zzz3532000))",fontsize=16,color="green",shape="box"];46856 -> 46879[label="",style="dashed", color="green", weight=3]; 130.29/78.20 47856 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.20 47856[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];47856 -> 47976[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 47856 -> 47977[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34005[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Pos (primPlusNat (primPlusNat (primPlusNat (Succ (Succ (primPlusNat zzz33200 zzz33200))) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];34005 -> 34734[label="",style="solid", color="black", weight=3]; 130.29/78.20 34006[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ zzz523200)) zzz5233 zzz5234 True",fontsize=16,color="black",shape="box"];34006 -> 34735[label="",style="solid", color="black", weight=3]; 130.29/78.20 34007[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 < FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];34007 -> 34736[label="",style="solid", color="black", weight=3]; 130.29/78.20 34008[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 < FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];34008 -> 34737[label="",style="solid", color="black", weight=3]; 130.29/78.20 34009[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 < FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];34009 -> 34738[label="",style="solid", color="black", weight=3]; 130.29/78.20 34010[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (Succ (Succ (primPlusNat zzz33200 zzz33200))) (Succ zzz33200)) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];34010 -> 34739[label="",style="solid", color="black", weight=3]; 130.29/78.20 34011 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.20 34011[label="FiniteMap.mkBalBranch zzz5230 zzz5231 (FiniteMap.mkVBalBranch (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334) zzz5233) zzz5234",fontsize=16,color="magenta"];34011 -> 63237[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34011 -> 63238[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34011 -> 63239[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34011 -> 63240[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34012[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 < FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];34012 -> 34744[label="",style="solid", color="black", weight=3]; 130.29/78.20 34013[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 False",fontsize=16,color="black",shape="box"];34013 -> 34745[label="",style="solid", color="black", weight=3]; 130.29/78.20 34014[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 < FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];34014 -> 34746[label="",style="solid", color="black", weight=3]; 130.29/78.20 41691[label="zzz2501",fontsize=16,color="green",shape="box"];41692[label="zzz340",fontsize=16,color="green",shape="box"];41693[label="zzz341",fontsize=16,color="green",shape="box"];41694[label="zzz344",fontsize=16,color="green",shape="box"];41695[label="zzz25020000",fontsize=16,color="green",shape="box"];41696[label="zzz31",fontsize=16,color="green",shape="box"];41697[label="zzz2504",fontsize=16,color="green",shape="box"];41698[label="zzz300",fontsize=16,color="green",shape="box"];41699[label="zzz2500",fontsize=16,color="green",shape="box"];41700[label="zzz343",fontsize=16,color="green",shape="box"];41701[label="zzz34200000",fontsize=16,color="green",shape="box"];41702[label="zzz2503",fontsize=16,color="green",shape="box"];41703[label="Succ (Succ (primPlusNat (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ zzz25020000)) (Succ (Succ zzz25020000)))) (Succ (Succ zzz25020000))) (Succ zzz25020000))) zzz25020000))",fontsize=16,color="green",shape="box"];41703 -> 41775[label="",style="dashed", color="green", weight=3]; 130.29/78.20 41704[label="Succ (Succ (Succ zzz34200000))",fontsize=16,color="green",shape="box"];41690[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpNat zzz4713 zzz4714 == LT)",fontsize=16,color="burlywood",shape="triangle"];65510[label="zzz4713/Succ zzz47130",fontsize=10,color="white",style="solid",shape="box"];41690 -> 65510[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65510 -> 41776[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65511[label="zzz4713/Zero",fontsize=10,color="white",style="solid",shape="box"];41690 -> 65511[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65511 -> 41777[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 39528[label="zzz300",fontsize=16,color="green",shape="box"];39529[label="zzz2504",fontsize=16,color="green",shape="box"];39530[label="Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ Zero) (Succ Zero))) (Succ Zero)) Zero)",fontsize=16,color="green",shape="box"];39530 -> 39561[label="",style="dashed", color="green", weight=3]; 130.29/78.20 39531[label="zzz31",fontsize=16,color="green",shape="box"];39532[label="zzz2501",fontsize=16,color="green",shape="box"];39533[label="zzz2503",fontsize=16,color="green",shape="box"];39534[label="zzz344",fontsize=16,color="green",shape="box"];39535[label="zzz343",fontsize=16,color="green",shape="box"];39536[label="zzz2500",fontsize=16,color="green",shape="box"];39537[label="Succ (Succ (Succ 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color="burlywood", weight=9]; 130.29/78.20 65513 -> 39563[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 34053[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];34053 -> 34809[label="",style="solid", color="black", weight=3]; 130.29/78.20 34054[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ 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(Succ (Succ zzz342000000)))))) zzz343 zzz344 (primCmpNat (primPlusNat Zero Zero) zzz342000000 == LT)",fontsize=16,color="black",shape="box"];34055 -> 34811[label="",style="solid", color="black", weight=3]; 130.29/78.20 34056[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (GT == LT)",fontsize=16,color="black",shape="box"];34056 -> 34812[label="",style="solid", color="black", weight=3]; 130.29/78.20 34057[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];34057 -> 34813[label="",style="solid", color="black", weight=3]; 130.29/78.20 34058[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];34058 -> 34814[label="",style="solid", color="black", weight=3]; 130.29/78.20 39577 -> 39342[label="",style="dashed", color="red", weight=0]; 130.29/78.20 39577[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ Zero)",fontsize=16,color="magenta"];39576[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpInt (Pos zzz4438) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) == LT)",fontsize=16,color="burlywood",shape="triangle"];65514[label="zzz4438/Succ zzz44380",fontsize=10,color="white",style="solid",shape="box"];39576 -> 65514[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65514 -> 39591[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65515[label="zzz4438/Zero",fontsize=10,color="white",style="solid",shape="box"];39576 -> 65515[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65515 -> 39592[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 34060[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (Pos (Succ zzz250200)) == LT)",fontsize=16,color="black",shape="box"];34060 -> 34816[label="",style="solid", color="black", weight=3]; 130.29/78.20 34061[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ Zero) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];34061 -> 34817[label="",style="solid", color="black", weight=3]; 130.29/78.20 34062[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];34062 -> 34818[label="",style="solid", color="black", weight=3]; 130.29/78.20 34064[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos 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color="magenta", weight=3]; 130.29/78.20 34066 -> 45833[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34066 -> 45834[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34066 -> 45835[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34066 -> 45836[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34066 -> 45837[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34066 -> 45838[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34066 -> 45839[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34066 -> 45840[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34066 -> 45841[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34066 -> 45842[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34066 -> 45843[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34066 -> 45844[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34066 -> 45845[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34067 -> 39687[label="",style="dashed", color="red", weight=0]; 130.29/78.20 34067[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ Zero))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ Zero))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (primCmpNat (Succ zzz342000000) (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ Zero) (Succ Zero))) (Succ Zero)) Zero))) == LT)",fontsize=16,color="magenta"];34067 -> 39688[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34067 -> 39689[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34067 -> 39690[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34067 -> 39691[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34067 -> 39692[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34067 -> 39693[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34067 -> 39694[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34067 -> 39695[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34067 -> 39696[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34067 -> 39697[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34067 -> 39698[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34067 -> 39699[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34067 -> 39700[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34068 -> 45831[label="",style="dashed", color="red", weight=0]; 130.29/78.20 34068[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ (Succ zzz25020000)))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ 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-> 45853[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34068 -> 45854[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34068 -> 45855[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34068 -> 45856[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34068 -> 45857[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34068 -> 45858[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34068 -> 45859[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34069 -> 39687[label="",style="dashed", color="red", weight=0]; 130.29/78.20 34069[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ (Succ Zero))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ (Succ Zero))) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpNat Zero (Succ (Succ (primPlusNat 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130.29/78.20 34069 -> 39712[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34069 -> 39713[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63451[label="FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ (Succ zzz2502000))) zzz2503 zzz2504",fontsize=16,color="green",shape="box"];63452[label="zzz343",fontsize=16,color="green",shape="box"];34072[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (primCmpNat zzz342000000 (primPlusNat Zero Zero) == LT)",fontsize=16,color="burlywood",shape="box"];65516[label="zzz342000000/Succ zzz3420000000",fontsize=10,color="white",style="solid",shape="box"];34072 -> 65516[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65516 -> 34907[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65517[label="zzz342000000/Zero",fontsize=10,color="white",style="solid",shape="box"];34072 -> 65517[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65517 -> 34908[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 34073[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];34073 -> 34909[label="",style="solid", color="black", weight=3]; 130.29/78.20 63221[label="zzz340",fontsize=16,color="green",shape="box"];63222[label="zzz344",fontsize=16,color="green",shape="box"];63223 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.20 63223[label="FiniteMap.mkVBalBranch (Pos zzz300) 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(FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpNat zzz635500 zzz635400 == GT)",fontsize=16,color="burlywood",shape="triangle"];65518[label="zzz635500/Succ zzz6355000",fontsize=10,color="white",style="solid",shape="box"];62927 -> 65518[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65518 -> 62954[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65519[label="zzz635500/Zero",fontsize=10,color="white",style="solid",shape="box"];62927 -> 65519[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65519 -> 62955[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 62928 -> 62886[label="",style="dashed", color="red", weight=0]; 130.29/78.20 62928[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (GT == GT)",fontsize=16,color="magenta"];62929 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.20 62929[label="FiniteMap.mkBalBranch (FiniteMap.glueBal2Mid_key2 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464)) (FiniteMap.glueBal2Mid_elt2 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464)) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.deleteMin (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034))",fontsize=16,color="magenta"];62929 -> 63241[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 62929 -> 63242[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 62929 -> 63243[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 62929 -> 63244[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 62930[label="Zero",fontsize=16,color="green",shape="box"];62931[label="zzz635400",fontsize=16,color="green",shape="box"];62932 -> 62912[label="",style="dashed", color="red", weight=0]; 130.29/78.20 62932[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) False",fontsize=16,color="magenta"];62933[label="FiniteMap.glueBal2GlueBal0 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) otherwise",fontsize=16,color="black",shape="box"];62933 -> 62957[label="",style="solid", color="black", weight=3]; 130.29/78.20 62934 -> 62927[label="",style="dashed", color="red", weight=0]; 130.29/78.20 62934[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpNat zzz635400 zzz635500 == GT)",fontsize=16,color="magenta"];62934 -> 62958[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 62934 -> 62959[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 62935 -> 62891[label="",style="dashed", color="red", weight=0]; 130.29/78.20 62935[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (LT == GT)",fontsize=16,color="magenta"];62936[label="Zero",fontsize=16,color="green",shape="box"];62937[label="zzz635400",fontsize=16,color="green",shape="box"];64300 -> 62524[label="",style="dashed", color="red", weight=0]; 130.29/78.20 64300[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64420",fontsize=16,color="magenta"];64300 -> 64315[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 64299[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos (Succ zzz644300)) (Pos zzz6444) == GT)",fontsize=16,color="black",shape="triangle"];64299 -> 64316[label="",style="solid", color="black", weight=3]; 130.29/78.20 64302 -> 62524[label="",style="dashed", color="red", weight=0]; 130.29/78.20 64302[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64420",fontsize=16,color="magenta"];64302 -> 64317[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 64301[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos (Succ zzz644300)) (Neg zzz6445) == GT)",fontsize=16,color="black",shape="triangle"];64301 -> 64318[label="",style="solid", color="black", weight=3]; 130.29/78.20 64304 -> 62524[label="",style="dashed", color="red", weight=0]; 130.29/78.20 64304[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64420",fontsize=16,color="magenta"];64304 -> 64319[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 64303[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (Pos zzz6446) == GT)",fontsize=16,color="burlywood",shape="triangle"];65520[label="zzz6446/Succ zzz64460",fontsize=10,color="white",style="solid",shape="box"];64303 -> 65520[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65520 -> 64320[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65521[label="zzz6446/Zero",fontsize=10,color="white",style="solid",shape="box"];64303 -> 65521[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65521 -> 64321[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 64306 -> 62524[label="",style="dashed", color="red", weight=0]; 130.29/78.20 64306[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64420",fontsize=16,color="magenta"];64306 -> 64322[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 64305[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (Neg zzz6447) == GT)",fontsize=16,color="burlywood",shape="triangle"];65522[label="zzz6447/Succ zzz64470",fontsize=10,color="white",style="solid",shape="box"];64305 -> 65522[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65522 -> 64323[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65523[label="zzz6447/Zero",fontsize=10,color="white",style="solid",shape="box"];64305 -> 65523[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65523 -> 64324[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 64308 -> 62524[label="",style="dashed", color="red", weight=0]; 130.29/78.20 64308[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64420",fontsize=16,color="magenta"];64308 -> 64325[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 64307[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg (Succ zzz644300)) (Pos zzz6448) == GT)",fontsize=16,color="black",shape="triangle"];64307 -> 64326[label="",style="solid", color="black", weight=3]; 130.29/78.20 64310 -> 62524[label="",style="dashed", color="red", weight=0]; 130.29/78.20 64310[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64420",fontsize=16,color="magenta"];64310 -> 64327[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 64309[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg (Succ zzz644300)) (Neg zzz6449) == GT)",fontsize=16,color="black",shape="triangle"];64309 -> 64328[label="",style="solid", color="black", weight=3]; 130.29/78.20 64312 -> 62524[label="",style="dashed", color="red", weight=0]; 130.29/78.20 64312[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64420",fontsize=16,color="magenta"];64312 -> 64329[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 64311[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (Pos zzz6450) == GT)",fontsize=16,color="burlywood",shape="triangle"];65524[label="zzz6450/Succ zzz64500",fontsize=10,color="white",style="solid",shape="box"];64311 -> 65524[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65524 -> 64330[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65525[label="zzz6450/Zero",fontsize=10,color="white",style="solid",shape="box"];64311 -> 65525[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65525 -> 64331[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 64314 -> 62524[label="",style="dashed", color="red", weight=0]; 130.29/78.20 64314[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64420",fontsize=16,color="magenta"];64314 -> 64332[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 64313[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (Neg zzz6451) == GT)",fontsize=16,color="burlywood",shape="triangle"];65526[label="zzz6451/Succ zzz64510",fontsize=10,color="white",style="solid",shape="box"];64313 -> 65526[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65526 -> 64333[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65527[label="zzz6451/Zero",fontsize=10,color="white",style="solid",shape="box"];64313 -> 65527[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65527 -> 64334[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 34144[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ (Succ zzz332000))) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ (Succ zzz4262000))) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ (Succ zzz332000))) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ (Succ zzz4262000))) zzz4263 zzz4264 (primCmpNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) zzz4262000 == LT)",fontsize=16,color="black",shape="box"];34144 -> 35073[label="",style="solid", color="black", weight=3]; 130.29/78.20 34145[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ Zero)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ (Succ zzz4262000))) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ Zero)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ (Succ zzz4262000))) zzz4263 zzz4264 (primCmpNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) Zero) zzz4262000 == LT)",fontsize=16,color="black",shape="box"];34145 -> 35074[label="",style="solid", color="black", weight=3]; 130.29/78.20 34146[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 False",fontsize=16,color="black",shape="box"];34146 -> 35075[label="",style="solid", color="black", weight=3]; 130.29/78.20 34147[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];34147 -> 35076[label="",style="solid", color="black", weight=3]; 130.29/78.20 34148[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];34148 -> 35077[label="",style="solid", color="black", weight=3]; 130.29/78.20 34149[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 False",fontsize=16,color="black",shape="box"];34149 -> 35078[label="",style="solid", color="black", weight=3]; 130.29/78.20 34151[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 False",fontsize=16,color="black",shape="box"];34151 -> 35080[label="",style="solid", color="black", weight=3]; 130.29/78.20 34152[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ (Succ zzz42620000)))) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ (Succ zzz42620000)))) zzz4263 zzz4264 (primCmpNat (Succ zzz42620000) (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200) == LT)",fontsize=16,color="burlywood",shape="box"];65528[label="zzz33200/Succ zzz332000",fontsize=10,color="white",style="solid",shape="box"];34152 -> 65528[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65528 -> 35081[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65529[label="zzz33200/Zero",fontsize=10,color="white",style="solid",shape="box"];34152 -> 65529[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65529 -> 35082[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 34153[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ Zero))) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ Zero))) zzz4263 zzz4264 (primCmpNat Zero (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200) == LT)",fontsize=16,color="burlywood",shape="box"];65530[label="zzz33200/Succ zzz332000",fontsize=10,color="white",style="solid",shape="box"];34153 -> 65530[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65530 -> 35083[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65531[label="zzz33200/Zero",fontsize=10,color="white",style="solid",shape="box"];34153 -> 65531[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65531 -> 35084[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 34154[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ Zero)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ Zero)) zzz4263 zzz4264 True",fontsize=16,color="black",shape="box"];34154 -> 35085[label="",style="solid", color="black", weight=3]; 130.29/78.20 63225[label="zzz4260",fontsize=16,color="green",shape="box"];63226[label="zzz4264",fontsize=16,color="green",shape="box"];63227 -> 7670[label="",style="dashed", color="red", weight=0]; 130.29/78.20 63227[label="FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334) zzz4263",fontsize=16,color="magenta"];63227 -> 63471[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63227 -> 63472[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63227 -> 63473[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63228[label="zzz4261",fontsize=16,color="green",shape="box"];34159[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 False",fontsize=16,color="black",shape="box"];34159 -> 35089[label="",style="solid", color="black", weight=3]; 130.29/78.20 34161[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 False",fontsize=16,color="black",shape="box"];34161 -> 35091[label="",style="solid", color="black", weight=3]; 130.29/78.20 45096[label="Succ zzz3532000",fontsize=16,color="green",shape="box"];45097[label="Succ zzz3532000",fontsize=16,color="green",shape="box"];45098[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002) (FiniteMap.mkVBalBranch3Size_l zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002) == LT)",fontsize=16,color="black",shape="box"];45098 -> 45177[label="",style="solid", color="black", weight=3]; 130.29/78.20 63453[label="Pos (Succ (Succ zzz4995))",fontsize=16,color="green",shape="box"];63454[label="zzz5003",fontsize=16,color="green",shape="box"];63455[label="zzz4997",fontsize=16,color="green",shape="box"];63456[label="zzz5001",fontsize=16,color="green",shape="box"];63457[label="zzz4993",fontsize=16,color="green",shape="box"];63458[label="zzz4996",fontsize=16,color="green",shape="box"];63459[label="zzz5004",fontsize=16,color="green",shape="box"];63460[label="zzz4994",fontsize=16,color="green",shape="box"];46147[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098) (FiniteMap.mkVBalBranch3Size_l zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098) == LT)",fontsize=16,color="black",shape="box"];46147 -> 46196[label="",style="solid", color="black", weight=3]; 130.29/78.20 63461[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];63462[label="zzz5099",fontsize=16,color="green",shape="box"];63463[label="zzz5093",fontsize=16,color="green",shape="box"];63464[label="zzz5097",fontsize=16,color="green",shape="box"];63465[label="zzz5090",fontsize=16,color="green",shape="box"];63466[label="zzz5092",fontsize=16,color="green",shape="box"];63467[label="zzz5100",fontsize=16,color="green",shape="box"];63468[label="zzz5091",fontsize=16,color="green",shape="box"];50855[label="zzz340",fontsize=16,color="green",shape="box"];50856[label="Zero",fontsize=16,color="green",shape="box"];50857[label="zzz3534",fontsize=16,color="green",shape="box"];50858[label="zzz343",fontsize=16,color="green",shape="box"];50859[label="zzz353200",fontsize=16,color="green",shape="box"];50860[label="zzz3530",fontsize=16,color="green",shape="box"];50861[label="zzz341",fontsize=16,color="green",shape="box"];50862[label="zzz3533",fontsize=16,color="green",shape="box"];50863 -> 43358[label="",style="dashed", color="red", weight=0]; 130.29/78.20 50863[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ Zero)",fontsize=16,color="magenta"];50863 -> 50890[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 50864[label="zzz3531",fontsize=16,color="green",shape="box"];50865[label="zzz344",fontsize=16,color="green",shape="box"];50854[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (primCmpInt (Pos zzz5541) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234) == LT)",fontsize=16,color="burlywood",shape="triangle"];65532[label="zzz5541/Succ zzz55410",fontsize=10,color="white",style="solid",shape="box"];50854 -> 65532[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65532 -> 50891[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65533[label="zzz5541/Zero",fontsize=10,color="white",style="solid",shape="box"];50854 -> 65533[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65533 -> 50892[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 34499[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpInt (Pos Zero) (Pos (Succ zzz353200)) == LT)",fontsize=16,color="black",shape="box"];34499 -> 35170[label="",style="solid", color="black", weight=3]; 130.29/78.20 49755[label="zzz34200",fontsize=16,color="green",shape="box"];49756[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg (Succ zzz54600)) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];49756 -> 49820[label="",style="solid", color="black", weight=3]; 130.29/78.20 49757[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];49757 -> 49821[label="",style="solid", color="black", weight=3]; 130.29/78.20 34501[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];34501 -> 35172[label="",style="solid", color="black", weight=3]; 130.29/78.20 46873 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.20 46873[label="primPlusNat (Succ zzz3532000) (Succ zzz3532000)",fontsize=16,color="magenta"];46873 -> 46966[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 46873 -> 46967[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 46874[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139) (FiniteMap.mkVBalBranch3Size_l zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139) == LT)",fontsize=16,color="black",shape="box"];46874 -> 46968[label="",style="solid", color="black", weight=3]; 130.29/78.20 63229[label="zzz5135",fontsize=16,color="green",shape="box"];63230[label="zzz5139",fontsize=16,color="green",shape="box"];63231 -> 7670[label="",style="dashed", color="red", weight=0]; 130.29/78.20 63231[label="FiniteMap.mkVBalBranch (Neg zzz5140) zzz5141 (FiniteMap.Branch zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134) zzz5138",fontsize=16,color="magenta"];63231 -> 63474[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63231 -> 63475[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63231 -> 63476[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63231 -> 63477[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63231 -> 63478[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63231 -> 63479[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63231 -> 63480[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63231 -> 63481[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63232[label="zzz5136",fontsize=16,color="green",shape="box"];47969[label="Zero",fontsize=16,color="green",shape="box"];47970[label="Zero",fontsize=16,color="green",shape="box"];47971[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255) (FiniteMap.mkVBalBranch3Size_l zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255) == LT)",fontsize=16,color="black",shape="box"];47971 -> 48075[label="",style="solid", color="black", weight=3]; 130.29/78.20 63233[label="zzz5251",fontsize=16,color="green",shape="box"];63234[label="zzz5255",fontsize=16,color="green",shape="box"];63235 -> 7670[label="",style="dashed", color="red", weight=0]; 130.29/78.20 63235[label="FiniteMap.mkVBalBranch (Neg zzz5256) zzz5257 (FiniteMap.Branch zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250) zzz5254",fontsize=16,color="magenta"];63235 -> 63482[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63235 -> 63483[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63235 -> 63484[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63235 -> 63485[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63235 -> 63486[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63235 -> 63487[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63235 -> 63488[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63235 -> 63489[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63236[label="zzz5252",fontsize=16,color="green",shape="box"];46879 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.20 46879[label="primPlusNat (Succ zzz3532000) (Succ zzz3532000)",fontsize=16,color="magenta"];46879 -> 46977[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 46879 -> 46978[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 47976[label="Zero",fontsize=16,color="green",shape="box"];47977[label="Zero",fontsize=16,color="green",shape="box"];34734[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Pos (primPlusNat (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200))) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];34734 -> 35518[label="",style="solid", color="black", weight=3]; 130.29/78.20 34735 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.20 34735[label="FiniteMap.mkBalBranch zzz5230 zzz5231 (FiniteMap.mkVBalBranch (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 (Pos Zero) zzz333 zzz334) zzz5233) zzz5234",fontsize=16,color="magenta"];34735 -> 63245[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34735 -> 63246[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34735 -> 63247[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34735 -> 63248[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 34736[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];34736 -> 35523[label="",style="solid", color="black", weight=3]; 130.29/78.20 34737[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];34737 -> 35524[label="",style="solid", color="black", weight=3]; 130.29/78.20 34738[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];34738 -> 35525[label="",style="solid", color="black", weight=3]; 130.29/78.20 34739[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Neg (primPlusNat (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200))) (Succ zzz33200)) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];34739 -> 35526[label="",style="solid", color="black", weight=3]; 130.29/78.20 63237[label="zzz5230",fontsize=16,color="green",shape="box"];63238[label="zzz5234",fontsize=16,color="green",shape="box"];63239 -> 7670[label="",style="dashed", color="red", weight=0]; 130.29/78.20 63239[label="FiniteMap.mkVBalBranch (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334) zzz5233",fontsize=16,color="magenta"];63239 -> 63490[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63239 -> 63491[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 63240[label="zzz5231",fontsize=16,color="green",shape="box"];34744[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];34744 -> 35529[label="",style="solid", color="black", weight=3]; 130.29/78.20 34745[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 < FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];34745 -> 35530[label="",style="solid", color="black", weight=3]; 130.29/78.20 34746[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];34746 -> 35531[label="",style="solid", color="black", weight=3]; 130.29/78.20 41775 -> 31992[label="",style="dashed", color="red", weight=0]; 130.29/78.20 41775[label="primPlusNat (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ zzz25020000)) (Succ (Succ zzz25020000)))) (Succ (Succ zzz25020000))) (Succ zzz25020000))) zzz25020000",fontsize=16,color="magenta"];41775 -> 41796[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 41776[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpNat (Succ zzz47130) zzz4714 == LT)",fontsize=16,color="burlywood",shape="box"];65534[label="zzz4714/Succ zzz47140",fontsize=10,color="white",style="solid",shape="box"];41776 -> 65534[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65534 -> 41797[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65535[label="zzz4714/Zero",fontsize=10,color="white",style="solid",shape="box"];41776 -> 65535[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65535 -> 41798[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 41777[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpNat Zero zzz4714 == LT)",fontsize=16,color="burlywood",shape="box"];65536[label="zzz4714/Succ zzz47140",fontsize=10,color="white",style="solid",shape="box"];41777 -> 65536[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65536 -> 41799[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65537[label="zzz4714/Zero",fontsize=10,color="white",style="solid",shape="box"];41777 -> 65537[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65537 -> 41800[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 39561 -> 38920[label="",style="dashed", color="red", weight=0]; 130.29/78.20 39561[label="primPlusNat (primPlusNat (Succ (primPlusNat (Succ Zero) (Succ Zero))) (Succ Zero)) Zero",fontsize=16,color="magenta"];39561 -> 39593[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 39562[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpNat (Succ zzz4436) (Succ zzz388700) == LT)",fontsize=16,color="black",shape="box"];39562 -> 39594[label="",style="solid", color="black", weight=3]; 130.29/78.20 39563[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpNat (Succ zzz4436) Zero == LT)",fontsize=16,color="black",shape="box"];39563 -> 39595[label="",style="solid", color="black", weight=3]; 130.29/78.20 34809[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];34809 -> 35545[label="",style="solid", color="black", weight=3]; 130.29/78.20 34810[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];34810 -> 35546[label="",style="solid", color="black", weight=3]; 130.29/78.20 34811[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ zzz342000000)))))) zzz343 zzz344 (primCmpNat Zero zzz342000000 == LT)",fontsize=16,color="burlywood",shape="box"];65538[label="zzz342000000/Succ zzz3420000000",fontsize=10,color="white",style="solid",shape="box"];34811 -> 65538[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65538 -> 35547[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65539[label="zzz342000000/Zero",fontsize=10,color="white",style="solid",shape="box"];34811 -> 65539[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65539 -> 35548[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 34812[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 False",fontsize=16,color="black",shape="box"];34812 -> 35549[label="",style="solid", color="black", weight=3]; 130.29/78.20 34813[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];34813 -> 35550[label="",style="solid", color="black", weight=3]; 130.29/78.20 34814[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];34814 -> 35551[label="",style="solid", color="black", weight=3]; 130.29/78.20 39342[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ Zero)",fontsize=16,color="black",shape="triangle"];39342 -> 39351[label="",style="solid", color="black", weight=3]; 130.29/78.20 39591[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpInt (Pos (Succ zzz44380)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];39591 -> 39669[label="",style="solid", color="black", weight=3]; 130.29/78.20 39592[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];39592 -> 39670[label="",style="solid", color="black", weight=3]; 130.29/78.20 34816[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpNat Zero (Succ zzz250200) == LT)",fontsize=16,color="black",shape="box"];34816 -> 35553[label="",style="solid", color="black", weight=3]; 130.29/78.20 34817[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat Zero (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];34817 -> 35554[label="",style="solid", color="black", weight=3]; 130.29/78.20 34818[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg Zero) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];34818 -> 35555[label="",style="solid", color="black", weight=3]; 130.29/78.20 34820[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];34820 -> 35557[label="",style="solid", color="black", weight=3]; 130.29/78.20 45832[label="zzz2503",fontsize=16,color="green",shape="box"];45833[label="zzz2501",fontsize=16,color="green",shape="box"];45834[label="zzz25020000",fontsize=16,color="green",shape="box"];45835[label="zzz340",fontsize=16,color="green",shape="box"];45836[label="Succ zzz342000000",fontsize=16,color="green",shape="box"];45837[label="zzz31",fontsize=16,color="green",shape="box"];45838[label="zzz341",fontsize=16,color="green",shape="box"];45839[label="Succ (Succ (Succ (Succ zzz342000000)))",fontsize=16,color="green",shape="box"];45840[label="Succ (Succ (primPlusNat (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ zzz25020000)) (Succ (Succ zzz25020000)))) (Succ (Succ zzz25020000))) (Succ zzz25020000))) zzz25020000))",fontsize=16,color="green",shape="box"];45840 -> 45979[label="",style="dashed", color="green", weight=3]; 130.29/78.20 45841[label="zzz2500",fontsize=16,color="green",shape="box"];45842[label="zzz2504",fontsize=16,color="green",shape="box"];45843[label="zzz343",fontsize=16,color="green",shape="box"];45844[label="zzz344",fontsize=16,color="green",shape="box"];45845[label="zzz300",fontsize=16,color="green",shape="box"];45831[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpNat zzz5124 zzz5125 == LT)",fontsize=16,color="burlywood",shape="triangle"];65540[label="zzz5124/Succ zzz51240",fontsize=10,color="white",style="solid",shape="box"];45831 -> 65540[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65540 -> 45980[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65541[label="zzz5124/Zero",fontsize=10,color="white",style="solid",shape="box"];45831 -> 65541[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65541 -> 45981[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 39688[label="Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ Zero) (Succ Zero))) (Succ Zero)) Zero)",fontsize=16,color="green",shape="box"];39688 -> 39758[label="",style="dashed", color="green", weight=3]; 130.29/78.20 39689[label="zzz343",fontsize=16,color="green",shape="box"];39690[label="zzz2504",fontsize=16,color="green",shape="box"];39691[label="zzz341",fontsize=16,color="green",shape="box"];39692[label="zzz300",fontsize=16,color="green",shape="box"];39693[label="zzz2500",fontsize=16,color="green",shape="box"];39694[label="zzz2503",fontsize=16,color="green",shape="box"];39695[label="Succ (Succ (Succ (Succ zzz342000000)))",fontsize=16,color="green",shape="box"];39696[label="zzz2501",fontsize=16,color="green",shape="box"];39697[label="zzz344",fontsize=16,color="green",shape="box"];39698[label="zzz340",fontsize=16,color="green",shape="box"];39699[label="zzz31",fontsize=16,color="green",shape="box"];39700[label="Succ zzz342000000",fontsize=16,color="green",shape="box"];39687[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpNat zzz4114 (Succ zzz4455) == LT)",fontsize=16,color="burlywood",shape="triangle"];65542[label="zzz4114/Succ zzz41140",fontsize=10,color="white",style="solid",shape="box"];39687 -> 65542[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65542 -> 39759[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65543[label="zzz4114/Zero",fontsize=10,color="white",style="solid",shape="box"];39687 -> 65543[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65543 -> 39760[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 45846[label="zzz2503",fontsize=16,color="green",shape="box"];45847[label="zzz2501",fontsize=16,color="green",shape="box"];45848[label="zzz25020000",fontsize=16,color="green",shape="box"];45849[label="zzz340",fontsize=16,color="green",shape="box"];45850[label="Zero",fontsize=16,color="green",shape="box"];45851[label="zzz31",fontsize=16,color="green",shape="box"];45852[label="zzz341",fontsize=16,color="green",shape="box"];45853[label="Succ (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];45854[label="Succ (Succ (primPlusNat (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ zzz25020000)) (Succ (Succ zzz25020000)))) (Succ (Succ zzz25020000))) (Succ zzz25020000))) zzz25020000))",fontsize=16,color="green",shape="box"];45854 -> 45982[label="",style="dashed", color="green", weight=3]; 130.29/78.20 45855[label="zzz2500",fontsize=16,color="green",shape="box"];45856[label="zzz2504",fontsize=16,color="green",shape="box"];45857[label="zzz343",fontsize=16,color="green",shape="box"];45858[label="zzz344",fontsize=16,color="green",shape="box"];45859[label="zzz300",fontsize=16,color="green",shape="box"];39701[label="Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ Zero) (Succ Zero))) (Succ Zero)) Zero)",fontsize=16,color="green",shape="box"];39701 -> 39761[label="",style="dashed", color="green", weight=3]; 130.29/78.20 39702[label="zzz343",fontsize=16,color="green",shape="box"];39703[label="zzz2504",fontsize=16,color="green",shape="box"];39704[label="zzz341",fontsize=16,color="green",shape="box"];39705[label="zzz300",fontsize=16,color="green",shape="box"];39706[label="zzz2500",fontsize=16,color="green",shape="box"];39707[label="zzz2503",fontsize=16,color="green",shape="box"];39708[label="Succ (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];39709[label="zzz2501",fontsize=16,color="green",shape="box"];39710[label="zzz344",fontsize=16,color="green",shape="box"];39711[label="zzz340",fontsize=16,color="green",shape="box"];39712[label="zzz31",fontsize=16,color="green",shape="box"];39713[label="Zero",fontsize=16,color="green",shape="box"];34907[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ (Succ zzz3420000000))))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ (Succ zzz3420000000))))))) zzz343 zzz344 (primCmpNat (Succ zzz3420000000) (primPlusNat Zero Zero) == LT)",fontsize=16,color="black",shape="box"];34907 -> 35566[label="",style="solid", color="black", weight=3]; 130.29/78.20 34908[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpNat Zero (primPlusNat Zero Zero) == LT)",fontsize=16,color="black",shape="box"];34908 -> 35567[label="",style="solid", color="black", weight=3]; 130.29/78.20 34909[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];34909 -> 35568[label="",style="solid", color="black", weight=3]; 130.29/78.20 63469[label="FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504",fontsize=16,color="green",shape="box"];63470[label="zzz343",fontsize=16,color="green",shape="box"];34913[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpNat Zero (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz34200 zzz34200)) zzz34200)) zzz34200)) zzz34200))) == LT)",fontsize=16,color="black",shape="box"];34913 -> 35570[label="",style="solid", color="black", weight=3]; 130.29/78.20 62954[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpNat (Succ zzz6355000) zzz635400 == GT)",fontsize=16,color="burlywood",shape="box"];65544[label="zzz635400/Succ zzz6354000",fontsize=10,color="white",style="solid",shape="box"];62954 -> 65544[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65544 -> 62980[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65545[label="zzz635400/Zero",fontsize=10,color="white",style="solid",shape="box"];62954 -> 65545[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65545 -> 62981[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 62955[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (primCmpNat Zero zzz635400 == GT)",fontsize=16,color="burlywood",shape="box"];65546[label="zzz635400/Succ zzz6354000",fontsize=10,color="white",style="solid",shape="box"];62955 -> 65546[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65546 -> 62982[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65547[label="zzz635400/Zero",fontsize=10,color="white",style="solid",shape="box"];62955 -> 65547[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65547 -> 62983[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 63241[label="FiniteMap.glueBal2Mid_key2 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464)",fontsize=16,color="black",shape="box"];63241 -> 63492[label="",style="solid", color="black", weight=3]; 130.29/78.20 63242[label="FiniteMap.deleteMin (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034)",fontsize=16,color="burlywood",shape="triangle"];65548[label="zzz474033/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];63242 -> 65548[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65548 -> 63493[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65549[label="zzz474033/FiniteMap.Branch zzz4740330 zzz4740331 zzz4740332 zzz4740333 zzz4740334",fontsize=10,color="white",style="solid",shape="box"];63242 -> 65549[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65549 -> 63494[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 63243[label="FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464",fontsize=16,color="green",shape="box"];63244[label="FiniteMap.glueBal2Mid_elt2 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464)",fontsize=16,color="black",shape="box"];63244 -> 63495[label="",style="solid", color="black", weight=3]; 130.29/78.20 62957[label="FiniteMap.glueBal2GlueBal0 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) True",fontsize=16,color="black",shape="box"];62957 -> 62985[label="",style="solid", color="black", weight=3]; 130.29/78.20 62958[label="zzz635500",fontsize=16,color="green",shape="box"];62959[label="zzz635400",fontsize=16,color="green",shape="box"];64315[label="zzz64420",fontsize=16,color="green",shape="box"];64316[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat (Succ zzz644300) zzz6444 == GT)",fontsize=16,color="burlywood",shape="triangle"];65550[label="zzz6444/Succ zzz64440",fontsize=10,color="white",style="solid",shape="box"];64316 -> 65550[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65550 -> 64335[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65551[label="zzz6444/Zero",fontsize=10,color="white",style="solid",shape="box"];64316 -> 65551[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65551 -> 64336[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 64317[label="zzz64420",fontsize=16,color="green",shape="box"];64318[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (GT == GT)",fontsize=16,color="black",shape="triangle"];64318 -> 64337[label="",style="solid", color="black", weight=3]; 130.29/78.20 64319[label="zzz64420",fontsize=16,color="green",shape="box"];64320[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (Pos (Succ zzz64460)) == GT)",fontsize=16,color="black",shape="box"];64320 -> 64338[label="",style="solid", color="black", weight=3]; 130.29/78.20 64321[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];64321 -> 64339[label="",style="solid", color="black", weight=3]; 130.29/78.20 64322[label="zzz64420",fontsize=16,color="green",shape="box"];64323[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (Neg (Succ zzz64470)) == GT)",fontsize=16,color="black",shape="box"];64323 -> 64340[label="",style="solid", color="black", weight=3]; 130.29/78.20 64324[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];64324 -> 64341[label="",style="solid", color="black", weight=3]; 130.29/78.20 64325[label="zzz64420",fontsize=16,color="green",shape="box"];64326[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (LT == GT)",fontsize=16,color="black",shape="triangle"];64326 -> 64342[label="",style="solid", color="black", weight=3]; 130.29/78.20 64327[label="zzz64420",fontsize=16,color="green",shape="box"];64328[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat zzz6449 (Succ zzz644300) == GT)",fontsize=16,color="burlywood",shape="triangle"];65552[label="zzz6449/Succ zzz64490",fontsize=10,color="white",style="solid",shape="box"];64328 -> 65552[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65552 -> 64343[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 65553[label="zzz6449/Zero",fontsize=10,color="white",style="solid",shape="box"];64328 -> 65553[label="",style="solid", color="burlywood", weight=9]; 130.29/78.20 65553 -> 64344[label="",style="solid", color="burlywood", weight=3]; 130.29/78.20 64329[label="zzz64420",fontsize=16,color="green",shape="box"];64330[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (Pos (Succ zzz64500)) == GT)",fontsize=16,color="black",shape="box"];64330 -> 64345[label="",style="solid", color="black", weight=3]; 130.29/78.20 64331[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];64331 -> 64346[label="",style="solid", color="black", weight=3]; 130.29/78.20 64332[label="zzz64420",fontsize=16,color="green",shape="box"];64333[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (Neg (Succ zzz64510)) == GT)",fontsize=16,color="black",shape="box"];64333 -> 64347[label="",style="solid", color="black", weight=3]; 130.29/78.20 64334[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];64334 -> 64348[label="",style="solid", color="black", weight=3]; 130.29/78.20 35073 -> 44629[label="",style="dashed", color="red", weight=0]; 130.29/78.20 35073[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ (Succ zzz332000))) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ (Succ zzz4262000))) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ (Succ zzz332000))) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ (Succ zzz4262000))) zzz4263 zzz4264 (primCmpNat (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) zzz332000))) zzz4262000 == LT)",fontsize=16,color="magenta"];35073 -> 44700[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35073 -> 44701[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35073 -> 44702[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35073 -> 44703[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35073 -> 44704[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35073 -> 44705[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35073 -> 44706[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35073 -> 44707[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35073 -> 44708[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35073 -> 44709[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35073 -> 44710[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35073 -> 44711[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35073 -> 44712[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35073 -> 44713[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35074 -> 45509[label="",style="dashed", color="red", weight=0]; 130.29/78.20 35074[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ Zero)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ (Succ zzz4262000))) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ Zero)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ (Succ zzz4262000))) zzz4263 zzz4264 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) zzz4262000 == LT)",fontsize=16,color="magenta"];35074 -> 45562[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35074 -> 45563[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35074 -> 45564[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35074 -> 45565[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35074 -> 45566[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35074 -> 45567[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35074 -> 45568[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35074 -> 45569[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35074 -> 45570[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35074 -> 45571[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35074 -> 45572[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35074 -> 45573[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35074 -> 45574[label="",style="dashed", color="magenta", weight=3]; 130.29/78.20 35075[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 < FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264)",fontsize=16,color="black",shape="box"];35075 -> 35616[label="",style="solid", color="black", weight=3]; 130.29/78.21 35076[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];35076 -> 35617[label="",style="solid", color="black", weight=3]; 130.29/78.21 35077[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];35077 -> 35618[label="",style="solid", color="black", weight=3]; 130.29/78.21 35078[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 otherwise",fontsize=16,color="black",shape="box"];35078 -> 35619[label="",style="solid", color="black", weight=3]; 130.29/78.21 35080[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 otherwise",fontsize=16,color="black",shape="box"];35080 -> 35621[label="",style="solid", color="black", weight=3]; 130.29/78.21 35081[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ (Succ zzz332000))) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ (Succ zzz42620000)))) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ (Succ zzz332000))) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ (Succ zzz42620000)))) zzz4263 zzz4264 (primCmpNat (Succ zzz42620000) (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) == LT)",fontsize=16,color="black",shape="box"];35081 -> 35622[label="",style="solid", color="black", weight=3]; 130.29/78.21 35082[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ Zero)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ (Succ zzz42620000)))) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ Zero)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ (Succ zzz42620000)))) zzz4263 zzz4264 (primCmpNat (Succ zzz42620000) (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) Zero) == LT)",fontsize=16,color="black",shape="box"];35082 -> 35623[label="",style="solid", color="black", weight=3]; 130.29/78.21 35083[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ (Succ zzz332000))) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ Zero))) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ (Succ zzz332000))) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ Zero))) zzz4263 zzz4264 (primCmpNat Zero (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) == LT)",fontsize=16,color="black",shape="box"];35083 -> 35624[label="",style="solid", color="black", weight=3]; 130.29/78.21 35084[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ Zero)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ Zero))) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ Zero)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ Zero))) zzz4263 zzz4264 (primCmpNat Zero (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) Zero) == LT)",fontsize=16,color="black",shape="box"];35084 -> 35625[label="",style="solid", color="black", weight=3]; 130.29/78.21 35085 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.21 35085[label="FiniteMap.mkBalBranch zzz4260 zzz4261 (FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334) zzz4263) zzz4264",fontsize=16,color="magenta"];35085 -> 63249[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35085 -> 63250[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35085 -> 63251[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35085 -> 63252[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63471[label="Neg (Succ zzz33200)",fontsize=16,color="green",shape="box"];63472[label="Succ zzz3000",fontsize=16,color="green",shape="box"];63473[label="zzz4263",fontsize=16,color="green",shape="box"];35089[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 otherwise",fontsize=16,color="black",shape="box"];35089 -> 35630[label="",style="solid", color="black", weight=3]; 130.29/78.21 35091[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 otherwise",fontsize=16,color="black",shape="box"];35091 -> 35632[label="",style="solid", color="black", weight=3]; 130.29/78.21 45177[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002)) (FiniteMap.mkVBalBranch3Size_l zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002) == LT)",fontsize=16,color="black",shape="box"];45177 -> 45225[label="",style="solid", color="black", weight=3]; 130.29/78.21 46196[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098)) (FiniteMap.mkVBalBranch3Size_l zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098) == LT)",fontsize=16,color="black",shape="box"];46196 -> 46378[label="",style="solid", color="black", weight=3]; 130.29/78.21 50890[label="Zero",fontsize=16,color="green",shape="box"];50891[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (primCmpInt (Pos (Succ zzz55410)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];50891 -> 51049[label="",style="solid", color="black", weight=3]; 130.29/78.21 50892[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];50892 -> 51050[label="",style="solid", color="black", weight=3]; 130.29/78.21 35170[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (primCmpNat Zero (Succ zzz353200) == LT)",fontsize=16,color="black",shape="box"];35170 -> 35719[label="",style="solid", color="black", weight=3]; 130.29/78.21 49820[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg (Succ zzz54600)) (Pos (Succ zzz33200)) == LT)",fontsize=16,color="black",shape="box"];49820 -> 49829[label="",style="solid", color="black", weight=3]; 130.29/78.21 49821[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg Zero) (Pos (Succ zzz33200)) == LT)",fontsize=16,color="black",shape="box"];49821 -> 49830[label="",style="solid", color="black", weight=3]; 130.29/78.21 35172[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Neg Zero) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];35172 -> 35721[label="",style="solid", color="black", weight=3]; 130.29/78.21 46966[label="Succ zzz3532000",fontsize=16,color="green",shape="box"];46967[label="Succ zzz3532000",fontsize=16,color="green",shape="box"];46968[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139) (FiniteMap.mkVBalBranch3Size_l zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139) == LT)",fontsize=16,color="black",shape="box"];46968 -> 46984[label="",style="solid", color="black", weight=3]; 130.29/78.21 63474[label="Neg (Succ (Succ zzz5132))",fontsize=16,color="green",shape="box"];63475[label="zzz5140",fontsize=16,color="green",shape="box"];63476[label="zzz5134",fontsize=16,color="green",shape="box"];63477[label="zzz5138",fontsize=16,color="green",shape="box"];63478[label="zzz5130",fontsize=16,color="green",shape="box"];63479[label="zzz5133",fontsize=16,color="green",shape="box"];63480[label="zzz5141",fontsize=16,color="green",shape="box"];63481[label="zzz5131",fontsize=16,color="green",shape="box"];48075[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255) (FiniteMap.mkVBalBranch3Size_l zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255) == LT)",fontsize=16,color="black",shape="box"];48075 -> 48174[label="",style="solid", color="black", weight=3]; 130.29/78.21 63482[label="Neg (Succ Zero)",fontsize=16,color="green",shape="box"];63483[label="zzz5256",fontsize=16,color="green",shape="box"];63484[label="zzz5250",fontsize=16,color="green",shape="box"];63485[label="zzz5254",fontsize=16,color="green",shape="box"];63486[label="zzz5247",fontsize=16,color="green",shape="box"];63487[label="zzz5249",fontsize=16,color="green",shape="box"];63488[label="zzz5257",fontsize=16,color="green",shape="box"];63489[label="zzz5248",fontsize=16,color="green",shape="box"];46977[label="Succ zzz3532000",fontsize=16,color="green",shape="box"];46978[label="Succ zzz3532000",fontsize=16,color="green",shape="box"];35518[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Pos (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200))) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];35518 -> 35975[label="",style="solid", color="black", weight=3]; 130.29/78.21 63245[label="zzz5230",fontsize=16,color="green",shape="box"];63246[label="zzz5234",fontsize=16,color="green",shape="box"];63247 -> 7670[label="",style="dashed", color="red", weight=0]; 130.29/78.21 63247[label="FiniteMap.mkVBalBranch (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 (Pos Zero) zzz333 zzz334) zzz5233",fontsize=16,color="magenta"];63247 -> 63496[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63247 -> 63497[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63248[label="zzz5231",fontsize=16,color="green",shape="box"];35523[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];35523 -> 35978[label="",style="solid", color="black", weight=3]; 130.29/78.21 35524[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];35524 -> 35979[label="",style="solid", color="black", weight=3]; 130.29/78.21 35525[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];35525 -> 35980[label="",style="solid", color="black", weight=3]; 130.29/78.21 35526[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Neg (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200))) (Succ zzz33200))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];35526 -> 35981[label="",style="solid", color="black", weight=3]; 130.29/78.21 63490[label="Neg Zero",fontsize=16,color="green",shape="box"];63491[label="zzz5233",fontsize=16,color="green",shape="box"];35529[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];35529 -> 35982[label="",style="solid", color="black", weight=3]; 130.29/78.21 35530[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];35530 -> 35983[label="",style="solid", color="black", weight=3]; 130.29/78.21 35531[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];35531 -> 35984[label="",style="solid", color="black", weight=3]; 130.29/78.21 41796[label="zzz25020000",fontsize=16,color="green",shape="box"];31992[label="primPlusNat (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ zzz620000)) (Succ (Succ zzz620000)))) (Succ (Succ zzz620000))) (Succ zzz620000))) zzz620000",fontsize=16,color="burlywood",shape="triangle"];65554[label="zzz620000/Succ zzz6200000",fontsize=10,color="white",style="solid",shape="box"];31992 -> 65554[label="",style="solid", color="burlywood", weight=9]; 130.29/78.21 65554 -> 32611[label="",style="solid", color="burlywood", weight=3]; 130.29/78.21 65555[label="zzz620000/Zero",fontsize=10,color="white",style="solid",shape="box"];31992 -> 65555[label="",style="solid", color="burlywood", weight=9]; 130.29/78.21 65555 -> 32612[label="",style="solid", color="burlywood", weight=3]; 130.29/78.21 41797[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpNat (Succ zzz47130) (Succ zzz47140) == LT)",fontsize=16,color="black",shape="box"];41797 -> 41822[label="",style="solid", color="black", weight=3]; 130.29/78.21 41798[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpNat (Succ zzz47130) Zero == LT)",fontsize=16,color="black",shape="box"];41798 -> 41823[label="",style="solid", color="black", weight=3]; 130.29/78.21 41799[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpNat Zero (Succ zzz47140) == LT)",fontsize=16,color="black",shape="box"];41799 -> 41824[label="",style="solid", color="black", weight=3]; 130.29/78.21 41800[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];41800 -> 41825[label="",style="solid", color="black", weight=3]; 130.29/78.21 39593 -> 38195[label="",style="dashed", color="red", weight=0]; 130.29/78.21 39593[label="primPlusNat (Succ (primPlusNat (Succ Zero) (Succ Zero))) (Succ Zero)",fontsize=16,color="magenta"];39593 -> 39671[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 38920[label="primPlusNat zzz37520 Zero",fontsize=16,color="burlywood",shape="triangle"];65556[label="zzz37520/Succ zzz375200",fontsize=10,color="white",style="solid",shape="box"];38920 -> 65556[label="",style="solid", color="burlywood", weight=9]; 130.29/78.21 65556 -> 38938[label="",style="solid", color="burlywood", weight=3]; 130.29/78.21 65557[label="zzz37520/Zero",fontsize=10,color="white",style="solid",shape="box"];38920 -> 65557[label="",style="solid", color="burlywood", weight=9]; 130.29/78.21 65557 -> 38939[label="",style="solid", color="burlywood", weight=3]; 130.29/78.21 39594[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpNat zzz4436 zzz388700 == LT)",fontsize=16,color="burlywood",shape="triangle"];65558[label="zzz4436/Succ zzz44360",fontsize=10,color="white",style="solid",shape="box"];39594 -> 65558[label="",style="solid", color="burlywood", weight=9]; 130.29/78.21 65558 -> 39672[label="",style="solid", color="burlywood", weight=3]; 130.29/78.21 65559[label="zzz4436/Zero",fontsize=10,color="white",style="solid",shape="box"];39594 -> 65559[label="",style="solid", color="burlywood", weight=9]; 130.29/78.21 65559 -> 39673[label="",style="solid", color="burlywood", weight=3]; 130.29/78.21 39595[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (GT == LT)",fontsize=16,color="black",shape="triangle"];39595 -> 39674[label="",style="solid", color="black", weight=3]; 130.29/78.21 35545[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt 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(Pos (Succ (Succ Zero))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];35546 -> 35999[label="",style="solid", color="black", weight=3]; 130.29/78.21 35547[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ (Succ zzz3420000000))))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ (Succ zzz3420000000))))))) zzz343 zzz344 (primCmpNat Zero (Succ zzz3420000000) == LT)",fontsize=16,color="black",shape="box"];35547 -> 36000[label="",style="solid", color="black", weight=3]; 130.29/78.21 35548[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];35548 -> 36001[label="",style="solid", color="black", weight=3]; 130.29/78.21 35549[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344)",fontsize=16,color="black",shape="box"];35549 -> 36002[label="",style="solid", color="black", weight=3]; 130.29/78.21 35550[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];35550 -> 36003[label="",style="solid", color="black", weight=3]; 130.29/78.21 35551[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos (Succ (Succ Zero)))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];35551 -> 36004[label="",style="solid", color="black", weight=3]; 130.29/78.21 39351 -> 38195[label="",style="dashed", color="red", weight=0]; 130.29/78.21 39351[label="primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];39351 -> 39379[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 39669[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpInt (Pos (Succ zzz44380)) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];39669 -> 39762[label="",style="solid", color="black", weight=3]; 130.29/78.21 39670[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];39670 -> 39763[label="",style="solid", color="black", weight=3]; 130.29/78.21 35553[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];35553 -> 36006[label="",style="solid", color="black", weight=3]; 130.29/78.21 35554[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat Zero (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];35554 -> 36007[label="",style="solid", color="black", weight=3]; 130.29/78.21 35555 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.21 35555[label="FiniteMap.mkBalBranch zzz2500 zzz2501 zzz2503 (FiniteMap.mkVBalBranch (Pos zzz300) zzz31 zzz2504 (FiniteMap.Branch zzz340 zzz341 (Neg Zero) zzz343 zzz344))",fontsize=16,color="magenta"];35555 -> 63253[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35555 -> 63254[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35555 -> 63255[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35555 -> 63256[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35557 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.21 35557[label="FiniteMap.mkBalBranch zzz2500 zzz2501 zzz2503 (FiniteMap.mkVBalBranch (Pos zzz300) zzz31 zzz2504 (FiniteMap.Branch zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344))",fontsize=16,color="magenta"];35557 -> 63257[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35557 -> 63258[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35557 -> 63259[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35557 -> 63260[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 45979 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.21 45979[label="primPlusNat (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ zzz25020000)) (Succ (Succ zzz25020000)))) (Succ (Succ zzz25020000))) (Succ zzz25020000))) zzz25020000",fontsize=16,color="magenta"];45979 -> 46073[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 45979 -> 46074[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 45980[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpNat (Succ zzz51240) zzz5125 == LT)",fontsize=16,color="burlywood",shape="box"];65560[label="zzz5125/Succ zzz51250",fontsize=10,color="white",style="solid",shape="box"];45980 -> 65560[label="",style="solid", color="burlywood", weight=9]; 130.29/78.21 65560 -> 46075[label="",style="solid", color="burlywood", weight=3]; 130.29/78.21 65561[label="zzz5125/Zero",fontsize=10,color="white",style="solid",shape="box"];45980 -> 65561[label="",style="solid", color="burlywood", weight=9]; 130.29/78.21 65561 -> 46076[label="",style="solid", color="burlywood", weight=3]; 130.29/78.21 45981[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpNat Zero zzz5125 == LT)",fontsize=16,color="burlywood",shape="box"];65562[label="zzz5125/Succ zzz51250",fontsize=10,color="white",style="solid",shape="box"];45981 -> 65562[label="",style="solid", color="burlywood", weight=9]; 130.29/78.21 65562 -> 46077[label="",style="solid", color="burlywood", weight=3]; 130.29/78.21 65563[label="zzz5125/Zero",fontsize=10,color="white",style="solid",shape="box"];45981 -> 65563[label="",style="solid", color="burlywood", weight=9]; 130.29/78.21 65563 -> 46078[label="",style="solid", color="burlywood", weight=3]; 130.29/78.21 39758 -> 38920[label="",style="dashed", color="red", weight=0]; 130.29/78.21 39758[label="primPlusNat (primPlusNat (Succ (primPlusNat (Succ Zero) (Succ Zero))) (Succ Zero)) Zero",fontsize=16,color="magenta"];39758 -> 39826[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 39759[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpNat (Succ zzz41140) (Succ zzz4455) == LT)",fontsize=16,color="black",shape="box"];39759 -> 39827[label="",style="solid", color="black", weight=3]; 130.29/78.21 39760[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpNat Zero (Succ zzz4455) == LT)",fontsize=16,color="black",shape="box"];39760 -> 39828[label="",style="solid", color="black", weight=3]; 130.29/78.21 45982 -> 42929[label="",style="dashed", color="red", weight=0]; 130.29/78.21 45982[label="primPlusNat (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ zzz25020000)) (Succ (Succ zzz25020000)))) (Succ (Succ zzz25020000))) (Succ zzz25020000))) zzz25020000",fontsize=16,color="magenta"];45982 -> 46079[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 45982 -> 46080[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 39761 -> 38920[label="",style="dashed", color="red", weight=0]; 130.29/78.21 39761[label="primPlusNat (primPlusNat (Succ (primPlusNat (Succ Zero) (Succ Zero))) (Succ Zero)) Zero",fontsize=16,color="magenta"];39761 -> 39829[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35566 -> 36026[label="",style="dashed", color="red", weight=0]; 130.29/78.21 35566[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ (Succ zzz3420000000))))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ (Succ zzz3420000000))))))) zzz343 zzz344 (primCmpNat (Succ zzz3420000000) Zero == LT)",fontsize=16,color="magenta"];35566 -> 36027[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35566 -> 36028[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35566 -> 36029[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35566 -> 36030[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35566 -> 36031[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35566 -> 36032[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35566 -> 36033[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35566 -> 36034[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35566 -> 36035[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35566 -> 36036[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35566 -> 36037[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35566 -> 36038[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35567[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 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63003[label="",style="solid", color="black", weight=3]; 130.29/78.21 63492[label="FiniteMap.glueBal2Mid_key20 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.glueBal2Vv3 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464))",fontsize=16,color="black",shape="box"];63492 -> 63580[label="",style="solid", color="black", weight=3]; 130.29/78.21 63493[label="FiniteMap.deleteMin (FiniteMap.Branch zzz474030 zzz474031 zzz474032 FiniteMap.EmptyFM zzz474034)",fontsize=16,color="black",shape="box"];63493 -> 63581[label="",style="solid", color="black", weight=3]; 130.29/78.21 63494[label="FiniteMap.deleteMin (FiniteMap.Branch zzz474030 zzz474031 zzz474032 (FiniteMap.Branch zzz4740330 zzz4740331 zzz4740332 zzz4740333 zzz4740334) zzz474034)",fontsize=16,color="black",shape="box"];63494 -> 63582[label="",style="solid", color="black", weight=3]; 130.29/78.21 63495[label="FiniteMap.glueBal2Mid_elt20 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.glueBal2Vv3 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464))",fontsize=16,color="black",shape="box"];63495 -> 63583[label="",style="solid", color="black", weight=3]; 130.29/78.21 62985 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.21 62985[label="FiniteMap.mkBalBranch (FiniteMap.glueBal2Mid_key1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464)) (FiniteMap.glueBal2Mid_elt1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464)) (FiniteMap.deleteMax (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464)) (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034)",fontsize=16,color="magenta"];62985 -> 63265[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 62985 -> 63266[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 62985 -> 63267[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 62985 -> 63268[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 64335[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat (Succ zzz644300) (Succ zzz64440) == GT)",fontsize=16,color="black",shape="box"];64335 -> 64349[label="",style="solid", color="black", weight=3]; 130.29/78.21 64336[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat (Succ zzz644300) Zero == GT)",fontsize=16,color="black",shape="box"];64336 -> 64350[label="",style="solid", color="black", weight=3]; 130.29/78.21 64337[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 True",fontsize=16,color="black",shape="box"];64337 -> 64351[label="",style="solid", color="black", weight=3]; 130.29/78.21 64338 -> 64328[label="",style="dashed", color="red", weight=0]; 130.29/78.21 64338[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat Zero (Succ zzz64460) == GT)",fontsize=16,color="magenta"];64338 -> 64352[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 64338 -> 64353[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 64339[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (EQ == GT)",fontsize=16,color="black",shape="triangle"];64339 -> 64354[label="",style="solid", color="black", weight=3]; 130.29/78.21 64340 -> 64318[label="",style="dashed", color="red", weight=0]; 130.29/78.21 64340[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (GT == GT)",fontsize=16,color="magenta"];64341 -> 64339[label="",style="dashed", color="red", weight=0]; 130.29/78.21 64341[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (EQ == GT)",fontsize=16,color="magenta"];64342[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 False",fontsize=16,color="black",shape="triangle"];64342 -> 64355[label="",style="solid", color="black", weight=3]; 130.29/78.21 64343[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat (Succ zzz64490) (Succ zzz644300) == GT)",fontsize=16,color="black",shape="box"];64343 -> 64356[label="",style="solid", color="black", weight=3]; 130.29/78.21 64344[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat Zero (Succ zzz644300) == GT)",fontsize=16,color="black",shape="box"];64344 -> 64357[label="",style="solid", color="black", weight=3]; 130.29/78.21 64345 -> 64326[label="",style="dashed", color="red", weight=0]; 130.29/78.21 64345[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (LT == GT)",fontsize=16,color="magenta"];64346 -> 64339[label="",style="dashed", color="red", weight=0]; 130.29/78.21 64346[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (EQ == GT)",fontsize=16,color="magenta"];64347 -> 64316[label="",style="dashed", color="red", weight=0]; 130.29/78.21 64347[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat (Succ zzz64510) Zero == GT)",fontsize=16,color="magenta"];64347 -> 64358[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 64347 -> 64359[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 64348 -> 64339[label="",style="dashed", color="red", weight=0]; 130.29/78.21 64348[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (EQ == GT)",fontsize=16,color="magenta"];44700[label="zzz332000",fontsize=16,color="green",shape="box"];44701[label="zzz31",fontsize=16,color="green",shape="box"];44702[label="Succ zzz4262000",fontsize=16,color="green",shape="box"];44703[label="zzz4264",fontsize=16,color="green",shape="box"];44704[label="zzz334",fontsize=16,color="green",shape="box"];44705[label="zzz4261",fontsize=16,color="green",shape="box"];44706[label="zzz333",fontsize=16,color="green",shape="box"];44707[label="zzz4263",fontsize=16,color="green",shape="box"];44708[label="Succ (Succ (primPlusNat (primPlusNat (Succ 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zzz3000",fontsize=16,color="green",shape="box"];45568[label="zzz4260",fontsize=16,color="green",shape="box"];45569[label="zzz4261",fontsize=16,color="green",shape="box"];45570[label="zzz4263",fontsize=16,color="green",shape="box"];45571[label="zzz4262000",fontsize=16,color="green",shape="box"];45572[label="zzz31",fontsize=16,color="green",shape="box"];45573[label="Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)",fontsize=16,color="green",shape="box"];45573 -> 45662[label="",style="dashed", color="green", weight=3]; 130.29/78.21 45574[label="zzz330",fontsize=16,color="green",shape="box"];35616[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];35616 -> 36222[label="",style="solid", color="black", weight=3]; 130.29/78.21 35617[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];35617 -> 36223[label="",style="solid", color="black", weight=3]; 130.29/78.21 35618[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];35618 -> 36224[label="",style="solid", color="black", weight=3]; 130.29/78.21 35619[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 True",fontsize=16,color="black",shape="box"];35619 -> 36225[label="",style="solid", color="black", weight=3]; 130.29/78.21 35621[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 True",fontsize=16,color="black",shape="box"];35621 -> 36227[label="",style="solid", color="black", weight=3]; 130.29/78.21 35622 -> 46205[label="",style="dashed", color="red", weight=0]; 130.29/78.21 35622[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ (Succ zzz332000))) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ (Succ zzz42620000)))) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ (Succ zzz332000))) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ (Succ zzz42620000)))) zzz4263 zzz4264 (primCmpNat (Succ zzz42620000) (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) zzz332000))) == LT)",fontsize=16,color="magenta"];35622 -> 46304[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35622 -> 46305[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35622 -> 46306[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35622 -> 46307[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35622 -> 46308[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35622 -> 46309[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35622 -> 46310[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35622 -> 46311[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35622 -> 46312[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35622 -> 46313[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35622 -> 46314[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35622 -> 46315[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35622 -> 46316[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35622 -> 46317[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35623 -> 47219[label="",style="dashed", color="red", weight=0]; 130.29/78.21 35623[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ Zero)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ (Succ zzz42620000)))) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ Zero)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ (Succ zzz42620000)))) zzz4263 zzz4264 (primCmpNat (Succ zzz42620000) (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) == LT)",fontsize=16,color="magenta"];35623 -> 47311[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35623 -> 47312[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35623 -> 47313[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35623 -> 47314[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35623 -> 47315[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35623 -> 47316[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35623 -> 47317[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35623 -> 47318[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35623 -> 47319[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35623 -> 47320[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35623 -> 47321[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35623 -> 47322[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35623 -> 47323[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35624 -> 46205[label="",style="dashed", color="red", weight=0]; 130.29/78.21 35624[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ (Succ zzz332000))) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ Zero))) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ (Succ zzz332000))) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ Zero))) zzz4263 zzz4264 (primCmpNat Zero (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) zzz332000))) == LT)",fontsize=16,color="magenta"];35624 -> 46318[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35624 -> 46319[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35624 -> 46320[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35624 -> 46321[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35624 -> 46322[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35624 -> 46323[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35624 -> 46324[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35624 -> 46325[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35624 -> 46326[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35624 -> 46327[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35624 -> 46328[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35624 -> 46329[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35624 -> 46330[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35624 -> 46331[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35625 -> 47219[label="",style="dashed", color="red", weight=0]; 130.29/78.21 35625[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ Zero)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ Zero))) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Neg (Succ Zero)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ (Succ Zero))) zzz4263 zzz4264 (primCmpNat Zero (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) == LT)",fontsize=16,color="magenta"];35625 -> 47324[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35625 -> 47325[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35625 -> 47326[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35625 -> 47327[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35625 -> 47328[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35625 -> 47329[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35625 -> 47330[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35625 -> 47331[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35625 -> 47332[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35625 -> 47333[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35625 -> 47334[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35625 -> 47335[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35625 -> 47336[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63249[label="zzz4260",fontsize=16,color="green",shape="box"];63250[label="zzz4264",fontsize=16,color="green",shape="box"];63251 -> 7670[label="",style="dashed", color="red", weight=0]; 130.29/78.21 63251[label="FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334) zzz4263",fontsize=16,color="magenta"];63251 -> 63498[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63251 -> 63499[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63251 -> 63500[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63252[label="zzz4261",fontsize=16,color="green",shape="box"];35630[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 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zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002)) (FiniteMap.mkVBalBranch3Size_l zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002) == LT)",fontsize=16,color="black",shape="box"];45225 -> 45417[label="",style="solid", color="black", weight=3]; 130.29/78.21 46378[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098)) (FiniteMap.mkVBalBranch3Size_l zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098) == LT)",fontsize=16,color="black",shape="box"];46378 -> 46590[label="",style="solid", color="black", weight=3]; 130.29/78.21 51049[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (primCmpInt (Pos (Succ zzz55410)) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];51049 -> 51079[label="",style="solid", color="black", weight=3]; 130.29/78.21 51050[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];51050 -> 51080[label="",style="solid", color="black", weight=3]; 130.29/78.21 35719[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];35719 -> 36504[label="",style="solid", color="black", weight=3]; 130.29/78.21 49829[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (LT == LT)",fontsize=16,color="black",shape="triangle"];49829 -> 49857[label="",style="solid", color="black", weight=3]; 130.29/78.21 49830 -> 49829[label="",style="dashed", color="red", weight=0]; 130.29/78.21 49830[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (LT == LT)",fontsize=16,color="magenta"];35721 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.21 35721[label="FiniteMap.mkBalBranch zzz3530 zzz3531 zzz3533 (FiniteMap.mkVBalBranch (Neg Zero) zzz31 zzz3534 (FiniteMap.Branch zzz340 zzz341 (Neg Zero) zzz343 zzz344))",fontsize=16,color="magenta"];35721 -> 63269[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35721 -> 63270[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35721 -> 63271[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 35721 -> 63272[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 46984[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139)) (FiniteMap.mkVBalBranch3Size_l zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139) == LT)",fontsize=16,color="black",shape="box"];46984 -> 47058[label="",style="solid", color="black", weight=3]; 130.29/78.21 48174[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255)) (FiniteMap.mkVBalBranch3Size_l zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255) == LT)",fontsize=16,color="black",shape="box"];48174 -> 48265[label="",style="solid", color="black", weight=3]; 130.29/78.21 35975[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];35975 -> 36553[label="",style="solid", color="black", weight=3]; 130.29/78.21 63496[label="Pos Zero",fontsize=16,color="green",shape="box"];63497[label="zzz5233",fontsize=16,color="green",shape="box"];35978[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];35978 -> 36554[label="",style="solid", color="black", weight=3]; 130.29/78.21 35979[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];35979 -> 36555[label="",style="solid", color="black", weight=3]; 130.29/78.21 35980[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];35980 -> 36556[label="",style="solid", color="black", weight=3]; 130.29/78.21 35981[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];35981 -> 36557[label="",style="solid", color="black", weight=3]; 130.29/78.21 35982[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];35982 -> 36558[label="",style="solid", color="black", weight=3]; 130.29/78.21 35983[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];35983 -> 36559[label="",style="solid", color="black", weight=3]; 130.29/78.21 35984[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];35984 -> 36560[label="",style="solid", color="black", weight=3]; 130.29/78.21 32611[label="primPlusNat (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ (Succ zzz6200000))) (Succ (Succ (Succ zzz6200000))))) (Succ (Succ (Succ zzz6200000)))) (Succ (Succ zzz6200000)))) (Succ zzz6200000)",fontsize=16,color="black",shape="box"];32611 -> 34080[label="",style="solid", color="black", weight=3]; 130.29/78.21 32612[label="primPlusNat (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ Zero)) (Succ (Succ Zero)))) (Succ (Succ Zero))) (Succ Zero))) Zero",fontsize=16,color="black",shape="box"];32612 -> 34081[label="",style="solid", color="black", weight=3]; 130.29/78.21 41822 -> 41690[label="",style="dashed", color="red", weight=0]; 130.29/78.21 41822[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpNat zzz47130 zzz47140 == LT)",fontsize=16,color="magenta"];41822 -> 41905[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 41822 -> 41906[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 41823[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (GT == LT)",fontsize=16,color="black",shape="box"];41823 -> 41907[label="",style="solid", color="black", weight=3]; 130.29/78.21 41824[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (LT == LT)",fontsize=16,color="black",shape="box"];41824 -> 41908[label="",style="solid", color="black", weight=3]; 130.29/78.21 41825[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (EQ == LT)",fontsize=16,color="black",shape="box"];41825 -> 41909[label="",style="solid", color="black", weight=3]; 130.29/78.21 39671[label="Succ (primPlusNat (Succ Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];39671 -> 39764[label="",style="dashed", color="green", weight=3]; 130.29/78.21 38195[label="primPlusNat zzz3752 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];65564[label="zzz3752/Succ zzz37520",fontsize=10,color="white",style="solid",shape="box"];38195 -> 65564[label="",style="solid", color="burlywood", weight=9]; 130.29/78.21 65564 -> 38742[label="",style="solid", color="burlywood", weight=3]; 130.29/78.21 65565[label="zzz3752/Zero",fontsize=10,color="white",style="solid",shape="box"];38195 -> 65565[label="",style="solid", color="burlywood", weight=9]; 130.29/78.21 65565 -> 38743[label="",style="solid", color="burlywood", weight=3]; 130.29/78.21 38938[label="primPlusNat (Succ zzz375200) Zero",fontsize=16,color="black",shape="box"];38938 -> 38960[label="",style="solid", color="black", weight=3]; 130.29/78.21 38939[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];38939 -> 38961[label="",style="solid", color="black", weight=3]; 130.29/78.21 39672[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpNat (Succ zzz44360) zzz388700 == LT)",fontsize=16,color="burlywood",shape="box"];65566[label="zzz388700/Succ zzz3887000",fontsize=10,color="white",style="solid",shape="box"];39672 -> 65566[label="",style="solid", color="burlywood", weight=9]; 130.29/78.21 65566 -> 39765[label="",style="solid", color="burlywood", weight=3]; 130.29/78.21 65567[label="zzz388700/Zero",fontsize=10,color="white",style="solid",shape="box"];39672 -> 65567[label="",style="solid", color="burlywood", weight=9]; 130.29/78.21 65567 -> 39766[label="",style="solid", color="burlywood", weight=3]; 130.29/78.21 39673[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpNat Zero zzz388700 == LT)",fontsize=16,color="burlywood",shape="box"];65568[label="zzz388700/Succ zzz3887000",fontsize=10,color="white",style="solid",shape="box"];39673 -> 65568[label="",style="solid", color="burlywood", weight=9]; 130.29/78.21 65568 -> 39767[label="",style="solid", color="burlywood", weight=3]; 130.29/78.21 65569[label="zzz388700/Zero",fontsize=10,color="white",style="solid",shape="box"];39673 -> 65569[label="",style="solid", color="burlywood", weight=9]; 130.29/78.21 65569 -> 39768[label="",style="solid", color="burlywood", weight=3]; 130.29/78.21 39674[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 False",fontsize=16,color="black",shape="triangle"];39674 -> 39769[label="",style="solid", color="black", weight=3]; 130.29/78.21 35998[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];35998 -> 36612[label="",style="solid", color="black", weight=3]; 130.29/78.21 35999 -> 41786[label="",style="dashed", color="red", weight=0]; 130.29/78.21 35999[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ (Succ Zero)))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) == LT)",fontsize=16,color="magenta"];35999 -> 41787[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 36000 -> 36614[label="",style="dashed", color="red", weight=0]; 130.29/78.21 36000[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ (Succ zzz3420000000))))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ (Succ zzz3420000000))))))) zzz343 zzz344 (LT == LT)",fontsize=16,color="magenta"];36000 -> 36615[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 36000 -> 36616[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 36000 -> 36617[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 36000 -> 36618[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 36000 -> 36619[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 36000 -> 36620[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 36000 -> 36621[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 36000 -> 36622[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 36000 -> 36623[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 36000 -> 36624[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 36000 -> 36625[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 36001[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (EQ == LT)",fontsize=16,color="black",shape="box"];36001 -> 36627[label="",style="solid", color="black", weight=3]; 130.29/78.21 36002[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];36002 -> 36628[label="",style="solid", color="black", weight=3]; 130.29/78.21 36003[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];36003 -> 36629[label="",style="solid", color="black", weight=3]; 130.29/78.21 36004 -> 41812[label="",style="dashed", color="red", weight=0]; 130.29/78.21 36004[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ (Succ Zero)))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) == LT)",fontsize=16,color="magenta"];36004 -> 41813[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 39379[label="primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ Zero)",fontsize=16,color="black",shape="box"];39379 -> 39477[label="",style="solid", color="black", weight=3]; 130.29/78.21 39762[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpInt (Pos (Succ zzz44380)) (Pos (Succ zzz250200)) == LT)",fontsize=16,color="black",shape="box"];39762 -> 39830[label="",style="solid", color="black", weight=3]; 130.29/78.21 39763[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpInt (Pos Zero) (Pos (Succ zzz250200)) == LT)",fontsize=16,color="black",shape="box"];39763 -> 39831[label="",style="solid", color="black", weight=3]; 130.29/78.21 36006[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos Zero) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];36006 -> 36632[label="",style="solid", color="black", weight=3]; 130.29/78.21 36007[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (primPlusNat (primPlusNat (Succ zzz34200) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];36007 -> 36633[label="",style="solid", color="black", weight=3]; 130.29/78.21 63253[label="zzz2500",fontsize=16,color="green",shape="box"];63254 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.21 63254[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 zzz2504 (FiniteMap.Branch zzz340 zzz341 (Neg Zero) zzz343 zzz344)",fontsize=16,color="magenta"];63254 -> 63501[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63254 -> 63502[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63255[label="zzz2503",fontsize=16,color="green",shape="box"];63256[label="zzz2501",fontsize=16,color="green",shape="box"];63257[label="zzz2500",fontsize=16,color="green",shape="box"];63258 -> 4125[label="",style="dashed", color="red", weight=0]; 130.29/78.21 63258[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 zzz2504 (FiniteMap.Branch zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344)",fontsize=16,color="magenta"];63258 -> 63503[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63258 -> 63504[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63259[label="zzz2503",fontsize=16,color="green",shape="box"];63260[label="zzz2501",fontsize=16,color="green",shape="box"];46073[label="zzz25020000",fontsize=16,color="green",shape="box"];46074[label="Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ zzz25020000)) (Succ (Succ zzz25020000)))) (Succ (Succ zzz25020000))) (Succ zzz25020000))",fontsize=16,color="green",shape="box"];46074 -> 46175[label="",style="dashed", color="green", weight=3]; 130.29/78.21 46075[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpNat (Succ zzz51240) (Succ zzz51250) == LT)",fontsize=16,color="black",shape="box"];46075 -> 46176[label="",style="solid", color="black", weight=3]; 130.29/78.21 46076[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpNat (Succ zzz51240) Zero == LT)",fontsize=16,color="black",shape="box"];46076 -> 46177[label="",style="solid", color="black", weight=3]; 130.29/78.21 46077[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpNat Zero (Succ zzz51250) == LT)",fontsize=16,color="black",shape="box"];46077 -> 46178[label="",style="solid", color="black", weight=3]; 130.29/78.21 46078[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];46078 -> 46179[label="",style="solid", color="black", weight=3]; 130.29/78.21 39826 -> 38195[label="",style="dashed", color="red", weight=0]; 130.29/78.21 39826[label="primPlusNat (Succ (primPlusNat (Succ Zero) (Succ Zero))) (Succ Zero)",fontsize=16,color="magenta"];39826 -> 39874[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 39827[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpNat zzz41140 zzz4455 == LT)",fontsize=16,color="burlywood",shape="triangle"];65570[label="zzz41140/Succ zzz411400",fontsize=10,color="white",style="solid",shape="box"];39827 -> 65570[label="",style="solid", color="burlywood", weight=9]; 130.29/78.21 65570 -> 39875[label="",style="solid", color="burlywood", weight=3]; 130.29/78.21 65571[label="zzz41140/Zero",fontsize=10,color="white",style="solid",shape="box"];39827 -> 65571[label="",style="solid", color="burlywood", weight=9]; 130.29/78.21 65571 -> 39876[label="",style="solid", color="burlywood", weight=3]; 130.29/78.21 39828[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (LT == LT)",fontsize=16,color="black",shape="triangle"];39828 -> 39877[label="",style="solid", color="black", weight=3]; 130.29/78.21 46079[label="zzz25020000",fontsize=16,color="green",shape="box"];46080[label="Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ zzz25020000)) (Succ (Succ zzz25020000)))) (Succ (Succ zzz25020000))) (Succ zzz25020000))",fontsize=16,color="green",shape="box"];46080 -> 46180[label="",style="dashed", color="green", weight=3]; 130.29/78.21 39829 -> 38195[label="",style="dashed", color="red", weight=0]; 130.29/78.21 39829[label="primPlusNat (Succ (primPlusNat (Succ Zero) (Succ Zero))) (Succ Zero)",fontsize=16,color="magenta"];39829 -> 39878[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 36027[label="zzz2503",fontsize=16,color="green",shape="box"];36028[label="zzz344",fontsize=16,color="green",shape="box"];36029[label="zzz340",fontsize=16,color="green",shape="box"];36030[label="zzz343",fontsize=16,color="green",shape="box"];36031[label="zzz300",fontsize=16,color="green",shape="box"];36032[label="zzz2504",fontsize=16,color="green",shape="box"];36033[label="zzz3420000000",fontsize=16,color="green",shape="box"];36034[label="Succ (Succ (Succ (Succ (Succ zzz3420000000))))",fontsize=16,color="green",shape="box"];36035[label="zzz2501",fontsize=16,color="green",shape="box"];36036[label="zzz341",fontsize=16,color="green",shape="box"];36037[label="zzz31",fontsize=16,color="green",shape="box"];36038[label="zzz2500",fontsize=16,color="green",shape="box"];36026[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3739 zzz3740 (Neg (Succ 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130.29/78.21 63263[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 (FiniteMap.Branch zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504) zzz343",fontsize=16,color="magenta"];63263 -> 63505[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63263 -> 63506[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63264[label="zzz341",fontsize=16,color="green",shape="box"];36059[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg Zero) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];36059 -> 36678[label="",style="solid", color="black", weight=3]; 130.29/78.21 63000 -> 62927[label="",style="dashed", color="red", weight=0]; 130.29/78.21 63000[label="FiniteMap.glueBal2GlueBal1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 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zzz474034))",fontsize=16,color="magenta"];63580 -> 63837[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63580 -> 63838[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63580 -> 63839[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63580 -> 63840[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63580 -> 63841[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63580 -> 63842[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63580 -> 63843[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63580 -> 63844[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63580 -> 63845[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63580 -> 63846[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63580 -> 63847[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63580 -> 63848[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63580 -> 63849[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63580 -> 63850[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63580 -> 63851[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63581[label="zzz474034",fontsize=16,color="green",shape="box"];63582 -> 63083[label="",style="dashed", color="red", weight=0]; 130.29/78.21 63582[label="FiniteMap.mkBalBranch zzz474030 zzz474031 (FiniteMap.deleteMin (FiniteMap.Branch zzz4740330 zzz4740331 zzz4740332 zzz4740333 zzz4740334)) zzz474034",fontsize=16,color="magenta"];63582 -> 63617[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63583 -> 63939[label="",style="dashed", color="red", weight=0]; 130.29/78.21 63583[label="FiniteMap.glueBal2Mid_elt20 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.findMin (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034))",fontsize=16,color="magenta"];63583 -> 63940[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63583 -> 63941[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63583 -> 63942[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63583 -> 63943[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63583 -> 63944[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63583 -> 63945[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63583 -> 63946[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63583 -> 63947[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63583 -> 63948[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63583 -> 63949[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63583 -> 63950[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63583 -> 63951[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63583 -> 63952[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63583 -> 63953[label="",style="dashed", color="magenta", weight=3]; 130.29/78.21 63583 -> 63954[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63265[label="FiniteMap.glueBal2Mid_key1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464)",fontsize=16,color="black",shape="box"];63265 -> 63507[label="",style="solid", color="black", weight=3]; 130.57/78.21 63266[label="FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034",fontsize=16,color="green",shape="box"];63267[label="FiniteMap.deleteMax (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464)",fontsize=16,color="burlywood",shape="triangle"];65572[label="zzz47464/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];63267 -> 65572[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65572 -> 63508[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65573[label="zzz47464/FiniteMap.Branch zzz474640 zzz474641 zzz474642 zzz474643 zzz474644",fontsize=10,color="white",style="solid",shape="box"];63267 -> 65573[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65573 -> 63509[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 63268[label="FiniteMap.glueBal2Mid_elt1 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464)",fontsize=16,color="black",shape="box"];63268 -> 63510[label="",style="solid", color="black", weight=3]; 130.57/78.21 64349[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat zzz644300 zzz64440 == GT)",fontsize=16,color="burlywood",shape="triangle"];65574[label="zzz644300/Succ zzz6443000",fontsize=10,color="white",style="solid",shape="box"];64349 -> 65574[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65574 -> 64360[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65575[label="zzz644300/Zero",fontsize=10,color="white",style="solid",shape="box"];64349 -> 65575[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65575 -> 64361[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 64350 -> 64318[label="",style="dashed", color="red", weight=0]; 130.57/78.21 64350[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (GT == GT)",fontsize=16,color="magenta"];64351[label="FiniteMap.mkBalBranch6MkBalBranch0 zzz474034 zzz474030 zzz474031 zzz6373 zzz6373 zzz474034 zzz474034",fontsize=16,color="burlywood",shape="box"];65576[label="zzz474034/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];64351 -> 65576[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65576 -> 64362[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65577[label="zzz474034/FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344",fontsize=10,color="white",style="solid",shape="box"];64351 -> 65577[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65577 -> 64363[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 64352[label="Zero",fontsize=16,color="green",shape="box"];64353[label="zzz64460",fontsize=16,color="green",shape="box"];64354 -> 64342[label="",style="dashed", color="red", weight=0]; 130.57/78.21 64354[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 False",fontsize=16,color="magenta"];64355 -> 64364[label="",style="dashed", color="red", weight=0]; 130.57/78.21 64355[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (FiniteMap.mkBalBranch6Size_l zzz474034 zzz474030 zzz474031 zzz6373 > FiniteMap.sIZE_RATIO * FiniteMap.mkBalBranch6Size_r zzz474034 zzz474030 zzz474031 zzz6373)",fontsize=16,color="magenta"];64355 -> 64365[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64355 -> 64366[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64356 -> 64349[label="",style="dashed", color="red", weight=0]; 130.57/78.21 64356[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat zzz64490 zzz644300 == GT)",fontsize=16,color="magenta"];64356 -> 64367[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64356 -> 64368[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64357 -> 64326[label="",style="dashed", color="red", weight=0]; 130.57/78.21 64357[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (LT == GT)",fontsize=16,color="magenta"];64358[label="Zero",fontsize=16,color="green",shape="box"];64359[label="zzz64510",fontsize=16,color="green",shape="box"];44781 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 44781[label="primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) zzz332000",fontsize=16,color="magenta"];44781 -> 44833[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 44781 -> 44834[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 45662 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 45662[label="primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero",fontsize=16,color="magenta"];45662 -> 45684[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 45662 -> 45685[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36222[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];36222 -> 36742[label="",style="solid", color="black", weight=3]; 130.57/78.21 36223[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) 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60457[label="",style="dashed", color="red", weight=0]; 130.57/78.21 36225[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Neg (Succ zzz3000)) zzz31 (FiniteMap.Branch zzz330 zzz331 (Pos Zero) zzz333 zzz334) (FiniteMap.Branch zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264)",fontsize=16,color="magenta"];36225 -> 60573[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36225 -> 60574[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36225 -> 60575[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36225 -> 60576[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36225 -> 60577[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36227 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.21 36227[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Neg (Succ zzz3000)) zzz31 (FiniteMap.Branch zzz330 zzz331 (Pos Zero) zzz333 zzz334) (FiniteMap.Branch zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264)",fontsize=16,color="magenta"];36227 -> 60578[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36227 -> 60579[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36227 -> 60580[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36227 -> 60581[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36227 -> 60582[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46304[label="zzz4261",fontsize=16,color="green",shape="box"];46305[label="zzz334",fontsize=16,color="green",shape="box"];46306[label="zzz4264",fontsize=16,color="green",shape="box"];46307[label="Succ zzz3000",fontsize=16,color="green",shape="box"];46308[label="zzz31",fontsize=16,color="green",shape="box"];46309[label="zzz330",fontsize=16,color="green",shape="box"];46310[label="zzz333",fontsize=16,color="green",shape="box"];46311[label="zzz4260",fontsize=16,color="green",shape="box"];46312[label="Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) zzz332000))",fontsize=16,color="green",shape="box"];46312 -> 46379[label="",style="dashed", color="green", weight=3]; 130.57/78.21 46313[label="Succ zzz42620000",fontsize=16,color="green",shape="box"];46314[label="zzz331",fontsize=16,color="green",shape="box"];46315[label="zzz4263",fontsize=16,color="green",shape="box"];46316[label="zzz332000",fontsize=16,color="green",shape="box"];46317[label="Succ (Succ zzz42620000)",fontsize=16,color="green",shape="box"];47311[label="Succ (Succ zzz42620000)",fontsize=16,color="green",shape="box"];47312[label="Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)",fontsize=16,color="green",shape="box"];47312 -> 47419[label="",style="dashed", color="green", weight=3]; 130.57/78.21 47313[label="zzz330",fontsize=16,color="green",shape="box"];47314[label="zzz4264",fontsize=16,color="green",shape="box"];47315[label="Succ zzz3000",fontsize=16,color="green",shape="box"];47316[label="zzz4263",fontsize=16,color="green",shape="box"];47317[label="zzz31",fontsize=16,color="green",shape="box"];47318[label="zzz333",fontsize=16,color="green",shape="box"];47319[label="zzz4261",fontsize=16,color="green",shape="box"];47320[label="zzz334",fontsize=16,color="green",shape="box"];47321[label="Succ zzz42620000",fontsize=16,color="green",shape="box"];47322[label="zzz331",fontsize=16,color="green",shape="box"];47323[label="zzz4260",fontsize=16,color="green",shape="box"];46318[label="zzz4261",fontsize=16,color="green",shape="box"];46319[label="zzz334",fontsize=16,color="green",shape="box"];46320[label="zzz4264",fontsize=16,color="green",shape="box"];46321[label="Succ zzz3000",fontsize=16,color="green",shape="box"];46322[label="zzz31",fontsize=16,color="green",shape="box"];46323[label="zzz330",fontsize=16,color="green",shape="box"];46324[label="zzz333",fontsize=16,color="green",shape="box"];46325[label="zzz4260",fontsize=16,color="green",shape="box"];46326[label="Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) zzz332000))",fontsize=16,color="green",shape="box"];46326 -> 46380[label="",style="dashed", color="green", weight=3]; 130.57/78.21 46327[label="Zero",fontsize=16,color="green",shape="box"];46328[label="zzz331",fontsize=16,color="green",shape="box"];46329[label="zzz4263",fontsize=16,color="green",shape="box"];46330[label="zzz332000",fontsize=16,color="green",shape="box"];46331[label="Succ Zero",fontsize=16,color="green",shape="box"];47324[label="Succ Zero",fontsize=16,color="green",shape="box"];47325[label="Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)",fontsize=16,color="green",shape="box"];47325 -> 47420[label="",style="dashed", color="green", weight=3]; 130.57/78.21 47326[label="zzz330",fontsize=16,color="green",shape="box"];47327[label="zzz4264",fontsize=16,color="green",shape="box"];47328[label="Succ zzz3000",fontsize=16,color="green",shape="box"];47329[label="zzz4263",fontsize=16,color="green",shape="box"];47330[label="zzz31",fontsize=16,color="green",shape="box"];47331[label="zzz333",fontsize=16,color="green",shape="box"];47332[label="zzz4261",fontsize=16,color="green",shape="box"];47333[label="zzz334",fontsize=16,color="green",shape="box"];47334[label="Zero",fontsize=16,color="green",shape="box"];47335[label="zzz331",fontsize=16,color="green",shape="box"];47336[label="zzz4260",fontsize=16,color="green",shape="box"];63498[label="Neg (Succ zzz33200)",fontsize=16,color="green",shape="box"];63499[label="Succ zzz3000",fontsize=16,color="green",shape="box"];63500[label="zzz4263",fontsize=16,color="green",shape="box"];36235 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.21 36235[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Neg (Succ zzz3000)) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334) (FiniteMap.Branch zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264)",fontsize=16,color="magenta"];36235 -> 60583[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36235 -> 60584[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36235 -> 60585[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36235 -> 60586[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36235 -> 60587[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36237 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.21 36237[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Neg (Succ zzz3000)) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334) (FiniteMap.Branch zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264)",fontsize=16,color="magenta"];36237 -> 60588[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36237 -> 60589[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36237 -> 60590[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36237 -> 60591[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36237 -> 60592[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 45417[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002))) (FiniteMap.mkVBalBranch3Size_l zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002) == LT)",fontsize=16,color="black",shape="box"];45417 -> 45464[label="",style="solid", color="black", weight=3]; 130.57/78.21 46590[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098))) (FiniteMap.mkVBalBranch3Size_l zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098) == LT)",fontsize=16,color="black",shape="box"];46590 -> 46662[label="",style="solid", color="black", weight=3]; 130.57/78.21 51079[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (primCmpInt (Pos (Succ zzz55410)) (Pos (Succ zzz33200)) == LT)",fontsize=16,color="black",shape="box"];51079 -> 51114[label="",style="solid", color="black", weight=3]; 130.57/78.21 51080[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (primCmpInt (Pos Zero) (Pos (Succ zzz33200)) == LT)",fontsize=16,color="black",shape="box"];51080 -> 51115[label="",style="solid", color="black", weight=3]; 130.57/78.21 36504[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 (Neg Zero) zzz31 zzz3530 zzz3531 (Pos (Succ zzz353200)) zzz3533 zzz3534 zzz340 zzz341 (Pos Zero) zzz343 zzz344 True",fontsize=16,color="black",shape="box"];36504 -> 36949[label="",style="solid", color="black", weight=3]; 130.57/78.21 49857[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 True",fontsize=16,color="black",shape="box"];49857 -> 49890[label="",style="solid", color="black", weight=3]; 130.57/78.21 63269[label="zzz3530",fontsize=16,color="green",shape="box"];63270 -> 5407[label="",style="dashed", color="red", weight=0]; 130.57/78.21 63270[label="FiniteMap.mkVBalBranch (Neg Zero) zzz31 zzz3534 (FiniteMap.Branch zzz340 zzz341 (Neg Zero) zzz343 zzz344)",fontsize=16,color="magenta"];63270 -> 63511[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63270 -> 63512[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63271[label="zzz3533",fontsize=16,color="green",shape="box"];63272[label="zzz3531",fontsize=16,color="green",shape="box"];47058[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139)) (FiniteMap.mkVBalBranch3Size_l zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139) == LT)",fontsize=16,color="black",shape="box"];47058 -> 47117[label="",style="solid", color="black", weight=3]; 130.57/78.21 48265[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255)) (FiniteMap.mkVBalBranch3Size_l zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255) == LT)",fontsize=16,color="black",shape="box"];48265 -> 48374[label="",style="solid", color="black", weight=3]; 130.57/78.21 36553[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)))) (FiniteMap.sizeFM (FiniteMap.Branch zzz5230 zzz5231 zzz5232 zzz5233 zzz5234)) == LT)",fontsize=16,color="black",shape="box"];36553 -> 37003[label="",style="solid", color="black", weight=3]; 130.57/78.21 36554[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];36554 -> 37004[label="",style="solid", color="black", weight=3]; 130.57/78.21 36555[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];36555 -> 37005[label="",style="solid", color="black", weight=3]; 130.57/78.21 36556[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];36556 -> 37006[label="",style="solid", color="black", weight=3]; 130.57/78.21 36557[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)))) (FiniteMap.sizeFM (FiniteMap.Branch zzz5230 zzz5231 zzz5232 zzz5233 zzz5234)) == LT)",fontsize=16,color="black",shape="box"];36557 -> 37007[label="",style="solid", color="black", weight=3]; 130.57/78.21 36558[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];36558 -> 37008[label="",style="solid", color="black", weight=3]; 130.57/78.21 36559[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];36559 -> 37009[label="",style="solid", color="black", weight=3]; 130.57/78.21 36560[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];36560 -> 37010[label="",style="solid", color="black", weight=3]; 130.57/78.21 34080[label="Succ (Succ (primPlusNat (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ (Succ zzz6200000))) (Succ (Succ (Succ zzz6200000))))) (Succ (Succ (Succ zzz6200000)))) (Succ (Succ zzz6200000))) zzz6200000))",fontsize=16,color="green",shape="box"];34080 -> 34914[label="",style="dashed", color="green", weight=3]; 130.57/78.21 34081[label="Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ Zero)) (Succ (Succ Zero)))) (Succ (Succ Zero))) (Succ Zero))",fontsize=16,color="green",shape="box"];34081 -> 34915[label="",style="dashed", color="green", weight=3]; 130.57/78.21 41905[label="zzz47140",fontsize=16,color="green",shape="box"];41906[label="zzz47130",fontsize=16,color="green",shape="box"];41907[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 False",fontsize=16,color="black",shape="triangle"];41907 -> 42015[label="",style="solid", color="black", weight=3]; 130.57/78.21 41908[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 True",fontsize=16,color="black",shape="box"];41908 -> 42016[label="",style="solid", color="black", weight=3]; 130.57/78.21 41909 -> 41907[label="",style="dashed", color="red", weight=0]; 130.57/78.21 41909[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 False",fontsize=16,color="magenta"];39764 -> 38195[label="",style="dashed", color="red", weight=0]; 130.57/78.21 39764[label="primPlusNat (Succ Zero) (Succ Zero)",fontsize=16,color="magenta"];39764 -> 39832[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 38742[label="primPlusNat (Succ zzz37520) (Succ Zero)",fontsize=16,color="black",shape="box"];38742 -> 38853[label="",style="solid", color="black", weight=3]; 130.57/78.21 38743[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];38743 -> 38854[label="",style="solid", color="black", weight=3]; 130.57/78.21 38960[label="Succ zzz375200",fontsize=16,color="green",shape="box"];38961[label="Zero",fontsize=16,color="green",shape="box"];39765[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpNat (Succ zzz44360) (Succ zzz3887000) == 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130.57/78.21 65580 -> 41826[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65581[label="zzz4719/Zero",fontsize=10,color="white",style="solid",shape="box"];41812 -> 65581[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65581 -> 41827[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 39477 -> 38195[label="",style="dashed", color="red", weight=0]; 130.57/78.21 39477[label="primPlusNat (primMulNat (Succ (Succ (Succ Zero))) (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];39477 -> 39564[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39830 -> 57269[label="",style="dashed", color="red", weight=0]; 130.57/78.21 39830[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ Zero)) zzz343 zzz344 (primCmpNat (Succ zzz44380) (Succ 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130.57/78.21 39831 -> 57289[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39831 -> 57290[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39831 -> 57291[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39831 -> 57292[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39831 -> 57293[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39831 -> 57294[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39831 -> 57295[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39831 -> 57296[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39831 -> 57297[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36632 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.21 36632[label="FiniteMap.mkBalBranch zzz2500 zzz2501 zzz2503 (FiniteMap.mkVBalBranch (Pos zzz300) zzz31 zzz2504 (FiniteMap.Branch zzz340 zzz341 (Pos Zero) zzz343 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39875[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpNat (Succ zzz411400) zzz4455 == LT)",fontsize=16,color="burlywood",shape="box"];65582[label="zzz4455/Succ zzz44550",fontsize=10,color="white",style="solid",shape="box"];39875 -> 65582[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65582 -> 39893[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65583[label="zzz4455/Zero",fontsize=10,color="white",style="solid",shape="box"];39875 -> 65583[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65583 -> 39894[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 39876[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 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(Neg (Succ zzz4109)) zzz4110 zzz4111 True",fontsize=16,color="black",shape="box"];39877 -> 39897[label="",style="solid", color="black", weight=3]; 130.57/78.21 46180 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 46180[label="primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ zzz25020000)) (Succ (Succ zzz25020000)))) (Succ (Succ zzz25020000))) (Succ zzz25020000)",fontsize=16,color="magenta"];46180 -> 46398[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46180 -> 46399[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39878[label="Succ (primPlusNat (Succ Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];39878 -> 39898[label="",style="dashed", color="green", weight=3]; 130.57/78.21 36673[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (Pos zzz3748) zzz3749 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 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zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344))",fontsize=16,color="magenta"];36678 -> 63277[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36678 -> 63278[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36678 -> 63279[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36678 -> 63280[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63018[label="zzz6354000",fontsize=16,color="green",shape="box"];63019[label="zzz6355000",fontsize=16,color="green",shape="box"];63837[label="zzz47464",fontsize=16,color="green",shape="box"];63838[label="zzz474032",fontsize=16,color="green",shape="box"];63839[label="zzz474034",fontsize=16,color="green",shape="box"];63840[label="zzz474033",fontsize=16,color="green",shape="box"];63841[label="zzz474031",fontsize=16,color="green",shape="box"];63842[label="zzz47460",fontsize=16,color="green",shape="box"];63843[label="zzz474030",fontsize=16,color="green",shape="box"];63844[label="zzz474033",fontsize=16,color="green",shape="box"];63845[label="zzz474032",fontsize=16,color="green",shape="box"];63846[label="zzz474030",fontsize=16,color="green",shape="box"];63847[label="zzz47461",fontsize=16,color="green",shape="box"];63848[label="zzz47462",fontsize=16,color="green",shape="box"];63849[label="zzz474031",fontsize=16,color="green",shape="box"];63850[label="zzz474034",fontsize=16,color="green",shape="box"];63851[label="zzz47463",fontsize=16,color="green",shape="box"];63836[label="FiniteMap.glueBal2Mid_key20 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zzz4740334)",fontsize=16,color="magenta"];63617 -> 63669[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63617 -> 63670[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63617 -> 63671[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63617 -> 63672[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63617 -> 63673[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63940[label="zzz47461",fontsize=16,color="green",shape="box"];63941[label="zzz474032",fontsize=16,color="green",shape="box"];63942[label="zzz47460",fontsize=16,color="green",shape="box"];63943[label="zzz474032",fontsize=16,color="green",shape="box"];63944[label="zzz474031",fontsize=16,color="green",shape="box"];63945[label="zzz474033",fontsize=16,color="green",shape="box"];63946[label="zzz474030",fontsize=16,color="green",shape="box"];63947[label="zzz474031",fontsize=16,color="green",shape="box"];63948[label="zzz474034",fontsize=16,color="green",shape="box"];63949[label="zzz47463",fontsize=16,color="green",shape="box"];63950[label="zzz474030",fontsize=16,color="green",shape="box"];63951[label="zzz474034",fontsize=16,color="green",shape="box"];63952[label="zzz474033",fontsize=16,color="green",shape="box"];63953[label="zzz47464",fontsize=16,color="green",shape="box"];63954[label="zzz47462",fontsize=16,color="green",shape="box"];63939[label="FiniteMap.glueBal2Mid_elt20 (FiniteMap.Branch zzz6395 zzz6396 zzz6397 zzz6398 zzz6399) (FiniteMap.Branch zzz6400 zzz6401 zzz6402 zzz6403 zzz6404) (FiniteMap.findMin (FiniteMap.Branch zzz6405 zzz6406 zzz6407 zzz6408 zzz6409))",fontsize=16,color="burlywood",shape="triangle"];65588[label="zzz6408/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];63939 -> 65588[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65588 -> 64032[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65589[label="zzz6408/FiniteMap.Branch zzz64080 zzz64081 zzz64082 zzz64083 zzz64084",fontsize=10,color="white",style="solid",shape="box"];63939 -> 65589[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65589 -> 64033[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 63507[label="FiniteMap.glueBal2Mid_key10 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.glueBal2Vv2 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464))",fontsize=16,color="black",shape="box"];63507 -> 63584[label="",style="solid", color="black", weight=3]; 130.57/78.21 63508[label="FiniteMap.deleteMax (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 FiniteMap.EmptyFM)",fontsize=16,color="black",shape="box"];63508 -> 63585[label="",style="solid", color="black", weight=3]; 130.57/78.21 63509[label="FiniteMap.deleteMax (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 (FiniteMap.Branch zzz474640 zzz474641 zzz474642 zzz474643 zzz474644))",fontsize=16,color="black",shape="box"];63509 -> 63586[label="",style="solid", color="black", weight=3]; 130.57/78.21 63510[label="FiniteMap.glueBal2Mid_elt10 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.glueBal2Vv2 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464))",fontsize=16,color="black",shape="box"];63510 -> 63587[label="",style="solid", color="black", weight=3]; 130.57/78.21 64360[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat (Succ zzz6443000) zzz64440 == GT)",fontsize=16,color="burlywood",shape="box"];65590[label="zzz64440/Succ zzz644400",fontsize=10,color="white",style="solid",shape="box"];64360 -> 65590[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65590 -> 64369[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65591[label="zzz64440/Zero",fontsize=10,color="white",style="solid",shape="box"];64360 -> 65591[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65591 -> 64370[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 64361[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat Zero zzz64440 == GT)",fontsize=16,color="burlywood",shape="box"];65592[label="zzz64440/Succ zzz644400",fontsize=10,color="white",style="solid",shape="box"];64361 -> 65592[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65592 -> 64371[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65593[label="zzz64440/Zero",fontsize=10,color="white",style="solid",shape="box"];64361 -> 65593[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65593 -> 64372[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 64362[label="FiniteMap.mkBalBranch6MkBalBranch0 FiniteMap.EmptyFM zzz474030 zzz474031 zzz6373 zzz6373 FiniteMap.EmptyFM FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];64362 -> 64373[label="",style="solid", color="black", weight=3]; 130.57/78.21 64363[label="FiniteMap.mkBalBranch6MkBalBranch0 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344)",fontsize=16,color="black",shape="box"];64363 -> 64374[label="",style="solid", color="black", weight=3]; 130.57/78.21 64365 -> 64265[label="",style="dashed", color="red", weight=0]; 130.57/78.21 64365[label="FiniteMap.mkBalBranch6Size_r zzz474034 zzz474030 zzz474031 zzz6373",fontsize=16,color="magenta"];64366 -> 63793[label="",style="dashed", color="red", weight=0]; 130.57/78.21 64366[label="FiniteMap.mkBalBranch6Size_l zzz474034 zzz474030 zzz474031 zzz6373",fontsize=16,color="magenta"];64364[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (zzz6452 > FiniteMap.sIZE_RATIO * zzz6453)",fontsize=16,color="black",shape="triangle"];64364 -> 64375[label="",style="solid", color="black", weight=3]; 130.57/78.21 64367[label="zzz644300",fontsize=16,color="green",shape="box"];64368[label="zzz64490",fontsize=16,color="green",shape="box"];44833[label="zzz332000",fontsize=16,color="green",shape="box"];44834 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 44834[label="primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)",fontsize=16,color="magenta"];44834 -> 44889[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 44834 -> 44890[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 45684[label="Zero",fontsize=16,color="green",shape="box"];45685[label="Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)",fontsize=16,color="green",shape="box"];45685 -> 45734[label="",style="dashed", color="green", weight=3]; 130.57/78.21 36742[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];36742 -> 37133[label="",style="solid", color="black", weight=3]; 130.57/78.21 36743[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];36743 -> 37134[label="",style="solid", color="black", weight=3]; 130.57/78.21 36744[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz42620)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg zzz42620) zzz4263 zzz4264) == LT)",fontsize=16,color="burlywood",shape="box"];65594[label="zzz42620/Succ zzz426200",fontsize=10,color="white",style="solid",shape="box"];36744 -> 65594[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65594 -> 37135[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65595[label="zzz42620/Zero",fontsize=10,color="white",style="solid",shape="box"];36744 -> 65595[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65595 -> 37136[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 60573[label="zzz31",fontsize=16,color="green",shape="box"];60574[label="Neg (Succ zzz3000)",fontsize=16,color="green",shape="box"];60575[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];60576[label="FiniteMap.Branch zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264",fontsize=16,color="green",shape="box"];60577[label="FiniteMap.Branch zzz330 zzz331 (Pos Zero) zzz333 zzz334",fontsize=16,color="green",shape="box"];60578[label="zzz31",fontsize=16,color="green",shape="box"];60579[label="Neg (Succ zzz3000)",fontsize=16,color="green",shape="box"];60580[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];60581[label="FiniteMap.Branch zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264",fontsize=16,color="green",shape="box"];60582[label="FiniteMap.Branch zzz330 zzz331 (Pos Zero) zzz333 zzz334",fontsize=16,color="green",shape="box"];46379 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 46379[label="primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) zzz332000",fontsize=16,color="magenta"];46379 -> 46591[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46379 -> 46592[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 47419 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 47419[label="primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero",fontsize=16,color="magenta"];47419 -> 47563[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 47419 -> 47564[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46380 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 46380[label="primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) zzz332000",fontsize=16,color="magenta"];46380 -> 46593[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46380 -> 46594[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 47420 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 47420[label="primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero",fontsize=16,color="magenta"];47420 -> 47565[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 47420 -> 47566[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 60583[label="zzz31",fontsize=16,color="green",shape="box"];60584[label="Neg (Succ zzz3000)",fontsize=16,color="green",shape="box"];60585[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];60586[label="FiniteMap.Branch zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264",fontsize=16,color="green",shape="box"];60587[label="FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334",fontsize=16,color="green",shape="box"];60588[label="zzz31",fontsize=16,color="green",shape="box"];60589[label="Neg (Succ zzz3000)",fontsize=16,color="green",shape="box"];60590[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];60591[label="FiniteMap.Branch zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264",fontsize=16,color="green",shape="box"];60592[label="FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334",fontsize=16,color="green",shape="box"];45464[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos (Succ zzz5000))) (FiniteMap.mkVBalBranch3Size_l zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002) == LT)",fontsize=16,color="black",shape="box"];45464 -> 45504[label="",style="solid", color="black", weight=3]; 130.57/78.21 46662[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos (Succ zzz5096))) (FiniteMap.mkVBalBranch3Size_l zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098) == LT)",fontsize=16,color="black",shape="box"];46662 -> 46753[label="",style="solid", color="black", weight=3]; 130.57/78.21 51114 -> 58875[label="",style="dashed", color="red", weight=0]; 130.57/78.21 51114[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (primCmpNat (Succ zzz55410) (Succ zzz33200) == LT)",fontsize=16,color="magenta"];51114 -> 58876[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51114 -> 58877[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51114 -> 58878[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51114 -> 58879[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51114 -> 58880[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51114 -> 58881[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51114 -> 58882[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51114 -> 58883[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51114 -> 58884[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51114 -> 58885[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51114 -> 58886[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51114 -> 58887[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51114 -> 58888[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51114 -> 58889[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51115 -> 58875[label="",style="dashed", color="red", weight=0]; 130.57/78.21 51115[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (primCmpNat Zero (Succ zzz33200) == LT)",fontsize=16,color="magenta"];51115 -> 58890[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51115 -> 58891[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51115 -> 58892[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51115 -> 58893[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51115 -> 58894[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51115 -> 58895[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51115 -> 58896[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51115 -> 58897[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51115 -> 58898[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51115 -> 58899[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51115 -> 58900[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51115 -> 58901[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51115 -> 58902[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 51115 -> 58903[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36949 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.21 36949[label="FiniteMap.mkBalBranch zzz3530 zzz3531 zzz3533 (FiniteMap.mkVBalBranch (Neg Zero) zzz31 zzz3534 (FiniteMap.Branch zzz340 zzz341 (Pos Zero) zzz343 zzz344))",fontsize=16,color="magenta"];36949 -> 63281[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36949 -> 63282[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36949 -> 63283[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 36949 -> 63284[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 49890 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.21 49890[label="FiniteMap.mkBalBranch zzz330 zzz331 zzz333 (FiniteMap.mkVBalBranch (Neg zzz300) zzz31 zzz334 (FiniteMap.Branch zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234))",fontsize=16,color="magenta"];49890 -> 63285[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 49890 -> 63286[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 49890 -> 63287[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 49890 -> 63288[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63511[label="zzz3534",fontsize=16,color="green",shape="box"];63512[label="FiniteMap.Branch zzz340 zzz341 (Neg Zero) zzz343 zzz344",fontsize=16,color="green",shape="box"];47117[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139))) (FiniteMap.mkVBalBranch3Size_l zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139) == LT)",fontsize=16,color="black",shape="box"];47117 -> 47166[label="",style="solid", color="black", weight=3]; 130.57/78.21 48374[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255))) (FiniteMap.mkVBalBranch3Size_l zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255) == LT)",fontsize=16,color="black",shape="box"];48374 -> 48475[label="",style="solid", color="black", weight=3]; 130.57/78.21 37003[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)))) zzz5232 == LT)",fontsize=16,color="burlywood",shape="box"];65596[label="zzz5232/Pos zzz52320",fontsize=10,color="white",style="solid",shape="box"];37003 -> 65596[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65596 -> 37447[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65597[label="zzz5232/Neg zzz52320",fontsize=10,color="white",style="solid",shape="box"];37003 -> 65597[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65597 -> 37448[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 37004[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];37004 -> 37449[label="",style="solid", color="black", weight=3]; 130.57/78.21 37005[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];37005 -> 37450[label="",style="solid", color="black", weight=3]; 130.57/78.21 37006[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];37006 -> 37451[label="",style="solid", color="black", weight=3]; 130.57/78.21 37007[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 zzz5232 zzz5233 zzz5234 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)))) zzz5232 == LT)",fontsize=16,color="burlywood",shape="box"];65598[label="zzz5232/Pos zzz52320",fontsize=10,color="white",style="solid",shape="box"];37007 -> 65598[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65598 -> 37452[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65599[label="zzz5232/Neg zzz52320",fontsize=10,color="white",style="solid",shape="box"];37007 -> 65599[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65599 -> 37453[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 37008[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];37008 -> 37454[label="",style="solid", color="black", weight=3]; 130.57/78.21 37009[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];37009 -> 37455[label="",style="solid", color="black", weight=3]; 130.57/78.21 37010[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];37010 -> 37456[label="",style="solid", color="black", weight=3]; 130.57/78.21 34914[label="primPlusNat (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ (Succ zzz6200000))) (Succ (Succ (Succ zzz6200000))))) (Succ (Succ (Succ zzz6200000)))) (Succ (Succ zzz6200000))) zzz6200000",fontsize=16,color="black",shape="box"];34914 -> 35571[label="",style="solid", color="black", weight=3]; 130.57/78.21 34915[label="primPlusNat (primPlusNat (Succ (primPlusNat (Succ (Succ Zero)) (Succ (Succ Zero)))) (Succ (Succ Zero))) (Succ Zero)",fontsize=16,color="black",shape="box"];34915 -> 35572[label="",style="solid", color="black", weight=3]; 130.57/78.21 42015[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 < FiniteMap.mkVBalBranch3Size_l zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710)",fontsize=16,color="black",shape="box"];42015 -> 42058[label="",style="solid", color="black", weight=3]; 130.57/78.21 42016 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.21 42016[label="FiniteMap.mkBalBranch zzz4706 zzz4707 (FiniteMap.mkVBalBranch (Pos zzz4711) zzz4712 (FiniteMap.Branch zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705) zzz4709) zzz4710",fontsize=16,color="magenta"];42016 -> 63289[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42016 -> 63290[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42016 -> 63291[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42016 -> 63292[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39832[label="Succ Zero",fontsize=16,color="green",shape="box"];38853[label="Succ (Succ (primPlusNat zzz37520 Zero))",fontsize=16,color="green",shape="box"];38853 -> 38920[label="",style="dashed", color="green", weight=3]; 130.57/78.21 38854[label="Succ Zero",fontsize=16,color="green",shape="box"];39833 -> 39594[label="",style="dashed", color="red", weight=0]; 130.57/78.21 39833[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpNat zzz44360 zzz3887000 == LT)",fontsize=16,color="magenta"];39833 -> 39881[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39833 -> 39882[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39834 -> 39595[label="",style="dashed", color="red", weight=0]; 130.57/78.21 39834[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (GT == LT)",fontsize=16,color="magenta"];39835[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (LT == LT)",fontsize=16,color="black",shape="box"];39835 -> 39883[label="",style="solid", color="black", weight=3]; 130.57/78.21 39836[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (EQ == LT)",fontsize=16,color="black",shape="box"];39836 -> 39884[label="",style="solid", color="black", weight=3]; 130.57/78.21 39837[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884) (FiniteMap.mkVBalBranch3Size_l zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884) == LT)",fontsize=16,color="black",shape="box"];39837 -> 39885[label="",style="solid", color="black", weight=3]; 130.57/78.21 37025[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ (Succ (Succ Zero))))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];37025 -> 37511[label="",style="solid", color="black", weight=3]; 130.57/78.21 41212[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ (Succ Zero))",fontsize=16,color="black",shape="triangle"];41212 -> 41223[label="",style="solid", color="black", weight=3]; 130.57/78.21 41801[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (Pos (Succ zzz47150)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];41801 -> 41828[label="",style="solid", color="black", weight=3]; 130.57/78.21 41802[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];41802 -> 41829[label="",style="solid", color="black", weight=3]; 130.57/78.21 37027[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3889 zzz3890 (Pos (Succ Zero)) zzz3891 zzz3892 zzz3893 zzz3894 (Pos (Succ zzz3895)) zzz3896 zzz3897 (Pos zzz3898) zzz3899 zzz3889 zzz3890 (Pos (Succ Zero)) zzz3891 zzz3892 zzz3893 zzz3894 (Pos (Succ zzz3895)) zzz3896 zzz3897 True",fontsize=16,color="black",shape="box"];37027 -> 37513[label="",style="solid", color="black", weight=3]; 130.57/78.21 37028[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344)",fontsize=16,color="black",shape="box"];37028 -> 37514[label="",style="solid", color="black", weight=3]; 130.57/78.21 37029[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];37029 -> 37515[label="",style="solid", color="black", weight=3]; 130.57/78.21 37030[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos (Succ (Succ (Succ Zero))))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];37030 -> 37516[label="",style="solid", color="black", weight=3]; 130.57/78.21 41826[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (Pos (Succ zzz47190)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];41826 -> 41910[label="",style="solid", color="black", weight=3]; 130.57/78.21 41827[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];41827 -> 41911[label="",style="solid", color="black", weight=3]; 130.57/78.21 39564[label="primMulNat (Succ (Succ (Succ Zero))) (Succ Zero)",fontsize=16,color="black",shape="box"];39564 -> 39596[label="",style="solid", color="black", weight=3]; 130.57/78.21 57270[label="Zero",fontsize=16,color="green",shape="box"];57271[label="zzz2504",fontsize=16,color="green",shape="box"];57272[label="zzz343",fontsize=16,color="green",shape="box"];57273[label="zzz340",fontsize=16,color="green",shape="box"];57274[label="zzz341",fontsize=16,color="green",shape="box"];57275[label="Succ zzz44380",fontsize=16,color="green",shape="box"];57276[label="Succ zzz250200",fontsize=16,color="green",shape="box"];57277[label="zzz300",fontsize=16,color="green",shape="box"];57278[label="zzz2501",fontsize=16,color="green",shape="box"];57279[label="zzz344",fontsize=16,color="green",shape="box"];57280[label="zzz250200",fontsize=16,color="green",shape="box"];57281[label="zzz31",fontsize=16,color="green",shape="box"];57282[label="zzz2503",fontsize=16,color="green",shape="box"];57283[label="zzz2500",fontsize=16,color="green",shape="box"];57269[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (Pos zzz6030) zzz6031 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (primCmpNat zzz6032 zzz6033 == LT)",fontsize=16,color="burlywood",shape="triangle"];65600[label="zzz6032/Succ zzz60320",fontsize=10,color="white",style="solid",shape="box"];57269 -> 65600[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65600 -> 57788[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65601[label="zzz6032/Zero",fontsize=10,color="white",style="solid",shape="box"];57269 -> 65601[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65601 -> 57789[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 57284[label="Zero",fontsize=16,color="green",shape="box"];57285[label="zzz2504",fontsize=16,color="green",shape="box"];57286[label="zzz343",fontsize=16,color="green",shape="box"];57287[label="zzz340",fontsize=16,color="green",shape="box"];57288[label="zzz341",fontsize=16,color="green",shape="box"];57289[label="Zero",fontsize=16,color="green",shape="box"];57290[label="Succ zzz250200",fontsize=16,color="green",shape="box"];57291[label="zzz300",fontsize=16,color="green",shape="box"];57292[label="zzz2501",fontsize=16,color="green",shape="box"];57293[label="zzz344",fontsize=16,color="green",shape="box"];57294[label="zzz250200",fontsize=16,color="green",shape="box"];57295[label="zzz31",fontsize=16,color="green",shape="box"];57296[label="zzz2503",fontsize=16,color="green",shape="box"];57297[label="zzz2500",fontsize=16,color="green",shape="box"];63273[label="zzz2500",fontsize=16,color="green",shape="box"];63274 -> 4125[label="",style="dashed", color="red", weight=0]; 130.57/78.21 63274[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 zzz2504 (FiniteMap.Branch zzz340 zzz341 (Pos Zero) zzz343 zzz344)",fontsize=16,color="magenta"];63274 -> 63513[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63274 -> 63514[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63275[label="zzz2503",fontsize=16,color="green",shape="box"];63276[label="zzz2501",fontsize=16,color="green",shape="box"];37037[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat zzz34200 zzz34200)) zzz34200))) (Succ zzz34200)) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];37037 -> 37521[label="",style="solid", color="black", weight=3]; 130.57/78.21 46391[label="Succ zzz25020000",fontsize=16,color="green",shape="box"];46392 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 46392[label="primPlusNat (Succ (primPlusNat (Succ (Succ zzz25020000)) (Succ (Succ zzz25020000)))) (Succ (Succ zzz25020000))",fontsize=16,color="magenta"];46392 -> 46666[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46392 -> 46667[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46393[label="zzz51240",fontsize=16,color="green",shape="box"];46394[label="zzz51250",fontsize=16,color="green",shape="box"];46395[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 False",fontsize=16,color="black",shape="triangle"];46395 -> 46668[label="",style="solid", color="black", weight=3]; 130.57/78.21 46396[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 True",fontsize=16,color="black",shape="box"];46396 -> 46669[label="",style="solid", color="black", weight=3]; 130.57/78.21 46397 -> 46395[label="",style="dashed", color="red", weight=0]; 130.57/78.21 46397[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 False",fontsize=16,color="magenta"];39892 -> 38195[label="",style="dashed", color="red", weight=0]; 130.57/78.21 39892[label="primPlusNat (Succ Zero) (Succ Zero)",fontsize=16,color="magenta"];39892 -> 39971[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39893[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpNat (Succ zzz411400) (Succ zzz44550) == LT)",fontsize=16,color="black",shape="box"];39893 -> 39972[label="",style="solid", color="black", weight=3]; 130.57/78.21 39894[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpNat (Succ zzz411400) Zero == LT)",fontsize=16,color="black",shape="box"];39894 -> 39973[label="",style="solid", color="black", weight=3]; 130.57/78.21 39895[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpNat Zero (Succ zzz44550) == LT)",fontsize=16,color="black",shape="box"];39895 -> 39974[label="",style="solid", color="black", weight=3]; 130.57/78.21 39896[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];39896 -> 39975[label="",style="solid", color="black", weight=3]; 130.57/78.21 39897 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.21 39897[label="FiniteMap.mkBalBranch zzz4107 zzz4108 (FiniteMap.mkVBalBranch (Pos zzz4112) zzz4113 (FiniteMap.Branch zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106) zzz4110) zzz4111",fontsize=16,color="magenta"];39897 -> 63293[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39897 -> 63294[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39897 -> 63295[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39897 -> 63296[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46398[label="Succ zzz25020000",fontsize=16,color="green",shape="box"];46399 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 46399[label="primPlusNat (Succ (primPlusNat (Succ (Succ zzz25020000)) (Succ (Succ zzz25020000)))) (Succ (Succ zzz25020000))",fontsize=16,color="magenta"];46399 -> 46670[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46399 -> 46671[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39898 -> 38195[label="",style="dashed", color="red", weight=0]; 130.57/78.21 39898[label="primPlusNat (Succ Zero) (Succ Zero)",fontsize=16,color="magenta"];39898 -> 39980[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 37054[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (Pos zzz3748) zzz3749 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 False",fontsize=16,color="black",shape="box"];37054 -> 37570[label="",style="solid", color="black", weight=3]; 130.57/78.21 37055[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 < FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344)",fontsize=16,color="black",shape="box"];37055 -> 37571[label="",style="solid", color="black", weight=3]; 130.57/78.21 63277[label="zzz2500",fontsize=16,color="green",shape="box"];63278 -> 4125[label="",style="dashed", color="red", weight=0]; 130.57/78.21 63278[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 zzz2504 (FiniteMap.Branch zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344)",fontsize=16,color="magenta"];63278 -> 63515[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63278 -> 63516[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63279[label="zzz2503",fontsize=16,color="green",shape="box"];63280[label="zzz2501",fontsize=16,color="green",shape="box"];63936[label="FiniteMap.glueBal2Mid_key20 (FiniteMap.Branch zzz6379 zzz6380 zzz6381 zzz6382 zzz6383) (FiniteMap.Branch zzz6384 zzz6385 zzz6386 zzz6387 zzz6388) (FiniteMap.findMin (FiniteMap.Branch zzz6389 zzz6390 zzz6391 FiniteMap.EmptyFM zzz6393))",fontsize=16,color="black",shape="box"];63936 -> 64034[label="",style="solid", color="black", weight=3]; 130.57/78.21 63937[label="FiniteMap.glueBal2Mid_key20 (FiniteMap.Branch zzz6379 zzz6380 zzz6381 zzz6382 zzz6383) (FiniteMap.Branch zzz6384 zzz6385 zzz6386 zzz6387 zzz6388) (FiniteMap.findMin (FiniteMap.Branch zzz6389 zzz6390 zzz6391 (FiniteMap.Branch zzz63920 zzz63921 zzz63922 zzz63923 zzz63924) zzz6393))",fontsize=16,color="black",shape="box"];63937 -> 64035[label="",style="solid", color="black", weight=3]; 130.57/78.21 63669[label="zzz4740330",fontsize=16,color="green",shape="box"];63670[label="zzz4740334",fontsize=16,color="green",shape="box"];63671[label="zzz4740333",fontsize=16,color="green",shape="box"];63672[label="zzz4740331",fontsize=16,color="green",shape="box"];63673[label="zzz4740332",fontsize=16,color="green",shape="box"];64032[label="FiniteMap.glueBal2Mid_elt20 (FiniteMap.Branch zzz6395 zzz6396 zzz6397 zzz6398 zzz6399) (FiniteMap.Branch zzz6400 zzz6401 zzz6402 zzz6403 zzz6404) (FiniteMap.findMin (FiniteMap.Branch zzz6405 zzz6406 zzz6407 FiniteMap.EmptyFM zzz6409))",fontsize=16,color="black",shape="box"];64032 -> 64130[label="",style="solid", color="black", weight=3]; 130.57/78.21 64033[label="FiniteMap.glueBal2Mid_elt20 (FiniteMap.Branch zzz6395 zzz6396 zzz6397 zzz6398 zzz6399) (FiniteMap.Branch zzz6400 zzz6401 zzz6402 zzz6403 zzz6404) (FiniteMap.findMin (FiniteMap.Branch zzz6405 zzz6406 zzz6407 (FiniteMap.Branch zzz64080 zzz64081 zzz64082 zzz64083 zzz64084) zzz6409))",fontsize=16,color="black",shape="box"];64033 -> 64131[label="",style="solid", color="black", weight=3]; 130.57/78.21 63584 -> 64037[label="",style="dashed", color="red", weight=0]; 130.57/78.21 63584[label="FiniteMap.glueBal2Mid_key10 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.findMax (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464))",fontsize=16,color="magenta"];63584 -> 64038[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63584 -> 64039[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63584 -> 64040[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63584 -> 64041[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63584 -> 64042[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63584 -> 64043[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63584 -> 64044[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63584 -> 64045[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63584 -> 64046[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63584 -> 64047[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63584 -> 64048[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63584 -> 64049[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63584 -> 64050[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63584 -> 64051[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63584 -> 64052[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63585[label="zzz47463",fontsize=16,color="green",shape="box"];63586 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.21 63586[label="FiniteMap.mkBalBranch zzz47460 zzz47461 zzz47463 (FiniteMap.deleteMax (FiniteMap.Branch zzz474640 zzz474641 zzz474642 zzz474643 zzz474644))",fontsize=16,color="magenta"];63586 -> 63622[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63586 -> 63623[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63586 -> 63624[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63586 -> 63625[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63587 -> 64141[label="",style="dashed", color="red", weight=0]; 130.57/78.21 63587[label="FiniteMap.glueBal2Mid_elt10 (FiniteMap.Branch zzz474030 zzz474031 zzz474032 zzz474033 zzz474034) (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464) (FiniteMap.findMax (FiniteMap.Branch zzz47460 zzz47461 zzz47462 zzz47463 zzz47464))",fontsize=16,color="magenta"];63587 -> 64142[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63587 -> 64143[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63587 -> 64144[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63587 -> 64145[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63587 -> 64146[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63587 -> 64147[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63587 -> 64148[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63587 -> 64149[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63587 -> 64150[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63587 -> 64151[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63587 -> 64152[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63587 -> 64153[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63587 -> 64154[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63587 -> 64155[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63587 -> 64156[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64369[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat (Succ zzz6443000) (Succ zzz644400) == GT)",fontsize=16,color="black",shape="box"];64369 -> 64376[label="",style="solid", color="black", weight=3]; 130.57/78.21 64370[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat (Succ zzz6443000) Zero == GT)",fontsize=16,color="black",shape="box"];64370 -> 64377[label="",style="solid", color="black", weight=3]; 130.57/78.21 64371[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat Zero (Succ zzz644400) == GT)",fontsize=16,color="black",shape="box"];64371 -> 64378[label="",style="solid", color="black", weight=3]; 130.57/78.21 64372[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];64372 -> 64379[label="",style="solid", color="black", weight=3]; 130.57/78.21 64373[label="error []",fontsize=16,color="red",shape="box"];64374[label="FiniteMap.mkBalBranch6MkBalBranch02 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344)",fontsize=16,color="black",shape="box"];64374 -> 64380[label="",style="solid", color="black", weight=3]; 130.57/78.21 64375[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (compare zzz6452 (FiniteMap.sIZE_RATIO * zzz6453) == GT)",fontsize=16,color="black",shape="box"];64375 -> 64381[label="",style="solid", color="black", weight=3]; 130.57/78.21 44889[label="Succ zzz332000",fontsize=16,color="green",shape="box"];44890[label="Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))",fontsize=16,color="green",shape="box"];44890 -> 44920[label="",style="dashed", color="green", weight=3]; 130.57/78.21 45734 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 45734[label="primPlusNat (Succ (primPlusNat Zero Zero)) Zero",fontsize=16,color="magenta"];45734 -> 45791[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 45734 -> 45792[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 37133[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];37133 -> 37709[label="",style="solid", color="black", weight=3]; 130.57/78.21 37134[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];37134 -> 37710[label="",style="solid", color="black", weight=3]; 130.57/78.21 37135[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz426200))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];37135 -> 37711[label="",style="solid", color="black", weight=3]; 130.57/78.21 37136[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];37136 -> 37712[label="",style="solid", color="black", weight=3]; 130.57/78.21 46591[label="zzz332000",fontsize=16,color="green",shape="box"];46592 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 46592[label="primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)",fontsize=16,color="magenta"];46592 -> 46672[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46592 -> 46673[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 47563[label="Zero",fontsize=16,color="green",shape="box"];47564[label="Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)",fontsize=16,color="green",shape="box"];47564 -> 47659[label="",style="dashed", color="green", weight=3]; 130.57/78.21 46593[label="zzz332000",fontsize=16,color="green",shape="box"];46594 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 46594[label="primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)",fontsize=16,color="magenta"];46594 -> 46674[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46594 -> 46675[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 47565[label="Zero",fontsize=16,color="green",shape="box"];47566[label="Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)",fontsize=16,color="green",shape="box"];47566 -> 47660[label="",style="dashed", color="green", weight=3]; 130.57/78.21 45504 -> 45665[label="",style="dashed", color="red", weight=0]; 130.57/78.21 45504[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz5000))) (FiniteMap.mkVBalBranch3Size_l zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002) == LT)",fontsize=16,color="magenta"];45504 -> 45666[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46753 -> 46861[label="",style="dashed", color="red", weight=0]; 130.57/78.21 46753[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz5096))) (FiniteMap.mkVBalBranch3Size_l zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098) == LT)",fontsize=16,color="magenta"];46753 -> 46862[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 58876[label="Succ zzz33200",fontsize=16,color="green",shape="box"];58877[label="zzz333",fontsize=16,color="green",shape="box"];58878[label="zzz5231",fontsize=16,color="green",shape="box"];58879[label="zzz5234",fontsize=16,color="green",shape="box"];58880[label="zzz33200",fontsize=16,color="green",shape="box"];58881[label="zzz5230",fontsize=16,color="green",shape="box"];58882[label="zzz330",fontsize=16,color="green",shape="box"];58883[label="zzz31",fontsize=16,color="green",shape="box"];58884[label="Succ zzz55410",fontsize=16,color="green",shape="box"];58885[label="zzz300",fontsize=16,color="green",shape="box"];58886[label="zzz5233",fontsize=16,color="green",shape="box"];58887[label="zzz331",fontsize=16,color="green",shape="box"];58888[label="zzz334",fontsize=16,color="green",shape="box"];58889[label="Zero",fontsize=16,color="green",shape="box"];58875[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (Neg zzz6130) zzz6131 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (primCmpNat zzz6132 zzz6133 == LT)",fontsize=16,color="burlywood",shape="triangle"];65602[label="zzz6132/Succ zzz61320",fontsize=10,color="white",style="solid",shape="box"];58875 -> 65602[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65602 -> 59128[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65603[label="zzz6132/Zero",fontsize=10,color="white",style="solid",shape="box"];58875 -> 65603[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65603 -> 59129[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 58890[label="Succ zzz33200",fontsize=16,color="green",shape="box"];58891[label="zzz333",fontsize=16,color="green",shape="box"];58892[label="zzz5231",fontsize=16,color="green",shape="box"];58893[label="zzz5234",fontsize=16,color="green",shape="box"];58894[label="zzz33200",fontsize=16,color="green",shape="box"];58895[label="zzz5230",fontsize=16,color="green",shape="box"];58896[label="zzz330",fontsize=16,color="green",shape="box"];58897[label="zzz31",fontsize=16,color="green",shape="box"];58898[label="Zero",fontsize=16,color="green",shape="box"];58899[label="zzz300",fontsize=16,color="green",shape="box"];58900[label="zzz5233",fontsize=16,color="green",shape="box"];58901[label="zzz331",fontsize=16,color="green",shape="box"];58902[label="zzz334",fontsize=16,color="green",shape="box"];58903[label="Zero",fontsize=16,color="green",shape="box"];63281[label="zzz3530",fontsize=16,color="green",shape="box"];63282 -> 5407[label="",style="dashed", color="red", weight=0]; 130.57/78.21 63282[label="FiniteMap.mkVBalBranch (Neg Zero) zzz31 zzz3534 (FiniteMap.Branch zzz340 zzz341 (Pos Zero) zzz343 zzz344)",fontsize=16,color="magenta"];63282 -> 63517[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63282 -> 63518[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63283[label="zzz3533",fontsize=16,color="green",shape="box"];63284[label="zzz3531",fontsize=16,color="green",shape="box"];63285[label="zzz330",fontsize=16,color="green",shape="box"];63286 -> 63190[label="",style="dashed", color="red", weight=0]; 130.57/78.21 63286[label="FiniteMap.mkVBalBranch (Neg zzz300) zzz31 zzz334 (FiniteMap.Branch zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234)",fontsize=16,color="magenta"];63287[label="zzz333",fontsize=16,color="green",shape="box"];63288[label="zzz331",fontsize=16,color="green",shape="box"];47166[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg (Succ zzz5137))) (FiniteMap.mkVBalBranch3Size_l zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139) == LT)",fontsize=16,color="black",shape="box"];47166 -> 47181[label="",style="solid", color="black", weight=3]; 130.57/78.21 48475[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg (Succ zzz5253))) (FiniteMap.mkVBalBranch3Size_l zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255) == LT)",fontsize=16,color="black",shape="box"];48475 -> 48501[label="",style="solid", color="black", weight=3]; 130.57/78.21 37447[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos zzz52320) zzz5233 zzz5234 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)))) (Pos zzz52320) == LT)",fontsize=16,color="black",shape="box"];37447 -> 38091[label="",style="solid", color="black", weight=3]; 130.57/78.21 37448[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)))) (Neg zzz52320) == LT)",fontsize=16,color="black",shape="box"];37448 -> 38092[label="",style="solid", color="black", weight=3]; 130.57/78.21 37449[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];37449 -> 38093[label="",style="solid", color="black", weight=3]; 130.57/78.21 37450[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg (Succ zzz523200))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];37450 -> 38094[label="",style="solid", color="black", weight=3]; 130.57/78.21 37451[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];37451 -> 38095[label="",style="solid", color="black", weight=3]; 130.57/78.21 37452[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos zzz52320) zzz5233 zzz5234 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)))) (Pos zzz52320) == LT)",fontsize=16,color="black",shape="box"];37452 -> 38096[label="",style="solid", color="black", weight=3]; 130.57/78.21 37453[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)))) (Neg zzz52320) == LT)",fontsize=16,color="black",shape="box"];37453 -> 38097[label="",style="solid", color="black", weight=3]; 130.57/78.21 37454[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];37454 -> 38098[label="",style="solid", color="black", weight=3]; 130.57/78.21 37455[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];37455 -> 38099[label="",style="solid", color="black", weight=3]; 130.57/78.21 37456[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];37456 -> 38100[label="",style="solid", color="black", weight=3]; 130.57/78.21 35571 -> 36060[label="",style="dashed", color="red", weight=0]; 130.57/78.21 35571[label="primPlusNat (primPlusNat (Succ (Succ (primPlusNat (primPlusNat (Succ (Succ (Succ zzz6200000))) (Succ (Succ (Succ zzz6200000)))) (Succ (Succ zzz6200000))))) (Succ (Succ zzz6200000))) zzz6200000",fontsize=16,color="magenta"];35571 -> 36061[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 35571 -> 36062[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 35572[label="primPlusNat (Succ (Succ (primPlusNat (primPlusNat (Succ (Succ Zero)) (Succ (Succ Zero))) (Succ Zero)))) (Succ Zero)",fontsize=16,color="black",shape="box"];35572 -> 36116[label="",style="solid", color="black", weight=3]; 130.57/78.21 42058[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710) (FiniteMap.mkVBalBranch3Size_l zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710) == LT)",fontsize=16,color="black",shape="box"];42058 -> 42095[label="",style="solid", color="black", weight=3]; 130.57/78.21 63289[label="zzz4706",fontsize=16,color="green",shape="box"];63290[label="zzz4710",fontsize=16,color="green",shape="box"];63291 -> 4125[label="",style="dashed", color="red", weight=0]; 130.57/78.21 63291[label="FiniteMap.mkVBalBranch (Pos zzz4711) zzz4712 (FiniteMap.Branch zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705) zzz4709",fontsize=16,color="magenta"];63291 -> 63519[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63291 -> 63520[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63291 -> 63521[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63291 -> 63522[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63292[label="zzz4707",fontsize=16,color="green",shape="box"];39881[label="zzz44360",fontsize=16,color="green",shape="box"];39882[label="zzz3887000",fontsize=16,color="green",shape="box"];39883[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 True",fontsize=16,color="black",shape="box"];39883 -> 39902[label="",style="solid", color="black", weight=3]; 130.57/78.21 39884 -> 39674[label="",style="dashed", color="red", weight=0]; 130.57/78.21 39884[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 False",fontsize=16,color="magenta"];39885[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884) (FiniteMap.mkVBalBranch3Size_l zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884) == LT)",fontsize=16,color="black",shape="box"];39885 -> 39903[label="",style="solid", color="black", weight=3]; 130.57/78.21 37511 -> 43165[label="",style="dashed", color="red", weight=0]; 130.57/78.21 37511[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (Pos (primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ (Succ (Succ Zero)))) (Succ (Succ (Succ Zero))))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="magenta"];37511 -> 43166[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 41223 -> 40784[label="",style="dashed", color="red", weight=0]; 130.57/78.21 41223[label="primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ (Succ Zero))) (Succ (Succ Zero))",fontsize=16,color="magenta"];41223 -> 41245[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 41828[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (Pos (Succ zzz47150)) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];41828 -> 41912[label="",style="solid", color="black", weight=3]; 130.57/78.21 41829[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];41829 -> 41913[label="",style="solid", color="black", weight=3]; 130.57/78.21 37513 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.21 37513[label="FiniteMap.mkBalBranch zzz3893 zzz3894 (FiniteMap.mkVBalBranch (Pos zzz3898) zzz3899 (FiniteMap.Branch zzz3889 zzz3890 (Pos (Succ Zero)) zzz3891 zzz3892) zzz3896) zzz3897",fontsize=16,color="magenta"];37513 -> 63297[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 37513 -> 63298[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 37513 -> 63299[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 37513 -> 63300[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 37514[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];37514 -> 38159[label="",style="solid", color="black", weight=3]; 130.57/78.21 37515[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];37515 -> 38160[label="",style="solid", color="black", weight=3]; 130.57/78.21 37516 -> 43115[label="",style="dashed", color="red", weight=0]; 130.57/78.21 37516[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ (Succ (Succ Zero))))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="magenta"];37516 -> 43116[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 41910[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (Pos (Succ zzz47190)) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];41910 -> 42017[label="",style="solid", color="black", weight=3]; 130.57/78.21 41911[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];41911 -> 42018[label="",style="solid", color="black", weight=3]; 130.57/78.21 39596 -> 38195[label="",style="dashed", color="red", weight=0]; 130.57/78.21 39596[label="primPlusNat (primMulNat (Succ (Succ Zero)) (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];39596 -> 39676[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 57788[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (Pos zzz6030) zzz6031 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (primCmpNat (Succ zzz60320) zzz6033 == LT)",fontsize=16,color="burlywood",shape="box"];65604[label="zzz6033/Succ zzz60330",fontsize=10,color="white",style="solid",shape="box"];57788 -> 65604[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65604 -> 57958[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65605[label="zzz6033/Zero",fontsize=10,color="white",style="solid",shape="box"];57788 -> 65605[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65605 -> 57959[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 57789[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (Pos zzz6030) zzz6031 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (primCmpNat Zero zzz6033 == LT)",fontsize=16,color="burlywood",shape="box"];65606[label="zzz6033/Succ zzz60330",fontsize=10,color="white",style="solid",shape="box"];57789 -> 65606[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65606 -> 57960[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65607[label="zzz6033/Zero",fontsize=10,color="white",style="solid",shape="box"];57789 -> 65607[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65607 -> 57961[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 63513[label="zzz2504",fontsize=16,color="green",shape="box"];63514[label="FiniteMap.Branch zzz340 zzz341 (Pos Zero) zzz343 zzz344",fontsize=16,color="green",shape="box"];37521[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz34200 zzz34200)) zzz34200)) zzz34200))) (Succ zzz34200))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];37521 -> 38164[label="",style="solid", color="black", weight=3]; 130.57/78.21 46666[label="Succ (Succ zzz25020000)",fontsize=16,color="green",shape="box"];46667[label="Succ (primPlusNat (Succ (Succ zzz25020000)) (Succ (Succ zzz25020000)))",fontsize=16,color="green",shape="box"];46667 -> 46757[label="",style="dashed", color="green", weight=3]; 130.57/78.21 46668[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 < FiniteMap.mkVBalBranch3Size_l zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121)",fontsize=16,color="black",shape="box"];46668 -> 46758[label="",style="solid", color="black", weight=3]; 130.57/78.21 46669 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.21 46669[label="FiniteMap.mkBalBranch zzz5117 zzz5118 (FiniteMap.mkVBalBranch (Pos zzz5122) zzz5123 (FiniteMap.Branch zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116) zzz5120) zzz5121",fontsize=16,color="magenta"];46669 -> 63301[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46669 -> 63302[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46669 -> 63303[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46669 -> 63304[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39971[label="Succ Zero",fontsize=16,color="green",shape="box"];39972 -> 39827[label="",style="dashed", color="red", weight=0]; 130.57/78.21 39972[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpNat zzz411400 zzz44550 == LT)",fontsize=16,color="magenta"];39972 -> 40042[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39972 -> 40043[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39973[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (GT == LT)",fontsize=16,color="black",shape="box"];39973 -> 40044[label="",style="solid", color="black", weight=3]; 130.57/78.21 39974 -> 39828[label="",style="dashed", color="red", weight=0]; 130.57/78.21 39974[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (LT == LT)",fontsize=16,color="magenta"];39975[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (EQ == LT)",fontsize=16,color="black",shape="box"];39975 -> 40045[label="",style="solid", color="black", weight=3]; 130.57/78.21 63293[label="zzz4107",fontsize=16,color="green",shape="box"];63294[label="zzz4111",fontsize=16,color="green",shape="box"];63295 -> 4125[label="",style="dashed", color="red", weight=0]; 130.57/78.21 63295[label="FiniteMap.mkVBalBranch (Pos zzz4112) zzz4113 (FiniteMap.Branch zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106) zzz4110",fontsize=16,color="magenta"];63295 -> 63523[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63295 -> 63524[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63295 -> 63525[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63295 -> 63526[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63296[label="zzz4108",fontsize=16,color="green",shape="box"];46670[label="Succ (Succ zzz25020000)",fontsize=16,color="green",shape="box"];46671[label="Succ (primPlusNat (Succ (Succ zzz25020000)) (Succ (Succ zzz25020000)))",fontsize=16,color="green",shape="box"];46671 -> 46763[label="",style="dashed", color="green", weight=3]; 130.57/78.21 39980[label="Succ Zero",fontsize=16,color="green",shape="box"];37570[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (Pos zzz3748) zzz3749 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 < FiniteMap.mkVBalBranch3Size_l zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747)",fontsize=16,color="black",shape="box"];37570 -> 38190[label="",style="solid", color="black", weight=3]; 130.57/78.21 37571[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ 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zzz63924))",fontsize=16,color="magenta"];64035 -> 64133[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64035 -> 64134[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64035 -> 64135[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64035 -> 64136[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64035 -> 64137[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64130[label="FiniteMap.glueBal2Mid_elt20 (FiniteMap.Branch zzz6395 zzz6396 zzz6397 zzz6398 zzz6399) (FiniteMap.Branch zzz6400 zzz6401 zzz6402 zzz6403 zzz6404) (zzz6405,zzz6406)",fontsize=16,color="black",shape="box"];64130 -> 64234[label="",style="solid", color="black", weight=3]; 130.57/78.21 64131 -> 63939[label="",style="dashed", color="red", weight=0]; 130.57/78.21 64131[label="FiniteMap.glueBal2Mid_elt20 (FiniteMap.Branch zzz6395 zzz6396 zzz6397 zzz6398 zzz6399) (FiniteMap.Branch zzz6400 zzz6401 zzz6402 zzz6403 zzz6404) (FiniteMap.findMin 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64038[label="zzz474031",fontsize=16,color="green",shape="box"];64039[label="zzz474032",fontsize=16,color="green",shape="box"];64040[label="zzz47461",fontsize=16,color="green",shape="box"];64041[label="zzz47460",fontsize=16,color="green",shape="box"];64042[label="zzz474030",fontsize=16,color="green",shape="box"];64043[label="zzz47463",fontsize=16,color="green",shape="box"];64044[label="zzz474034",fontsize=16,color="green",shape="box"];64045[label="zzz47460",fontsize=16,color="green",shape="box"];64046[label="zzz47464",fontsize=16,color="green",shape="box"];64047[label="zzz47462",fontsize=16,color="green",shape="box"];64048[label="zzz47463",fontsize=16,color="green",shape="box"];64049[label="zzz47462",fontsize=16,color="green",shape="box"];64050[label="zzz474033",fontsize=16,color="green",shape="box"];64051[label="zzz47464",fontsize=16,color="green",shape="box"];64052[label="zzz47461",fontsize=16,color="green",shape="box"];64037[label="FiniteMap.glueBal2Mid_key10 (FiniteMap.Branch zzz6411 zzz6412 zzz6413 zzz6414 zzz6415) (FiniteMap.Branch zzz6416 zzz6417 zzz6418 zzz6419 zzz6420) (FiniteMap.findMax (FiniteMap.Branch zzz6421 zzz6422 zzz6423 zzz6424 zzz6425))",fontsize=16,color="burlywood",shape="triangle"];65608[label="zzz6425/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];64037 -> 65608[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65608 -> 64138[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65609[label="zzz6425/FiniteMap.Branch zzz64250 zzz64251 zzz64252 zzz64253 zzz64254",fontsize=10,color="white",style="solid",shape="box"];64037 -> 65609[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65609 -> 64139[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 63622[label="zzz47460",fontsize=16,color="green",shape="box"];63623 -> 63267[label="",style="dashed", color="red", weight=0]; 130.57/78.21 63623[label="FiniteMap.deleteMax (FiniteMap.Branch zzz474640 zzz474641 zzz474642 zzz474643 zzz474644)",fontsize=16,color="magenta"];63623 -> 63678[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63623 -> 63679[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63623 -> 63680[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63623 -> 63681[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63623 -> 63682[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63624[label="zzz47463",fontsize=16,color="green",shape="box"];63625[label="zzz47461",fontsize=16,color="green",shape="box"];64142[label="zzz47463",fontsize=16,color="green",shape="box"];64143[label="zzz474034",fontsize=16,color="green",shape="box"];64144[label="zzz47462",fontsize=16,color="green",shape="box"];64145[label="zzz47464",fontsize=16,color="green",shape="box"];64146[label="zzz47460",fontsize=16,color="green",shape="box"];64147[label="zzz47460",fontsize=16,color="green",shape="box"];64148[label="zzz47461",fontsize=16,color="green",shape="box"];64149[label="zzz474032",fontsize=16,color="green",shape="box"];64150[label="zzz47461",fontsize=16,color="green",shape="box"];64151[label="zzz47462",fontsize=16,color="green",shape="box"];64152[label="zzz474030",fontsize=16,color="green",shape="box"];64153[label="zzz474031",fontsize=16,color="green",shape="box"];64154[label="zzz47463",fontsize=16,color="green",shape="box"];64155[label="zzz474033",fontsize=16,color="green",shape="box"];64156[label="zzz47464",fontsize=16,color="green",shape="box"];64141[label="FiniteMap.glueBal2Mid_elt10 (FiniteMap.Branch zzz6427 zzz6428 zzz6429 zzz6430 zzz6431) (FiniteMap.Branch zzz6432 zzz6433 zzz6434 zzz6435 zzz6436) (FiniteMap.findMax (FiniteMap.Branch zzz6437 zzz6438 zzz6439 zzz6440 zzz6441))",fontsize=16,color="burlywood",shape="triangle"];65610[label="zzz6441/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];64141 -> 65610[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65610 -> 64240[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65611[label="zzz6441/FiniteMap.Branch zzz64410 zzz64411 zzz64412 zzz64413 zzz64414",fontsize=10,color="white",style="solid",shape="box"];64141 -> 65611[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65611 -> 64241[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 64376 -> 64349[label="",style="dashed", color="red", weight=0]; 130.57/78.21 64376[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat zzz6443000 zzz644400 == GT)",fontsize=16,color="magenta"];64376 -> 64382[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64376 -> 64383[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64377 -> 64318[label="",style="dashed", color="red", weight=0]; 130.57/78.21 64377[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (GT == GT)",fontsize=16,color="magenta"];64378 -> 64326[label="",style="dashed", color="red", weight=0]; 130.57/78.21 64378[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (LT == GT)",fontsize=16,color="magenta"];64379 -> 64339[label="",style="dashed", color="red", weight=0]; 130.57/78.21 64379[label="FiniteMap.mkBalBranch6MkBalBranch4 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (EQ == GT)",fontsize=16,color="magenta"];64380 -> 64384[label="",style="dashed", color="red", weight=0]; 130.57/78.21 64380[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (FiniteMap.sizeFM zzz4740343 < Pos (Succ (Succ Zero)) * FiniteMap.sizeFM zzz4740344)",fontsize=16,color="magenta"];64380 -> 64385[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64380 -> 64386[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64381[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt zzz6452 (FiniteMap.sIZE_RATIO * zzz6453) == GT)",fontsize=16,color="burlywood",shape="box"];65612[label="zzz6452/Pos zzz64520",fontsize=10,color="white",style="solid",shape="box"];64381 -> 65612[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65612 -> 64387[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65613[label="zzz6452/Neg zzz64520",fontsize=10,color="white",style="solid",shape="box"];64381 -> 65613[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65613 -> 64388[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 44920 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 44920[label="primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000)",fontsize=16,color="magenta"];44920 -> 45035[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 44920 -> 45036[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 45791[label="Zero",fontsize=16,color="green",shape="box"];45792[label="Succ (primPlusNat Zero Zero)",fontsize=16,color="green",shape="box"];45792 -> 45985[label="",style="dashed", color="green", weight=3]; 130.57/78.21 37709[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];37709 -> 38264[label="",style="solid", color="black", weight=3]; 130.57/78.21 37710[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];37710 -> 38265[label="",style="solid", color="black", weight=3]; 130.57/78.21 37711 -> 49578[label="",style="dashed", color="red", weight=0]; 130.57/78.21 37711[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264 (primCmpInt (Neg (primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz426200)) (Succ zzz426200))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg (Succ zzz426200)) zzz4263 zzz4264) == LT)",fontsize=16,color="magenta"];37711 -> 49687[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 37711 -> 49688[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 37711 -> 49689[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 37711 -> 49690[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 37711 -> 49691[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 37711 -> 49692[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 37711 -> 49693[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 37712[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];37712 -> 38267[label="",style="solid", color="black", weight=3]; 130.57/78.21 46672[label="Succ zzz332000",fontsize=16,color="green",shape="box"];46673[label="Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))",fontsize=16,color="green",shape="box"];46673 -> 46764[label="",style="dashed", color="green", weight=3]; 130.57/78.21 47659 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 47659[label="primPlusNat (Succ (primPlusNat Zero Zero)) Zero",fontsize=16,color="magenta"];47659 -> 47758[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 47659 -> 47759[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46674[label="Succ zzz332000",fontsize=16,color="green",shape="box"];46675[label="Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))",fontsize=16,color="green",shape="box"];46675 -> 46765[label="",style="dashed", color="green", weight=3]; 130.57/78.21 47660 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 47660[label="primPlusNat (Succ (primPlusNat Zero Zero)) Zero",fontsize=16,color="magenta"];47660 -> 47760[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 47660 -> 47761[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 45666 -> 43358[label="",style="dashed", color="red", weight=0]; 130.57/78.21 45666[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz5000)",fontsize=16,color="magenta"];45666 -> 45690[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 45665[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpInt (Pos zzz5103) (FiniteMap.mkVBalBranch3Size_l zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002) == LT)",fontsize=16,color="burlywood",shape="triangle"];65614[label="zzz5103/Succ zzz51030",fontsize=10,color="white",style="solid",shape="box"];45665 -> 65614[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65614 -> 45691[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65615[label="zzz5103/Zero",fontsize=10,color="white",style="solid",shape="box"];45665 -> 65615[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65615 -> 45692[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 46862 -> 43358[label="",style="dashed", color="red", weight=0]; 130.57/78.21 46862[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz5096)",fontsize=16,color="magenta"];46862 -> 46888[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46861[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpInt (Pos zzz5192) (FiniteMap.mkVBalBranch3Size_l zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098) == LT)",fontsize=16,color="burlywood",shape="triangle"];65616[label="zzz5192/Succ zzz51920",fontsize=10,color="white",style="solid",shape="box"];46861 -> 65616[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65616 -> 46889[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65617[label="zzz5192/Zero",fontsize=10,color="white",style="solid",shape="box"];46861 -> 65617[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65617 -> 46890[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 59128[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (Neg zzz6130) zzz6131 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (primCmpNat (Succ zzz61320) zzz6133 == LT)",fontsize=16,color="burlywood",shape="box"];65618[label="zzz6133/Succ zzz61330",fontsize=10,color="white",style="solid",shape="box"];59128 -> 65618[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65618 -> 59258[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65619[label="zzz6133/Zero",fontsize=10,color="white",style="solid",shape="box"];59128 -> 65619[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65619 -> 59259[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 59129[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (Neg zzz6130) zzz6131 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (primCmpNat Zero zzz6133 == LT)",fontsize=16,color="burlywood",shape="box"];65620[label="zzz6133/Succ zzz61330",fontsize=10,color="white",style="solid",shape="box"];59129 -> 65620[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65620 -> 59260[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65621[label="zzz6133/Zero",fontsize=10,color="white",style="solid",shape="box"];59129 -> 65621[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65621 -> 59261[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 63517[label="zzz3534",fontsize=16,color="green",shape="box"];63518[label="FiniteMap.Branch zzz340 zzz341 (Pos Zero) zzz343 zzz344",fontsize=16,color="green",shape="box"];47181 -> 47202[label="",style="dashed", color="red", weight=0]; 130.57/78.21 47181[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz5137))) (FiniteMap.mkVBalBranch3Size_l zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139) == LT)",fontsize=16,color="magenta"];47181 -> 47203[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 48501 -> 48539[label="",style="dashed", color="red", weight=0]; 130.57/78.21 48501[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz5253))) (FiniteMap.mkVBalBranch3Size_l zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255) == LT)",fontsize=16,color="magenta"];48501 -> 48540[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 38091[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos zzz52320) zzz5233 zzz5234 (primCmpNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200))) zzz52320 == LT)",fontsize=16,color="burlywood",shape="box"];65622[label="zzz52320/Succ zzz523200",fontsize=10,color="white",style="solid",shape="box"];38091 -> 65622[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65622 -> 38567[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65623[label="zzz52320/Zero",fontsize=10,color="white",style="solid",shape="box"];38091 -> 65623[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65623 -> 38568[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 38092[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (GT == LT)",fontsize=16,color="black",shape="box"];38092 -> 38569[label="",style="solid", color="black", weight=3]; 130.57/78.21 38093[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];38093 -> 38570[label="",style="solid", color="black", weight=3]; 130.57/78.21 38094 -> 43855[label="",style="dashed", color="red", weight=0]; 130.57/78.21 38094[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz523200))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="magenta"];38094 -> 44072[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 38095[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];38095 -> 38572[label="",style="solid", color="black", weight=3]; 130.57/78.21 38096[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos zzz52320) zzz5233 zzz5234 (LT == LT)",fontsize=16,color="black",shape="box"];38096 -> 38573[label="",style="solid", color="black", weight=3]; 130.57/78.21 38097[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (primCmpNat zzz52320 (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200))) == LT)",fontsize=16,color="burlywood",shape="box"];65624[label="zzz52320/Succ zzz523200",fontsize=10,color="white",style="solid",shape="box"];38097 -> 65624[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65624 -> 38574[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65625[label="zzz52320/Zero",fontsize=10,color="white",style="solid",shape="box"];38097 -> 65625[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65625 -> 38575[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 38098[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];38098 -> 38576[label="",style="solid", color="black", weight=3]; 130.57/78.21 38099[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg (Succ zzz523200))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];38099 -> 38577[label="",style="solid", color="black", weight=3]; 130.57/78.21 38100[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];38100 -> 38578[label="",style="solid", color="black", weight=3]; 130.57/78.21 36061[label="zzz6200000",fontsize=16,color="green",shape="box"];36062[label="Succ (primPlusNat (primPlusNat (Succ (Succ (Succ zzz6200000))) (Succ (Succ (Succ zzz6200000)))) (Succ (Succ zzz6200000)))",fontsize=16,color="green",shape="box"];36062 -> 36679[label="",style="dashed", color="green", weight=3]; 130.57/78.21 36060[label="primPlusNat (primPlusNat (Succ zzz3752) (Succ (Succ zzz3753))) zzz3753",fontsize=16,color="black",shape="triangle"];36060 -> 36680[label="",style="solid", color="black", weight=3]; 130.57/78.21 36116[label="Succ (Succ (primPlusNat (Succ (primPlusNat (primPlusNat (Succ (Succ Zero)) (Succ (Succ Zero))) (Succ Zero))) Zero))",fontsize=16,color="green",shape="box"];36116 -> 36681[label="",style="dashed", color="green", weight=3]; 130.57/78.21 42095[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710) (FiniteMap.mkVBalBranch3Size_l zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710) == LT)",fontsize=16,color="black",shape="box"];42095 -> 42243[label="",style="solid", color="black", weight=3]; 130.57/78.21 63519[label="FiniteMap.Branch zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705",fontsize=16,color="green",shape="box"];63520[label="zzz4711",fontsize=16,color="green",shape="box"];63521[label="zzz4709",fontsize=16,color="green",shape="box"];63522[label="zzz4712",fontsize=16,color="green",shape="box"];39902 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.21 39902[label="FiniteMap.mkBalBranch zzz3880 zzz3881 (FiniteMap.mkVBalBranch (Pos zzz3885) zzz3886 (FiniteMap.Branch zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879) zzz3883) zzz3884",fontsize=16,color="magenta"];39902 -> 63306[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39902 -> 63307[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39902 -> 63308[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39902 -> 63309[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39903[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884)) (FiniteMap.mkVBalBranch3Size_l zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884) == LT)",fontsize=16,color="black",shape="box"];39903 -> 39990[label="",style="solid", color="black", weight=3]; 130.57/78.21 43166[label="primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ (Succ (Succ Zero)))",fontsize=16,color="black",shape="triangle"];43166 -> 43174[label="",style="solid", color="black", weight=3]; 130.57/78.21 43165[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (Pos (primPlusNat zzz4811 (Succ (Succ (Succ Zero))))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="burlywood",shape="triangle"];65626[label="zzz4811/Succ zzz48110",fontsize=10,color="white",style="solid",shape="box"];43165 -> 65626[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65626 -> 43175[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65627[label="zzz4811/Zero",fontsize=10,color="white",style="solid",shape="box"];43165 -> 65627[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65627 -> 43176[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 41245[label="primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];41245 -> 41323[label="",style="solid", color="black", weight=3]; 130.57/78.21 40784[label="primPlusNat zzz3752 (Succ (Succ Zero))",fontsize=16,color="burlywood",shape="triangle"];65628[label="zzz3752/Succ zzz37520",fontsize=10,color="white",style="solid",shape="box"];40784 -> 65628[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65628 -> 41196[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65629[label="zzz3752/Zero",fontsize=10,color="white",style="solid",shape="box"];40784 -> 65629[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65629 -> 41197[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 41912[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (Pos (Succ zzz47150)) (Pos (Succ (Succ zzz2502000))) == LT)",fontsize=16,color="black",shape="box"];41912 -> 42019[label="",style="solid", color="black", weight=3]; 130.57/78.21 41913[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (Pos Zero) (Pos (Succ (Succ zzz2502000))) == LT)",fontsize=16,color="black",shape="box"];41913 -> 42020[label="",style="solid", color="black", weight=3]; 130.57/78.21 63297[label="zzz3893",fontsize=16,color="green",shape="box"];63298[label="zzz3897",fontsize=16,color="green",shape="box"];63299 -> 4125[label="",style="dashed", color="red", weight=0]; 130.57/78.21 63299[label="FiniteMap.mkVBalBranch (Pos zzz3898) zzz3899 (FiniteMap.Branch zzz3889 zzz3890 (Pos (Succ Zero)) zzz3891 zzz3892) zzz3896",fontsize=16,color="magenta"];63299 -> 63527[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63299 -> 63528[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63299 -> 63529[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63299 -> 63530[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63300[label="zzz3894",fontsize=16,color="green",shape="box"];38159[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];38159 -> 38719[label="",style="solid", color="black", weight=3]; 130.57/78.21 38160[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];38160 -> 38720[label="",style="solid", color="black", weight=3]; 130.57/78.21 43116 -> 42246[label="",style="dashed", color="red", weight=0]; 130.57/78.21 43116[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ (Succ (Succ Zero)))",fontsize=16,color="magenta"];43115[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (Pos zzz4809) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="burlywood",shape="triangle"];65630[label="zzz4809/Succ zzz48090",fontsize=10,color="white",style="solid",shape="box"];43115 -> 65630[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65630 -> 43127[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65631[label="zzz4809/Zero",fontsize=10,color="white",style="solid",shape="box"];43115 -> 65631[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65631 -> 43128[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 42017[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (Pos (Succ zzz47190)) (Pos (Succ Zero)) == LT)",fontsize=16,color="black",shape="box"];42017 -> 42066[label="",style="solid", color="black", weight=3]; 130.57/78.21 42018[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpInt (Pos Zero) (Pos (Succ Zero)) == LT)",fontsize=16,color="black",shape="box"];42018 -> 42067[label="",style="solid", color="black", weight=3]; 130.57/78.21 39676[label="primMulNat (Succ (Succ Zero)) (Succ Zero)",fontsize=16,color="black",shape="box"];39676 -> 39771[label="",style="solid", color="black", weight=3]; 130.57/78.21 57958[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (Pos zzz6030) zzz6031 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (primCmpNat (Succ zzz60320) (Succ zzz60330) == LT)",fontsize=16,color="black",shape="box"];57958 -> 57976[label="",style="solid", color="black", weight=3]; 130.57/78.21 57959[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (Pos zzz6030) zzz6031 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (primCmpNat (Succ zzz60320) Zero == LT)",fontsize=16,color="black",shape="box"];57959 -> 57977[label="",style="solid", color="black", weight=3]; 130.57/78.21 57960[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (Pos zzz6030) zzz6031 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (primCmpNat Zero (Succ zzz60330) == LT)",fontsize=16,color="black",shape="box"];57960 -> 57978[label="",style="solid", color="black", weight=3]; 130.57/78.21 57961[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (Pos zzz6030) zzz6031 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];57961 -> 57979[label="",style="solid", color="black", weight=3]; 130.57/78.21 38164[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz34200 zzz34200)) zzz34200)) zzz34200)) zzz34200)))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];38164 -> 38724[label="",style="solid", color="black", weight=3]; 130.57/78.21 46757 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 46757[label="primPlusNat (Succ (Succ zzz25020000)) (Succ (Succ zzz25020000))",fontsize=16,color="magenta"];46757 -> 46893[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46757 -> 46894[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46758[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121) (FiniteMap.mkVBalBranch3Size_l zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121) == LT)",fontsize=16,color="black",shape="box"];46758 -> 46895[label="",style="solid", color="black", weight=3]; 130.57/78.21 63301[label="zzz5117",fontsize=16,color="green",shape="box"];63302[label="zzz5121",fontsize=16,color="green",shape="box"];63303 -> 4125[label="",style="dashed", color="red", weight=0]; 130.57/78.21 63303[label="FiniteMap.mkVBalBranch (Pos zzz5122) zzz5123 (FiniteMap.Branch zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116) zzz5120",fontsize=16,color="magenta"];63303 -> 63531[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63303 -> 63532[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63303 -> 63533[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63303 -> 63534[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63304[label="zzz5118",fontsize=16,color="green",shape="box"];40042[label="zzz44550",fontsize=16,color="green",shape="box"];40043[label="zzz411400",fontsize=16,color="green",shape="box"];40044[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 False",fontsize=16,color="black",shape="triangle"];40044 -> 40065[label="",style="solid", color="black", weight=3]; 130.57/78.21 40045 -> 40044[label="",style="dashed", color="red", weight=0]; 130.57/78.21 40045[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 False",fontsize=16,color="magenta"];63523[label="FiniteMap.Branch zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106",fontsize=16,color="green",shape="box"];63524[label="zzz4112",fontsize=16,color="green",shape="box"];63525[label="zzz4110",fontsize=16,color="green",shape="box"];63526[label="zzz4113",fontsize=16,color="green",shape="box"];46763 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 46763[label="primPlusNat (Succ (Succ zzz25020000)) (Succ (Succ zzz25020000))",fontsize=16,color="magenta"];46763 -> 46900[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46763 -> 46901[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 38190[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (Pos zzz3748) zzz3749 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747) (FiniteMap.mkVBalBranch3Size_l zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747) == LT)",fontsize=16,color="black",shape="box"];38190 -> 38737[label="",style="solid", color="black", weight=3]; 130.57/78.21 38191[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];38191 -> 38738[label="",style="solid", color="black", weight=3]; 130.57/78.21 64132[label="zzz6389",fontsize=16,color="green",shape="box"];64133[label="zzz63924",fontsize=16,color="green",shape="box"];64134[label="zzz63921",fontsize=16,color="green",shape="box"];64135[label="zzz63923",fontsize=16,color="green",shape="box"];64136[label="zzz63922",fontsize=16,color="green",shape="box"];64137[label="zzz63920",fontsize=16,color="green",shape="box"];64234[label="zzz6406",fontsize=16,color="green",shape="box"];64235[label="zzz64082",fontsize=16,color="green",shape="box"];64236[label="zzz64081",fontsize=16,color="green",shape="box"];64237[label="zzz64083",fontsize=16,color="green",shape="box"];64238[label="zzz64080",fontsize=16,color="green",shape="box"];64239[label="zzz64084",fontsize=16,color="green",shape="box"];64138[label="FiniteMap.glueBal2Mid_key10 (FiniteMap.Branch zzz6411 zzz6412 zzz6413 zzz6414 zzz6415) (FiniteMap.Branch zzz6416 zzz6417 zzz6418 zzz6419 zzz6420) (FiniteMap.findMax (FiniteMap.Branch zzz6421 zzz6422 zzz6423 zzz6424 FiniteMap.EmptyFM))",fontsize=16,color="black",shape="box"];64138 -> 64242[label="",style="solid", color="black", weight=3]; 130.57/78.21 64139[label="FiniteMap.glueBal2Mid_key10 (FiniteMap.Branch zzz6411 zzz6412 zzz6413 zzz6414 zzz6415) (FiniteMap.Branch zzz6416 zzz6417 zzz6418 zzz6419 zzz6420) (FiniteMap.findMax (FiniteMap.Branch zzz6421 zzz6422 zzz6423 zzz6424 (FiniteMap.Branch zzz64250 zzz64251 zzz64252 zzz64253 zzz64254)))",fontsize=16,color="black",shape="box"];64139 -> 64243[label="",style="solid", color="black", weight=3]; 130.57/78.21 63678[label="zzz474640",fontsize=16,color="green",shape="box"];63679[label="zzz474642",fontsize=16,color="green",shape="box"];63680[label="zzz474643",fontsize=16,color="green",shape="box"];63681[label="zzz474644",fontsize=16,color="green",shape="box"];63682[label="zzz474641",fontsize=16,color="green",shape="box"];64240[label="FiniteMap.glueBal2Mid_elt10 (FiniteMap.Branch zzz6427 zzz6428 zzz6429 zzz6430 zzz6431) (FiniteMap.Branch zzz6432 zzz6433 zzz6434 zzz6435 zzz6436) (FiniteMap.findMax (FiniteMap.Branch zzz6437 zzz6438 zzz6439 zzz6440 FiniteMap.EmptyFM))",fontsize=16,color="black",shape="box"];64240 -> 64245[label="",style="solid", color="black", weight=3]; 130.57/78.21 64241[label="FiniteMap.glueBal2Mid_elt10 (FiniteMap.Branch zzz6427 zzz6428 zzz6429 zzz6430 zzz6431) (FiniteMap.Branch zzz6432 zzz6433 zzz6434 zzz6435 zzz6436) (FiniteMap.findMax (FiniteMap.Branch zzz6437 zzz6438 zzz6439 zzz6440 (FiniteMap.Branch zzz64410 zzz64411 zzz64412 zzz64413 zzz64414)))",fontsize=16,color="black",shape="box"];64241 -> 64246[label="",style="solid", color="black", weight=3]; 130.57/78.21 64382[label="zzz644400",fontsize=16,color="green",shape="box"];64383[label="zzz6443000",fontsize=16,color="green",shape="box"];64385 -> 54589[label="",style="dashed", color="red", weight=0]; 130.57/78.21 64385[label="FiniteMap.sizeFM zzz4740343",fontsize=16,color="magenta"];64385 -> 64389[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64386 -> 54589[label="",style="dashed", color="red", weight=0]; 130.57/78.21 64386[label="FiniteMap.sizeFM zzz4740344",fontsize=16,color="magenta"];64386 -> 64390[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64384[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (zzz6454 < Pos (Succ (Succ Zero)) * zzz6455)",fontsize=16,color="black",shape="triangle"];64384 -> 64391[label="",style="solid", color="black", weight=3]; 130.57/78.21 64387[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos zzz64520) (FiniteMap.sIZE_RATIO * zzz6453) == GT)",fontsize=16,color="burlywood",shape="box"];65632[label="zzz64520/Succ zzz645200",fontsize=10,color="white",style="solid",shape="box"];64387 -> 65632[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65632 -> 64392[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65633[label="zzz64520/Zero",fontsize=10,color="white",style="solid",shape="box"];64387 -> 65633[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65633 -> 64393[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 64388[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg zzz64520) (FiniteMap.sIZE_RATIO * zzz6453) == GT)",fontsize=16,color="burlywood",shape="box"];65634[label="zzz64520/Succ zzz645200",fontsize=10,color="white",style="solid",shape="box"];64388 -> 65634[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65634 -> 64394[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65635[label="zzz64520/Zero",fontsize=10,color="white",style="solid",shape="box"];64388 -> 65635[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65635 -> 64395[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 45035[label="Succ zzz332000",fontsize=16,color="green",shape="box"];45036[label="Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))",fontsize=16,color="green",shape="box"];45036 -> 45109[label="",style="dashed", color="green", weight=3]; 130.57/78.21 45985 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 45985[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];45985 -> 46085[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 45985 -> 46086[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 38264[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos (Succ Zero))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];38264 -> 38880[label="",style="solid", color="black", weight=3]; 130.57/78.21 38265[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264) == LT)",fontsize=16,color="black",shape="box"];38265 -> 38881[label="",style="solid", color="black", weight=3]; 130.57/78.21 49687[label="Succ zzz3000",fontsize=16,color="green",shape="box"];49688[label="zzz4263",fontsize=16,color="green",shape="box"];49689[label="zzz4261",fontsize=16,color="green",shape="box"];49690[label="zzz4264",fontsize=16,color="green",shape="box"];49691[label="zzz4260",fontsize=16,color="green",shape="box"];49692 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 49692[label="primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz426200)) (Succ zzz426200)",fontsize=16,color="magenta"];49692 -> 49734[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 49692 -> 49735[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 49693[label="zzz426200",fontsize=16,color="green",shape="box"];38267[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];38267 -> 38883[label="",style="solid", color="black", weight=3]; 130.57/78.21 46764 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 46764[label="primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000)",fontsize=16,color="magenta"];46764 -> 46902[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46764 -> 46903[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 47758[label="Zero",fontsize=16,color="green",shape="box"];47759[label="Succ (primPlusNat Zero Zero)",fontsize=16,color="green",shape="box"];47759 -> 47861[label="",style="dashed", color="green", weight=3]; 130.57/78.21 46765 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 46765[label="primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000)",fontsize=16,color="magenta"];46765 -> 46904[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46765 -> 46905[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 47760[label="Zero",fontsize=16,color="green",shape="box"];47761[label="Succ (primPlusNat Zero Zero)",fontsize=16,color="green",shape="box"];47761 -> 47862[label="",style="dashed", color="green", weight=3]; 130.57/78.21 45690[label="zzz5000",fontsize=16,color="green",shape="box"];45691[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpInt (Pos (Succ zzz51030)) (FiniteMap.mkVBalBranch3Size_l zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002) == LT)",fontsize=16,color="black",shape="box"];45691 -> 45737[label="",style="solid", color="black", weight=3]; 130.57/78.21 45692[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002) == LT)",fontsize=16,color="black",shape="box"];45692 -> 45738[label="",style="solid", color="black", weight=3]; 130.57/78.21 46888[label="zzz5096",fontsize=16,color="green",shape="box"];46889[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpInt (Pos (Succ zzz51920)) (FiniteMap.mkVBalBranch3Size_l zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098) == LT)",fontsize=16,color="black",shape="box"];46889 -> 46979[label="",style="solid", color="black", weight=3]; 130.57/78.21 46890[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098) == LT)",fontsize=16,color="black",shape="box"];46890 -> 46980[label="",style="solid", color="black", weight=3]; 130.57/78.21 59258[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (Neg zzz6130) zzz6131 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (primCmpNat (Succ zzz61320) (Succ zzz61330) == LT)",fontsize=16,color="black",shape="box"];59258 -> 59279[label="",style="solid", color="black", weight=3]; 130.57/78.21 59259[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (Neg zzz6130) zzz6131 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (primCmpNat (Succ zzz61320) Zero == LT)",fontsize=16,color="black",shape="box"];59259 -> 59280[label="",style="solid", color="black", weight=3]; 130.57/78.21 59260[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (Neg zzz6130) zzz6131 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (primCmpNat Zero (Succ zzz61330) == LT)",fontsize=16,color="black",shape="box"];59260 -> 59281[label="",style="solid", color="black", weight=3]; 130.57/78.21 59261[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (Neg zzz6130) zzz6131 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];59261 -> 59282[label="",style="solid", color="black", weight=3]; 130.57/78.21 47203 -> 43358[label="",style="dashed", color="red", weight=0]; 130.57/78.21 47203[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz5137)",fontsize=16,color="magenta"];47203 -> 47205[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 47202[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpInt (Neg zzz5244) (FiniteMap.mkVBalBranch3Size_l zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139) == LT)",fontsize=16,color="burlywood",shape="triangle"];65636[label="zzz5244/Succ zzz52440",fontsize=10,color="white",style="solid",shape="box"];47202 -> 65636[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65636 -> 47206[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65637[label="zzz5244/Zero",fontsize=10,color="white",style="solid",shape="box"];47202 -> 65637[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65637 -> 47207[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 48540 -> 43358[label="",style="dashed", color="red", weight=0]; 130.57/78.21 48540[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz5253)",fontsize=16,color="magenta"];48540 -> 48545[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 48539[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpInt (Neg zzz5386) (FiniteMap.mkVBalBranch3Size_l zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255) == LT)",fontsize=16,color="burlywood",shape="triangle"];65638[label="zzz5386/Succ zzz53860",fontsize=10,color="white",style="solid",shape="box"];48539 -> 65638[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65638 -> 48546[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65639[label="zzz5386/Zero",fontsize=10,color="white",style="solid",shape="box"];48539 -> 65639[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65639 -> 48547[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 38567[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ zzz523200)) zzz5233 zzz5234 (primCmpNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200))) (Succ zzz523200) == LT)",fontsize=16,color="black",shape="box"];38567 -> 39483[label="",style="solid", color="black", weight=3]; 130.57/78.21 38568[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpNat (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200))) Zero == LT)",fontsize=16,color="black",shape="box"];38568 -> 39484[label="",style="solid", color="black", weight=3]; 130.57/78.21 38569[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 False",fontsize=16,color="black",shape="box"];38569 -> 39485[label="",style="solid", color="black", weight=3]; 130.57/78.21 38570[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];38570 -> 39486[label="",style="solid", color="black", weight=3]; 130.57/78.21 44072 -> 43358[label="",style="dashed", color="red", weight=0]; 130.57/78.21 44072[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz523200)",fontsize=16,color="magenta"];44072 -> 44092[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 38572[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];38572 -> 39488[label="",style="solid", color="black", weight=3]; 130.57/78.21 38573[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos zzz52320) zzz5233 zzz5234 True",fontsize=16,color="black",shape="box"];38573 -> 39489[label="",style="solid", color="black", weight=3]; 130.57/78.21 38574[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpNat (Succ zzz523200) (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200))) == LT)",fontsize=16,color="black",shape="box"];38574 -> 39490[label="",style="solid", color="black", weight=3]; 130.57/78.21 38575[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpNat Zero (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200))) == LT)",fontsize=16,color="black",shape="box"];38575 -> 39491[label="",style="solid", color="black", weight=3]; 130.57/78.21 38576[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];38576 -> 39492[label="",style="solid", color="black", weight=3]; 130.57/78.21 38577 -> 44103[label="",style="dashed", color="red", weight=0]; 130.57/78.21 38577[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz523200))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="magenta"];38577 -> 44320[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 38578[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];38578 -> 39494[label="",style="solid", color="black", weight=3]; 130.57/78.21 36679[label="primPlusNat (primPlusNat (Succ (Succ (Succ zzz6200000))) (Succ (Succ (Succ zzz6200000)))) (Succ (Succ zzz6200000))",fontsize=16,color="black",shape="box"];36679 -> 37061[label="",style="solid", color="black", weight=3]; 130.57/78.21 36680[label="primPlusNat (Succ (Succ (primPlusNat zzz3752 (Succ zzz3753)))) zzz3753",fontsize=16,color="burlywood",shape="box"];65640[label="zzz3753/Succ zzz37530",fontsize=10,color="white",style="solid",shape="box"];36680 -> 65640[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65640 -> 37062[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65641[label="zzz3753/Zero",fontsize=10,color="white",style="solid",shape="box"];36680 -> 65641[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65641 -> 37063[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 36681[label="primPlusNat (Succ (primPlusNat (primPlusNat (Succ (Succ Zero)) (Succ (Succ Zero))) (Succ Zero))) Zero",fontsize=16,color="black",shape="box"];36681 -> 37064[label="",style="solid", color="black", weight=3]; 130.57/78.21 42243[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710)) (FiniteMap.mkVBalBranch3Size_l zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710) == LT)",fontsize=16,color="black",shape="box"];42243 -> 42265[label="",style="solid", color="black", weight=3]; 130.57/78.21 63306[label="zzz3880",fontsize=16,color="green",shape="box"];63307[label="zzz3884",fontsize=16,color="green",shape="box"];63308 -> 4125[label="",style="dashed", color="red", weight=0]; 130.57/78.21 63308[label="FiniteMap.mkVBalBranch (Pos zzz3885) zzz3886 (FiniteMap.Branch zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879) zzz3883",fontsize=16,color="magenta"];63308 -> 63535[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63308 -> 63536[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63308 -> 63537[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63308 -> 63538[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63309[label="zzz3881",fontsize=16,color="green",shape="box"];39990[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884)) (FiniteMap.mkVBalBranch3Size_l zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884) == LT)",fontsize=16,color="black",shape="box"];39990 -> 40062[label="",style="solid", color="black", weight=3]; 130.57/78.21 43174 -> 43224[label="",style="dashed", color="red", weight=0]; 130.57/78.21 43174[label="primPlusNat (primMulNat (Succ (Succ (Succ Zero))) (Succ (Succ (Succ Zero)))) (Succ (Succ (Succ Zero)))",fontsize=16,color="magenta"];43174 -> 43229[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 43175[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (Pos (primPlusNat (Succ zzz48110) (Succ (Succ (Succ Zero))))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];43175 -> 43222[label="",style="solid", color="black", weight=3]; 130.57/78.21 43176[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (Pos (primPlusNat Zero (Succ (Succ (Succ Zero))))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];43176 -> 43223[label="",style="solid", color="black", weight=3]; 130.57/78.21 41323 -> 40784[label="",style="dashed", color="red", weight=0]; 130.57/78.21 41323[label="primPlusNat (primMulNat (Succ (Succ (Succ Zero))) (Succ (Succ Zero))) (Succ (Succ Zero))",fontsize=16,color="magenta"];41323 -> 41341[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 41196[label="primPlusNat (Succ zzz37520) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];41196 -> 41326[label="",style="solid", color="black", weight=3]; 130.57/78.21 41197[label="primPlusNat Zero (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];41197 -> 41327[label="",style="solid", color="black", weight=3]; 130.57/78.21 42019 -> 57269[label="",style="dashed", color="red", weight=0]; 130.57/78.21 42019[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpNat (Succ zzz47150) (Succ (Succ zzz2502000)) == LT)",fontsize=16,color="magenta"];42019 -> 57312[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42019 -> 57313[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42019 -> 57314[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42019 -> 57315[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42019 -> 57316[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42019 -> 57317[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42019 -> 57318[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42019 -> 57319[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42019 -> 57320[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42019 -> 57321[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42019 -> 57322[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42019 -> 57323[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42019 -> 57324[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42019 -> 57325[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42020 -> 57269[label="",style="dashed", color="red", weight=0]; 130.57/78.21 42020[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpNat Zero (Succ (Succ zzz2502000)) == LT)",fontsize=16,color="magenta"];42020 -> 57326[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42020 -> 57327[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42020 -> 57328[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42020 -> 57329[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42020 -> 57330[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42020 -> 57331[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42020 -> 57332[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42020 -> 57333[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42020 -> 57334[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42020 -> 57335[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42020 -> 57336[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42020 -> 57337[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42020 -> 57338[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42020 -> 57339[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 63527[label="FiniteMap.Branch zzz3889 zzz3890 (Pos (Succ Zero)) zzz3891 zzz3892",fontsize=16,color="green",shape="box"];63528[label="zzz3898",fontsize=16,color="green",shape="box"];63529[label="zzz3896",fontsize=16,color="green",shape="box"];63530[label="zzz3899",fontsize=16,color="green",shape="box"];38719[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];38719 -> 39572[label="",style="solid", color="black", weight=3]; 130.57/78.21 38720[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];38720 -> 39573[label="",style="solid", color="black", weight=3]; 130.57/78.21 42246[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ (Succ (Succ Zero)))",fontsize=16,color="black",shape="triangle"];42246 -> 42260[label="",style="solid", color="black", weight=3]; 130.57/78.21 43127[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (Pos (Succ zzz48090)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];43127 -> 43150[label="",style="solid", color="black", weight=3]; 130.57/78.21 43128[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];43128 -> 43151[label="",style="solid", color="black", weight=3]; 130.57/78.21 42066 -> 57269[label="",style="dashed", color="red", weight=0]; 130.57/78.21 42066[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpNat (Succ zzz47190) (Succ Zero) == LT)",fontsize=16,color="magenta"];42066 -> 57340[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42066 -> 57341[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42066 -> 57342[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42066 -> 57343[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42066 -> 57344[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42066 -> 57345[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42066 -> 57346[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42066 -> 57347[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42066 -> 57348[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42066 -> 57349[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42066 -> 57350[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42066 -> 57351[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42066 -> 57352[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42066 -> 57353[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42067 -> 57269[label="",style="dashed", color="red", weight=0]; 130.57/78.21 42067[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ Zero))) zzz343 zzz344 (primCmpNat Zero (Succ Zero) == LT)",fontsize=16,color="magenta"];42067 -> 57354[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42067 -> 57355[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42067 -> 57356[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42067 -> 57357[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42067 -> 57358[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42067 -> 57359[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42067 -> 57360[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42067 -> 57361[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42067 -> 57362[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42067 -> 57363[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42067 -> 57364[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42067 -> 57365[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42067 -> 57366[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 42067 -> 57367[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39771 -> 38195[label="",style="dashed", color="red", weight=0]; 130.57/78.21 39771[label="primPlusNat (primMulNat (Succ Zero) (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];39771 -> 39842[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 57976 -> 57269[label="",style="dashed", color="red", weight=0]; 130.57/78.21 57976[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (Pos zzz6030) zzz6031 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (primCmpNat zzz60320 zzz60330 == LT)",fontsize=16,color="magenta"];57976 -> 57989[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 57976 -> 57990[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 57977[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (Pos zzz6030) zzz6031 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (GT == LT)",fontsize=16,color="black",shape="box"];57977 -> 57991[label="",style="solid", color="black", weight=3]; 130.57/78.21 57978[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (Pos zzz6030) zzz6031 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (LT == LT)",fontsize=16,color="black",shape="box"];57978 -> 57992[label="",style="solid", color="black", weight=3]; 130.57/78.21 57979[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (Pos zzz6030) zzz6031 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (EQ == LT)",fontsize=16,color="black",shape="box"];57979 -> 57993[label="",style="solid", color="black", weight=3]; 130.57/78.21 38724[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz34200 zzz34200)) zzz34200)) zzz34200)) zzz34200)))) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];38724 -> 39612[label="",style="solid", color="black", weight=3]; 130.57/78.21 46893[label="Succ (Succ zzz25020000)",fontsize=16,color="green",shape="box"];46894[label="Succ (Succ zzz25020000)",fontsize=16,color="green",shape="box"];46895[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121) (FiniteMap.mkVBalBranch3Size_l zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121) == LT)",fontsize=16,color="black",shape="box"];46895 -> 46985[label="",style="solid", color="black", weight=3]; 130.57/78.21 63531[label="FiniteMap.Branch zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116",fontsize=16,color="green",shape="box"];63532[label="zzz5122",fontsize=16,color="green",shape="box"];63533[label="zzz5120",fontsize=16,color="green",shape="box"];63534[label="zzz5123",fontsize=16,color="green",shape="box"];40065[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 < FiniteMap.mkVBalBranch3Size_l zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111)",fontsize=16,color="black",shape="box"];40065 -> 40081[label="",style="solid", color="black", weight=3]; 130.57/78.21 46900[label="Succ (Succ zzz25020000)",fontsize=16,color="green",shape="box"];46901[label="Succ (Succ zzz25020000)",fontsize=16,color="green",shape="box"];38737[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (Pos zzz3748) zzz3749 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747) (FiniteMap.mkVBalBranch3Size_l zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747) == LT)",fontsize=16,color="black",shape="box"];38737 -> 39781[label="",style="solid", color="black", weight=3]; 130.57/78.21 38738[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];38738 -> 39782[label="",style="solid", color="black", weight=3]; 130.57/78.21 64242[label="FiniteMap.glueBal2Mid_key10 (FiniteMap.Branch zzz6411 zzz6412 zzz6413 zzz6414 zzz6415) (FiniteMap.Branch zzz6416 zzz6417 zzz6418 zzz6419 zzz6420) (zzz6421,zzz6422)",fontsize=16,color="black",shape="box"];64242 -> 64247[label="",style="solid", color="black", weight=3]; 130.57/78.21 64243 -> 64037[label="",style="dashed", color="red", weight=0]; 130.57/78.21 64243[label="FiniteMap.glueBal2Mid_key10 (FiniteMap.Branch zzz6411 zzz6412 zzz6413 zzz6414 zzz6415) (FiniteMap.Branch zzz6416 zzz6417 zzz6418 zzz6419 zzz6420) (FiniteMap.findMax (FiniteMap.Branch zzz64250 zzz64251 zzz64252 zzz64253 zzz64254))",fontsize=16,color="magenta"];64243 -> 64248[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64243 -> 64249[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64243 -> 64250[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64243 -> 64251[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64243 -> 64252[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64245[label="FiniteMap.glueBal2Mid_elt10 (FiniteMap.Branch zzz6427 zzz6428 zzz6429 zzz6430 zzz6431) (FiniteMap.Branch zzz6432 zzz6433 zzz6434 zzz6435 zzz6436) (zzz6437,zzz6438)",fontsize=16,color="black",shape="box"];64245 -> 64256[label="",style="solid", color="black", weight=3]; 130.57/78.21 64246 -> 64141[label="",style="dashed", color="red", weight=0]; 130.57/78.21 64246[label="FiniteMap.glueBal2Mid_elt10 (FiniteMap.Branch zzz6427 zzz6428 zzz6429 zzz6430 zzz6431) (FiniteMap.Branch zzz6432 zzz6433 zzz6434 zzz6435 zzz6436) (FiniteMap.findMax (FiniteMap.Branch zzz64410 zzz64411 zzz64412 zzz64413 zzz64414))",fontsize=16,color="magenta"];64246 -> 64257[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64246 -> 64258[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64246 -> 64259[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64246 -> 64260[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64246 -> 64261[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 64389[label="zzz4740343",fontsize=16,color="green",shape="box"];64390[label="zzz4740344",fontsize=16,color="green",shape="box"];64391[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (compare zzz6454 (Pos (Succ (Succ Zero)) * zzz6455) == LT)",fontsize=16,color="black",shape="box"];64391 -> 64396[label="",style="solid", color="black", weight=3]; 130.57/78.21 64392[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos (Succ zzz645200)) (FiniteMap.sIZE_RATIO * zzz6453) == GT)",fontsize=16,color="black",shape="box"];64392 -> 64397[label="",style="solid", color="black", weight=3]; 130.57/78.21 64393[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (FiniteMap.sIZE_RATIO * zzz6453) == GT)",fontsize=16,color="black",shape="box"];64393 -> 64398[label="",style="solid", color="black", weight=3]; 130.57/78.21 64394[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg (Succ zzz645200)) (FiniteMap.sIZE_RATIO * zzz6453) == GT)",fontsize=16,color="black",shape="box"];64394 -> 64399[label="",style="solid", color="black", weight=3]; 130.57/78.21 64395[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (FiniteMap.sIZE_RATIO * zzz6453) == GT)",fontsize=16,color="black",shape="box"];64395 -> 64400[label="",style="solid", color="black", weight=3]; 130.57/78.21 45109 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 45109[label="primPlusNat (Succ zzz332000) (Succ zzz332000)",fontsize=16,color="magenta"];45109 -> 45190[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 45109 -> 45191[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46085[label="Zero",fontsize=16,color="green",shape="box"];46086[label="Zero",fontsize=16,color="green",shape="box"];38880 -> 50854[label="",style="dashed", color="red", weight=0]; 130.57/78.21 38880[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ Zero))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos (Succ Zero)) zzz4263 zzz4264) == LT)",fontsize=16,color="magenta"];38880 -> 50877[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 38880 -> 50878[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 38880 -> 50879[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 38880 -> 50880[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 38880 -> 50881[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 38880 -> 50882[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 38881[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];38881 -> 40082[label="",style="solid", color="black", weight=3]; 130.57/78.21 49734[label="Succ zzz426200",fontsize=16,color="green",shape="box"];49735 -> 43384[label="",style="dashed", color="red", weight=0]; 130.57/78.21 49735[label="primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz426200)",fontsize=16,color="magenta"];49735 -> 49762[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 38883[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (primCmpInt (Neg Zero) (Pos (Succ zzz33200)) == LT)",fontsize=16,color="black",shape="box"];38883 -> 40084[label="",style="solid", color="black", weight=3]; 130.57/78.21 46902[label="Succ zzz332000",fontsize=16,color="green",shape="box"];46903[label="Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))",fontsize=16,color="green",shape="box"];46903 -> 46986[label="",style="dashed", color="green", weight=3]; 130.57/78.21 47861 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 47861[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];47861 -> 47988[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 47861 -> 47989[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 46904[label="Succ zzz332000",fontsize=16,color="green",shape="box"];46905[label="Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))",fontsize=16,color="green",shape="box"];46905 -> 46987[label="",style="dashed", color="green", weight=3]; 130.57/78.21 47862 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.21 47862[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];47862 -> 47990[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 47862 -> 47991[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 45737[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpInt (Pos (Succ zzz51030)) (FiniteMap.sizeFM (FiniteMap.Branch zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997)) == LT)",fontsize=16,color="black",shape="box"];45737 -> 45797[label="",style="solid", color="black", weight=3]; 130.57/78.21 45738[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997)) == LT)",fontsize=16,color="black",shape="box"];45738 -> 45798[label="",style="solid", color="black", weight=3]; 130.57/78.21 46979[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpInt (Pos (Succ zzz51920)) (FiniteMap.sizeFM (FiniteMap.Branch zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093)) == LT)",fontsize=16,color="black",shape="box"];46979 -> 46988[label="",style="solid", color="black", weight=3]; 130.57/78.21 46980[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093)) == LT)",fontsize=16,color="black",shape="box"];46980 -> 46989[label="",style="solid", color="black", weight=3]; 130.57/78.21 59279 -> 58875[label="",style="dashed", color="red", weight=0]; 130.57/78.21 59279[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (Neg zzz6130) zzz6131 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (primCmpNat zzz61320 zzz61330 == LT)",fontsize=16,color="magenta"];59279 -> 59312[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 59279 -> 59313[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 59280[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (Neg zzz6130) zzz6131 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (GT == LT)",fontsize=16,color="black",shape="box"];59280 -> 59314[label="",style="solid", color="black", weight=3]; 130.57/78.21 59281[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (Neg zzz6130) zzz6131 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (LT == LT)",fontsize=16,color="black",shape="box"];59281 -> 59315[label="",style="solid", color="black", weight=3]; 130.57/78.21 59282[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (Neg zzz6130) zzz6131 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (EQ == LT)",fontsize=16,color="black",shape="box"];59282 -> 59316[label="",style="solid", color="black", weight=3]; 130.57/78.21 47205[label="zzz5137",fontsize=16,color="green",shape="box"];47206[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpInt (Neg (Succ zzz52440)) (FiniteMap.mkVBalBranch3Size_l zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139) == LT)",fontsize=16,color="black",shape="box"];47206 -> 47211[label="",style="solid", color="black", weight=3]; 130.57/78.21 47207[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139) == LT)",fontsize=16,color="black",shape="box"];47207 -> 47212[label="",style="solid", color="black", weight=3]; 130.57/78.21 48545[label="zzz5253",fontsize=16,color="green",shape="box"];48546[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpInt (Neg (Succ zzz53860)) (FiniteMap.mkVBalBranch3Size_l zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255) == LT)",fontsize=16,color="black",shape="box"];48546 -> 48554[label="",style="solid", color="black", weight=3]; 130.57/78.21 48547[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255) == LT)",fontsize=16,color="black",shape="box"];48547 -> 48555[label="",style="solid", color="black", weight=3]; 130.57/78.21 39483[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ zzz523200)) zzz5233 zzz5234 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)) zzz523200 == LT)",fontsize=16,color="burlywood",shape="box"];65642[label="zzz523200/Succ zzz5232000",fontsize=10,color="white",style="solid",shape="box"];39483 -> 65642[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65642 -> 40725[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65643[label="zzz523200/Zero",fontsize=10,color="white",style="solid",shape="box"];39483 -> 65643[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65643 -> 40726[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 39484[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (GT == LT)",fontsize=16,color="black",shape="box"];39484 -> 40727[label="",style="solid", color="black", weight=3]; 130.57/78.21 39485[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 < FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];39485 -> 40728[label="",style="solid", color="black", weight=3]; 130.57/78.21 39486[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Pos Zero) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];39486 -> 40729[label="",style="solid", color="black", weight=3]; 130.57/78.21 44092[label="zzz523200",fontsize=16,color="green",shape="box"];39488[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Pos Zero) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];39488 -> 40731[label="",style="solid", color="black", weight=3]; 130.57/78.21 39489 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.21 39489[label="FiniteMap.mkBalBranch zzz5230 zzz5231 (FiniteMap.mkVBalBranch (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334) zzz5233) zzz5234",fontsize=16,color="magenta"];39489 -> 63310[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39489 -> 63311[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39489 -> 63312[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39489 -> 63313[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39490[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpNat zzz523200 (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)) == LT)",fontsize=16,color="burlywood",shape="box"];65644[label="zzz523200/Succ zzz5232000",fontsize=10,color="white",style="solid",shape="box"];39490 -> 65644[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65644 -> 40736[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 65645[label="zzz523200/Zero",fontsize=10,color="white",style="solid",shape="box"];39490 -> 65645[label="",style="solid", color="burlywood", weight=9]; 130.57/78.21 65645 -> 40737[label="",style="solid", color="burlywood", weight=3]; 130.57/78.21 39491[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (LT == LT)",fontsize=16,color="black",shape="box"];39491 -> 40738[label="",style="solid", color="black", weight=3]; 130.57/78.21 39492[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];39492 -> 40739[label="",style="solid", color="black", weight=3]; 130.57/78.21 44320 -> 43358[label="",style="dashed", color="red", weight=0]; 130.57/78.21 44320[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz523200)",fontsize=16,color="magenta"];44320 -> 44347[label="",style="dashed", color="magenta", weight=3]; 130.57/78.21 39494[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];39494 -> 40741[label="",style="solid", color="black", weight=3]; 130.57/78.21 37061[label="primPlusNat (Succ (Succ (primPlusNat (Succ (Succ zzz6200000)) (Succ (Succ zzz6200000))))) (Succ (Succ zzz6200000))",fontsize=16,color="black",shape="box"];37061 -> 37575[label="",style="solid", color="black", weight=3]; 130.57/78.21 37062[label="primPlusNat (Succ (Succ (primPlusNat zzz3752 (Succ (Succ zzz37530))))) (Succ zzz37530)",fontsize=16,color="black",shape="box"];37062 -> 37576[label="",style="solid", color="black", weight=3]; 130.57/78.21 37063[label="primPlusNat (Succ (Succ (primPlusNat zzz3752 (Succ Zero)))) Zero",fontsize=16,color="black",shape="box"];37063 -> 37577[label="",style="solid", color="black", weight=3]; 130.57/78.21 37064[label="Succ (primPlusNat (primPlusNat (Succ (Succ Zero)) (Succ (Succ Zero))) (Succ Zero))",fontsize=16,color="green",shape="box"];37064 -> 37578[label="",style="dashed", color="green", weight=3]; 130.57/78.21 42265[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710)) (FiniteMap.mkVBalBranch3Size_l zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710) == LT)",fontsize=16,color="black",shape="box"];42265 -> 42593[label="",style="solid", color="black", weight=3]; 130.57/78.21 63535[label="FiniteMap.Branch zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879",fontsize=16,color="green",shape="box"];63536[label="zzz3885",fontsize=16,color="green",shape="box"];63537[label="zzz3883",fontsize=16,color="green",shape="box"];63538[label="zzz3886",fontsize=16,color="green",shape="box"];40062[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884))) (FiniteMap.mkVBalBranch3Size_l zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884) == LT)",fontsize=16,color="black",shape="box"];40062 -> 40747[label="",style="solid", color="black", weight=3]; 130.57/78.21 43229[label="primMulNat (Succ (Succ (Succ Zero))) (Succ (Succ (Succ Zero)))",fontsize=16,color="black",shape="box"];43229 -> 43241[label="",style="solid", color="black", weight=3]; 130.57/78.21 43224[label="primPlusNat zzz4825 (Succ (Succ (Succ Zero)))",fontsize=16,color="burlywood",shape="triangle"];65646[label="zzz4825/Succ zzz48250",fontsize=10,color="white",style="solid",shape="box"];43224 -> 65646[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65646 -> 43238[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65647[label="zzz4825/Zero",fontsize=10,color="white",style="solid",shape="box"];43224 -> 65647[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65647 -> 43239[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 43222 -> 43242[label="",style="dashed", color="red", weight=0]; 130.57/78.22 43222[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (Pos (Succ (Succ (primPlusNat zzz48110 (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="magenta"];43222 -> 43243[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43223 -> 43242[label="",style="dashed", color="red", weight=0]; 130.57/78.22 43223[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (Pos (Succ (Succ (Succ Zero)))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="magenta"];43223 -> 43244[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41341[label="primMulNat (Succ (Succ (Succ Zero))) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];41341 -> 41425[label="",style="solid", color="black", weight=3]; 130.57/78.22 41326[label="Succ (Succ (primPlusNat zzz37520 (Succ Zero)))",fontsize=16,color="green",shape="box"];41326 -> 41344[label="",style="dashed", color="green", weight=3]; 130.57/78.22 41327[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];57312[label="Succ Zero",fontsize=16,color="green",shape="box"];57313[label="zzz2504",fontsize=16,color="green",shape="box"];57314[label="zzz343",fontsize=16,color="green",shape="box"];57315[label="zzz340",fontsize=16,color="green",shape="box"];57316[label="zzz341",fontsize=16,color="green",shape="box"];57317[label="Succ zzz47150",fontsize=16,color="green",shape="box"];57318[label="Succ (Succ 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zzz2502000)",fontsize=16,color="green",shape="box"];57333[label="zzz300",fontsize=16,color="green",shape="box"];57334[label="zzz2501",fontsize=16,color="green",shape="box"];57335[label="zzz344",fontsize=16,color="green",shape="box"];57336[label="Succ zzz2502000",fontsize=16,color="green",shape="box"];57337[label="zzz31",fontsize=16,color="green",shape="box"];57338[label="zzz2503",fontsize=16,color="green",shape="box"];57339[label="zzz2500",fontsize=16,color="green",shape="box"];39572[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ 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44437[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 42260 -> 43224[label="",style="dashed", color="red", weight=0]; 130.57/78.22 42260[label="primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ (Succ (Succ Zero)))) (Succ (Succ (Succ Zero)))",fontsize=16,color="magenta"];42260 -> 43225[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43150[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (Pos (Succ zzz48090)) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];43150 -> 43181[label="",style="solid", color="black", weight=3]; 130.57/78.22 43151[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];43151 -> 43182[label="",style="solid", color="black", weight=3]; 130.57/78.22 57340[label="Succ Zero",fontsize=16,color="green",shape="box"];57341[label="zzz2504",fontsize=16,color="green",shape="box"];57342[label="zzz343",fontsize=16,color="green",shape="box"];57343[label="zzz340",fontsize=16,color="green",shape="box"];57344[label="zzz341",fontsize=16,color="green",shape="box"];57345[label="Succ zzz47190",fontsize=16,color="green",shape="box"];57346[label="Succ 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zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 False",fontsize=16,color="black",shape="triangle"];57991 -> 58009[label="",style="solid", color="black", weight=3]; 130.57/78.22 57992[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (Pos zzz6030) zzz6031 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 True",fontsize=16,color="black",shape="box"];57992 -> 58010[label="",style="solid", color="black", weight=3]; 130.57/78.22 57993 -> 57991[label="",style="dashed", color="red", weight=0]; 130.57/78.22 57993[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (Pos zzz6030) zzz6031 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 False",fontsize=16,color="magenta"];39612[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (primCmpInt (Neg (Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz34200 zzz34200)) zzz34200)) zzz34200)) zzz34200)))) (Pos (Succ zzz250200)) == LT)",fontsize=16,color="black",shape="box"];39612 -> 40759[label="",style="solid", color="black", weight=3]; 130.57/78.22 46985[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121)) (FiniteMap.mkVBalBranch3Size_l zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121) == LT)",fontsize=16,color="black",shape="box"];46985 -> 47059[label="",style="solid", color="black", weight=3]; 130.57/78.22 40081[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111) (FiniteMap.mkVBalBranch3Size_l zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111) == LT)",fontsize=16,color="black",shape="box"];40081 -> 40778[label="",style="solid", color="black", weight=3]; 130.57/78.22 39781[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (Pos zzz3748) zzz3749 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747)) (FiniteMap.mkVBalBranch3Size_l zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747) == LT)",fontsize=16,color="black",shape="box"];39781 -> 40779[label="",style="solid", color="black", weight=3]; 130.57/78.22 39782[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];39782 -> 40780[label="",style="solid", color="black", weight=3]; 130.57/78.22 64247[label="zzz6421",fontsize=16,color="green",shape="box"];64248[label="zzz64253",fontsize=16,color="green",shape="box"];64249[label="zzz64250",fontsize=16,color="green",shape="box"];64250[label="zzz64254",fontsize=16,color="green",shape="box"];64251[label="zzz64252",fontsize=16,color="green",shape="box"];64252[label="zzz64251",fontsize=16,color="green",shape="box"];64256[label="zzz6438",fontsize=16,color="green",shape="box"];64257[label="zzz64413",fontsize=16,color="green",shape="box"];64258[label="zzz64412",fontsize=16,color="green",shape="box"];64259[label="zzz64414",fontsize=16,color="green",shape="box"];64260[label="zzz64410",fontsize=16,color="green",shape="box"];64261[label="zzz64411",fontsize=16,color="green",shape="box"];64396[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt zzz6454 (Pos (Succ (Succ Zero)) * zzz6455) == LT)",fontsize=16,color="burlywood",shape="box"];65648[label="zzz6454/Pos zzz64540",fontsize=10,color="white",style="solid",shape="box"];64396 -> 65648[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65648 -> 64401[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65649[label="zzz6454/Neg zzz64540",fontsize=10,color="white",style="solid",shape="box"];64396 -> 65649[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65649 -> 64402[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 64397[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos (Succ zzz645200)) (primMulInt FiniteMap.sIZE_RATIO zzz6453) == GT)",fontsize=16,color="black",shape="box"];64397 -> 64403[label="",style="solid", color="black", weight=3]; 130.57/78.22 64398[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (primMulInt FiniteMap.sIZE_RATIO zzz6453) == GT)",fontsize=16,color="black",shape="box"];64398 -> 64404[label="",style="solid", color="black", weight=3]; 130.57/78.22 64399[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg (Succ zzz645200)) (primMulInt FiniteMap.sIZE_RATIO zzz6453) == GT)",fontsize=16,color="black",shape="box"];64399 -> 64405[label="",style="solid", color="black", weight=3]; 130.57/78.22 64400[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (primMulInt FiniteMap.sIZE_RATIO zzz6453) == GT)",fontsize=16,color="black",shape="box"];64400 -> 64406[label="",style="solid", color="black", weight=3]; 130.57/78.22 45190[label="Succ zzz332000",fontsize=16,color="green",shape="box"];45191[label="Succ zzz332000",fontsize=16,color="green",shape="box"];50877[label="zzz4260",fontsize=16,color="green",shape="box"];50878[label="Succ zzz3000",fontsize=16,color="green",shape="box"];50879[label="zzz4263",fontsize=16,color="green",shape="box"];50880[label="zzz4261",fontsize=16,color="green",shape="box"];50881 -> 43358[label="",style="dashed", color="red", weight=0]; 130.57/78.22 50881[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ Zero)",fontsize=16,color="magenta"];50881 -> 50898[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 50882[label="zzz4264",fontsize=16,color="green",shape="box"];40082[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpInt (Pos Zero) (Pos (Succ zzz33200)) == LT)",fontsize=16,color="black",shape="box"];40082 -> 40878[label="",style="solid", color="black", weight=3]; 130.57/78.22 49762[label="zzz426200",fontsize=16,color="green",shape="box"];40084[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 (LT == LT)",fontsize=16,color="black",shape="box"];40084 -> 40880[label="",style="solid", color="black", weight=3]; 130.57/78.22 46986 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.22 46986[label="primPlusNat (Succ zzz332000) (Succ zzz332000)",fontsize=16,color="magenta"];46986 -> 47060[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 46986 -> 47061[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47988[label="Zero",fontsize=16,color="green",shape="box"];47989[label="Zero",fontsize=16,color="green",shape="box"];46987 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.22 46987[label="primPlusNat (Succ zzz332000) (Succ zzz332000)",fontsize=16,color="magenta"];46987 -> 47062[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 46987 -> 47063[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47990[label="Zero",fontsize=16,color="green",shape="box"];47991[label="Zero",fontsize=16,color="green",shape="box"];45797[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpInt (Pos (Succ zzz51030)) (Pos (Succ (Succ zzz4995))) == LT)",fontsize=16,color="black",shape="box"];45797 -> 45986[label="",style="solid", color="black", weight=3]; 130.57/78.22 45798[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpInt (Pos Zero) (Pos (Succ (Succ zzz4995))) == LT)",fontsize=16,color="black",shape="box"];45798 -> 45987[label="",style="solid", color="black", weight=3]; 130.57/78.22 46988[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpInt (Pos (Succ zzz51920)) (Pos (Succ Zero)) == LT)",fontsize=16,color="black",shape="box"];46988 -> 47064[label="",style="solid", color="black", weight=3]; 130.57/78.22 46989[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpInt (Pos Zero) (Pos (Succ Zero)) == LT)",fontsize=16,color="black",shape="box"];46989 -> 47065[label="",style="solid", color="black", weight=3]; 130.57/78.22 59312[label="zzz61330",fontsize=16,color="green",shape="box"];59313[label="zzz61320",fontsize=16,color="green",shape="box"];59314[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (Neg zzz6130) zzz6131 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 False",fontsize=16,color="black",shape="triangle"];59314 -> 59383[label="",style="solid", color="black", weight=3]; 130.57/78.22 59315[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (Neg zzz6130) zzz6131 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 True",fontsize=16,color="black",shape="box"];59315 -> 59384[label="",style="solid", color="black", weight=3]; 130.57/78.22 59316 -> 59314[label="",style="dashed", color="red", weight=0]; 130.57/78.22 59316[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (Neg zzz6130) zzz6131 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 False",fontsize=16,color="magenta"];47211[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpInt (Neg (Succ zzz52440)) (FiniteMap.sizeFM (FiniteMap.Branch zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134)) == LT)",fontsize=16,color="black",shape="box"];47211 -> 47421[label="",style="solid", color="black", weight=3]; 130.57/78.22 47212[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134)) == LT)",fontsize=16,color="black",shape="box"];47212 -> 47422[label="",style="solid", color="black", weight=3]; 130.57/78.22 48554[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpInt (Neg (Succ zzz53860)) (FiniteMap.sizeFM (FiniteMap.Branch zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250)) == LT)",fontsize=16,color="black",shape="box"];48554 -> 48609[label="",style="solid", color="black", weight=3]; 130.57/78.22 48555[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250)) == LT)",fontsize=16,color="black",shape="box"];48555 -> 48610[label="",style="solid", color="black", weight=3]; 130.57/78.22 40725[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ (Succ zzz5232000))) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ (Succ zzz5232000))) zzz5233 zzz5234 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)) (Succ zzz5232000) == LT)",fontsize=16,color="black",shape="box"];40725 -> 41152[label="",style="solid", color="black", weight=3]; 130.57/78.22 40726[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)) Zero == LT)",fontsize=16,color="black",shape="box"];40726 -> 41153[label="",style="solid", color="black", weight=3]; 130.57/78.22 40727[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 False",fontsize=16,color="black",shape="box"];40727 -> 41154[label="",style="solid", color="black", weight=3]; 130.57/78.22 40728[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];40728 -> 41155[label="",style="solid", color="black", weight=3]; 130.57/78.22 40729[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];40729 -> 41156[label="",style="solid", color="black", weight=3]; 130.57/78.22 40731[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];40731 -> 41158[label="",style="solid", color="black", weight=3]; 130.57/78.22 63310[label="zzz5230",fontsize=16,color="green",shape="box"];63311[label="zzz5234",fontsize=16,color="green",shape="box"];63312 -> 7670[label="",style="dashed", color="red", weight=0]; 130.57/78.22 63312[label="FiniteMap.mkVBalBranch (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334) zzz5233",fontsize=16,color="magenta"];63312 -> 63539[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63312 -> 63540[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63313[label="zzz5231",fontsize=16,color="green",shape="box"];40736[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ zzz5232000))) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ zzz5232000))) zzz5233 zzz5234 (primCmpNat (Succ zzz5232000) (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)) == LT)",fontsize=16,color="black",shape="box"];40736 -> 41161[label="",style="solid", color="black", weight=3]; 130.57/78.22 40737[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ Zero)) zzz5233 zzz5234 (primCmpNat Zero (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200)) == LT)",fontsize=16,color="black",shape="box"];40737 -> 41162[label="",style="solid", color="black", weight=3]; 130.57/78.22 40738[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 True",fontsize=16,color="black",shape="box"];40738 -> 41163[label="",style="solid", color="black", weight=3]; 130.57/78.22 40739[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];40739 -> 41164[label="",style="solid", color="black", weight=3]; 130.57/78.22 44347[label="zzz523200",fontsize=16,color="green",shape="box"];40741[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];40741 -> 41166[label="",style="solid", color="black", weight=3]; 130.57/78.22 37575[label="Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (Succ zzz6200000)) (Succ (Succ zzz6200000)))) (Succ zzz6200000)))",fontsize=16,color="green",shape="box"];37575 -> 38193[label="",style="dashed", color="green", weight=3]; 130.57/78.22 37576[label="Succ (Succ (primPlusNat (Succ (primPlusNat zzz3752 (Succ (Succ zzz37530)))) zzz37530))",fontsize=16,color="green",shape="box"];37576 -> 38194[label="",style="dashed", color="green", weight=3]; 130.57/78.22 37577[label="Succ (Succ (primPlusNat zzz3752 (Succ Zero)))",fontsize=16,color="green",shape="box"];37577 -> 38195[label="",style="dashed", color="green", weight=3]; 130.57/78.22 37578[label="primPlusNat (primPlusNat (Succ (Succ Zero)) (Succ (Succ Zero))) (Succ Zero)",fontsize=16,color="black",shape="box"];37578 -> 38196[label="",style="solid", color="black", weight=3]; 130.57/78.22 42593[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710))) (FiniteMap.mkVBalBranch3Size_l zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710) == LT)",fontsize=16,color="black",shape="box"];42593 -> 42869[label="",style="solid", color="black", weight=3]; 130.57/78.22 40747[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos (Succ zzz3882))) (FiniteMap.mkVBalBranch3Size_l zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884) == LT)",fontsize=16,color="black",shape="box"];40747 -> 41172[label="",style="solid", color="black", weight=3]; 130.57/78.22 43241 -> 43224[label="",style="dashed", color="red", weight=0]; 130.57/78.22 43241[label="primPlusNat (primMulNat (Succ (Succ Zero)) (Succ (Succ (Succ Zero)))) (Succ (Succ (Succ Zero)))",fontsize=16,color="magenta"];43241 -> 43262[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43238[label="primPlusNat (Succ zzz48250) (Succ (Succ (Succ Zero)))",fontsize=16,color="black",shape="box"];43238 -> 43246[label="",style="solid", color="black", weight=3]; 130.57/78.22 43239[label="primPlusNat Zero (Succ (Succ (Succ Zero)))",fontsize=16,color="black",shape="box"];43239 -> 43247[label="",style="solid", color="black", weight=3]; 130.57/78.22 43243 -> 40784[label="",style="dashed", color="red", weight=0]; 130.57/78.22 43243[label="primPlusNat zzz48110 (Succ (Succ Zero))",fontsize=16,color="magenta"];43243 -> 43266[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43242[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (Pos (Succ (Succ zzz4827))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="triangle"];43242 -> 43267[label="",style="solid", color="black", weight=3]; 130.57/78.22 43244[label="Succ Zero",fontsize=16,color="green",shape="box"];41425 -> 40784[label="",style="dashed", color="red", weight=0]; 130.57/78.22 41425[label="primPlusNat (primMulNat (Succ (Succ Zero)) (Succ (Succ Zero))) (Succ (Succ Zero))",fontsize=16,color="magenta"];41425 -> 41447[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41344 -> 38195[label="",style="dashed", color="red", weight=0]; 130.57/78.22 41344[label="primPlusNat zzz37520 (Succ Zero)",fontsize=16,color="magenta"];41344 -> 41428[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 40750[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];40750 -> 41175[label="",style="solid", color="black", weight=3]; 130.57/78.22 44437 -> 43358[label="",style="dashed", color="red", weight=0]; 130.57/78.22 44437[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ (Succ (Succ (Succ Zero))))",fontsize=16,color="magenta"];44437 -> 44461[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44436[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpInt (Pos zzz4963) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344) == LT)",fontsize=16,color="burlywood",shape="triangle"];65650[label="zzz4963/Succ zzz49630",fontsize=10,color="white",style="solid",shape="box"];44436 -> 65650[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65650 -> 44462[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65651[label="zzz4963/Zero",fontsize=10,color="white",style="solid",shape="box"];44436 -> 65651[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65651 -> 44463[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 43225 -> 43166[label="",style="dashed", color="red", weight=0]; 130.57/78.22 43225[label="primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ (Succ (Succ Zero)))",fontsize=16,color="magenta"];43181[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (Pos (Succ zzz48090)) (Pos (Succ Zero)) == LT)",fontsize=16,color="black",shape="box"];43181 -> 43268[label="",style="solid", color="black", weight=3]; 130.57/78.22 43182[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (Pos Zero) (Pos (Succ Zero)) == LT)",fontsize=16,color="black",shape="box"];43182 -> 43269[label="",style="solid", color="black", weight=3]; 130.57/78.22 40652 -> 38195[label="",style="dashed", color="red", weight=0]; 130.57/78.22 40652[label="primPlusNat (primMulNat Zero (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];40652 -> 41125[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 58009[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (Pos zzz6030) zzz6031 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 otherwise",fontsize=16,color="black",shape="box"];58009 -> 58020[label="",style="solid", color="black", weight=3]; 130.57/78.22 58010 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.22 58010[label="FiniteMap.mkBalBranch zzz6020 zzz6021 zzz6023 (FiniteMap.mkVBalBranch (Pos zzz6030) zzz6031 zzz6024 (FiniteMap.Branch zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029))",fontsize=16,color="magenta"];58010 -> 63314[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 58010 -> 63315[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 58010 -> 63316[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 58010 -> 63317[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 40759[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ zzz250200)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344 (LT == LT)",fontsize=16,color="black",shape="box"];40759 -> 41184[label="",style="solid", color="black", weight=3]; 130.57/78.22 47059[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121)) (FiniteMap.mkVBalBranch3Size_l zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121) == LT)",fontsize=16,color="black",shape="box"];47059 -> 47118[label="",style="solid", color="black", weight=3]; 130.57/78.22 40778[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111) (FiniteMap.mkVBalBranch3Size_l zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111) == LT)",fontsize=16,color="black",shape="box"];40778 -> 41191[label="",style="solid", color="black", weight=3]; 130.57/78.22 40779[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (Pos zzz3748) zzz3749 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747)) (FiniteMap.mkVBalBranch3Size_l zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747) == LT)",fontsize=16,color="black",shape="box"];40779 -> 41192[label="",style="solid", color="black", weight=3]; 130.57/78.22 40780[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];40780 -> 41193[label="",style="solid", color="black", weight=3]; 130.57/78.22 64401[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Pos zzz64540) (Pos (Succ (Succ Zero)) * zzz6455) == LT)",fontsize=16,color="burlywood",shape="box"];65652[label="zzz64540/Succ zzz645400",fontsize=10,color="white",style="solid",shape="box"];64401 -> 65652[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65652 -> 64407[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65653[label="zzz64540/Zero",fontsize=10,color="white",style="solid",shape="box"];64401 -> 65653[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65653 -> 64408[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 64402[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Neg zzz64540) (Pos (Succ (Succ Zero)) * zzz6455) == LT)",fontsize=16,color="burlywood",shape="box"];65654[label="zzz64540/Succ zzz645400",fontsize=10,color="white",style="solid",shape="box"];64402 -> 65654[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65654 -> 64409[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65655[label="zzz64540/Zero",fontsize=10,color="white",style="solid",shape="box"];64402 -> 65655[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65655 -> 64410[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 64403[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos (Succ zzz645200)) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz6453) == GT)",fontsize=16,color="burlywood",shape="box"];65656[label="zzz6453/Pos zzz64530",fontsize=10,color="white",style="solid",shape="box"];64403 -> 65656[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65656 -> 64411[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65657[label="zzz6453/Neg zzz64530",fontsize=10,color="white",style="solid",shape="box"];64403 -> 65657[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65657 -> 64412[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 64404[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz6453) == GT)",fontsize=16,color="burlywood",shape="box"];65658[label="zzz6453/Pos zzz64530",fontsize=10,color="white",style="solid",shape="box"];64404 -> 65658[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65658 -> 64413[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65659[label="zzz6453/Neg zzz64530",fontsize=10,color="white",style="solid",shape="box"];64404 -> 65659[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65659 -> 64414[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 64405[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg (Succ zzz645200)) (primMulInt (Pos (Succ (Succ 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color="burlywood", weight=9]; 130.57/78.22 65662 -> 64417[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65663[label="zzz6453/Neg zzz64530",fontsize=10,color="white",style="solid",shape="box"];64406 -> 65663[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65663 -> 64418[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 50898[label="Zero",fontsize=16,color="green",shape="box"];40878[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (primCmpNat Zero (Succ zzz33200) == LT)",fontsize=16,color="black",shape="box"];40878 -> 41296[label="",style="solid", color="black", weight=3]; 130.57/78.22 40880[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264 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58946[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45986 -> 58947[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45986 -> 58948[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45986 -> 58949[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45986 -> 58950[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45986 -> 58951[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45986 -> 58952[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45986 -> 58953[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45986 -> 58954[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45986 -> 58955[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45986 -> 58956[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45986 -> 58957[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45986 -> 58958[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45986 -> 58959[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45987 -> 58875[label="",style="dashed", color="red", weight=0]; 130.57/78.22 45987[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (Neg zzz5003) zzz5004 zzz4993 zzz4994 (Pos (Succ (Succ zzz4995))) zzz4996 zzz4997 zzz4998 zzz4999 (Pos (Succ zzz5000)) zzz5001 zzz5002 (primCmpNat Zero (Succ (Succ zzz4995)) == LT)",fontsize=16,color="magenta"];45987 -> 58960[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45987 -> 58961[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45987 -> 58962[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45987 -> 58963[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45987 -> 58964[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45987 -> 58965[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45987 -> 58966[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45987 -> 58967[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45987 -> 58968[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45987 -> 58969[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45987 -> 58970[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45987 -> 58971[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45987 -> 58972[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45987 -> 58973[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47064 -> 58875[label="",style="dashed", color="red", weight=0]; 130.57/78.22 47064[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpNat (Succ zzz51920) (Succ Zero) == LT)",fontsize=16,color="magenta"];47064 -> 58974[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47064 -> 58975[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47064 -> 58976[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47064 -> 58977[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47064 -> 58978[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47064 -> 58979[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47064 -> 58980[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47064 -> 58981[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47064 -> 58982[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47064 -> 58983[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47064 -> 58984[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47064 -> 58985[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47064 -> 58986[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47064 -> 58987[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47065 -> 58875[label="",style="dashed", color="red", weight=0]; 130.57/78.22 47065[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (Neg zzz5099) zzz5100 zzz5090 zzz5091 (Pos (Succ Zero)) zzz5092 zzz5093 zzz5094 zzz5095 (Pos (Succ zzz5096)) zzz5097 zzz5098 (primCmpNat Zero (Succ Zero) == LT)",fontsize=16,color="magenta"];47065 -> 58988[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47065 -> 58989[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47065 -> 58990[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47065 -> 58991[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47065 -> 58992[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47065 -> 58993[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47065 -> 58994[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47065 -> 58995[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47065 -> 58996[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47065 -> 58997[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47065 -> 58998[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47065 -> 58999[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47065 -> 59000[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47065 -> 59001[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 59383[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 (Neg zzz6130) zzz6131 zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124 zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129 otherwise",fontsize=16,color="black",shape="box"];59383 -> 59463[label="",style="solid", color="black", weight=3]; 130.57/78.22 59384 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.22 59384[label="FiniteMap.mkBalBranch zzz6120 zzz6121 zzz6123 (FiniteMap.mkVBalBranch (Neg zzz6130) zzz6131 zzz6124 (FiniteMap.Branch zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129))",fontsize=16,color="magenta"];59384 -> 63318[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 59384 -> 63319[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 59384 -> 63320[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 59384 -> 63321[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47421[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpInt (Neg (Succ zzz52440)) (Neg (Succ (Succ zzz5132))) == LT)",fontsize=16,color="black",shape="box"];47421 -> 47569[label="",style="solid", color="black", weight=3]; 130.57/78.22 47422[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpInt (Neg Zero) (Neg (Succ (Succ zzz5132))) == LT)",fontsize=16,color="black",shape="box"];47422 -> 47570[label="",style="solid", color="black", weight=3]; 130.57/78.22 48609[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpInt (Neg (Succ zzz53860)) (Neg (Succ Zero)) == LT)",fontsize=16,color="black",shape="box"];48609 -> 48720[label="",style="solid", color="black", weight=3]; 130.57/78.22 48610[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpInt (Neg Zero) (Neg (Succ Zero)) == LT)",fontsize=16,color="black",shape="box"];48610 -> 48721[label="",style="solid", color="black", weight=3]; 130.57/78.22 41152[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ (Succ zzz5232000))) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ (Succ zzz5232000))) zzz5233 zzz5234 (primCmpNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200) zzz5232000 == LT)",fontsize=16,color="burlywood",shape="box"];65664[label="zzz33200/Succ zzz332000",fontsize=10,color="white",style="solid",shape="box"];41152 -> 65664[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65664 -> 41672[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65665[label="zzz33200/Zero",fontsize=10,color="white",style="solid",shape="box"];41152 -> 65665[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65665 -> 41673[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 41153[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (GT == LT)",fontsize=16,color="black",shape="box"];41153 -> 41674[label="",style="solid", color="black", weight=3]; 130.57/78.22 41154[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 < FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];41154 -> 41675[label="",style="solid", color="black", weight=3]; 130.57/78.22 41155[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];41155 -> 41676[label="",style="solid", color="black", weight=3]; 130.57/78.22 41156[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (EQ == LT)",fontsize=16,color="black",shape="box"];41156 -> 41677[label="",style="solid", color="black", weight=3]; 130.57/78.22 41158[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (EQ == LT)",fontsize=16,color="black",shape="box"];41158 -> 41679[label="",style="solid", color="black", weight=3]; 130.57/78.22 63539[label="Neg (Succ zzz33200)",fontsize=16,color="green",shape="box"];63540[label="zzz5233",fontsize=16,color="green",shape="box"];41161[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ zzz5232000))) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ zzz5232000))) zzz5233 zzz5234 (primCmpNat zzz5232000 (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200) == LT)",fontsize=16,color="burlywood",shape="box"];65666[label="zzz5232000/Succ zzz52320000",fontsize=10,color="white",style="solid",shape="box"];41161 -> 65666[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65666 -> 41680[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65667[label="zzz5232000/Zero",fontsize=10,color="white",style="solid",shape="box"];41161 -> 65667[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65667 -> 41681[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 41162[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ Zero)) zzz5233 zzz5234 (LT == LT)",fontsize=16,color="black",shape="box"];41162 -> 41682[label="",style="solid", color="black", weight=3]; 130.57/78.22 41163 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.22 41163[label="FiniteMap.mkBalBranch zzz5230 zzz5231 (FiniteMap.mkVBalBranch (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334) zzz5233) zzz5234",fontsize=16,color="magenta"];41163 -> 63322[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41163 -> 63323[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41163 -> 63324[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41163 -> 63325[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41164[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (EQ == LT)",fontsize=16,color="black",shape="box"];41164 -> 41687[label="",style="solid", color="black", weight=3]; 130.57/78.22 41166[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (EQ == LT)",fontsize=16,color="black",shape="box"];41166 -> 41689[label="",style="solid", color="black", weight=3]; 130.57/78.22 38193[label="primPlusNat (Succ (primPlusNat (Succ (Succ zzz6200000)) (Succ (Succ zzz6200000)))) (Succ zzz6200000)",fontsize=16,color="black",shape="box"];38193 -> 38739[label="",style="solid", color="black", weight=3]; 130.57/78.22 38194[label="primPlusNat (Succ (primPlusNat zzz3752 (Succ (Succ zzz37530)))) zzz37530",fontsize=16,color="burlywood",shape="box"];65668[label="zzz37530/Succ zzz375300",fontsize=10,color="white",style="solid",shape="box"];38194 -> 65668[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65668 -> 38740[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65669[label="zzz37530/Zero",fontsize=10,color="white",style="solid",shape="box"];38194 -> 65669[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65669 -> 38741[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 38196 -> 38195[label="",style="dashed", color="red", weight=0]; 130.57/78.22 38196[label="primPlusNat (Succ (Succ (primPlusNat (Succ Zero) (Succ Zero)))) (Succ Zero)",fontsize=16,color="magenta"];38196 -> 38744[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 42869[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos (Succ zzz4708))) (FiniteMap.mkVBalBranch3Size_l zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710) == LT)",fontsize=16,color="black",shape="box"];42869 -> 42925[label="",style="solid", color="black", weight=3]; 130.57/78.22 41172 -> 44374[label="",style="dashed", color="red", weight=0]; 130.57/78.22 41172[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz3882))) (FiniteMap.mkVBalBranch3Size_l zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884) == LT)",fontsize=16,color="magenta"];41172 -> 44375[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43262[label="primMulNat (Succ (Succ Zero)) (Succ (Succ (Succ Zero)))",fontsize=16,color="black",shape="box"];43262 -> 43348[label="",style="solid", color="black", weight=3]; 130.57/78.22 43246[label="Succ (Succ (primPlusNat zzz48250 (Succ (Succ Zero))))",fontsize=16,color="green",shape="box"];43246 -> 43258[label="",style="dashed", color="green", weight=3]; 130.57/78.22 43247[label="Succ (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];43266[label="zzz48110",fontsize=16,color="green",shape="box"];43267[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (Pos (Succ (Succ zzz4827))) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];43267 -> 43352[label="",style="solid", color="black", weight=3]; 130.57/78.22 41447[label="primMulNat (Succ (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];41447 -> 41465[label="",style="solid", color="black", weight=3]; 130.57/78.22 41428[label="zzz37520",fontsize=16,color="green",shape="box"];41175[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos (Succ (Succ (Succ (Succ (Succ Zero))))))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];41175 -> 41809[label="",style="solid", color="black", weight=3]; 130.57/78.22 44461[label="Succ (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];44462[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpInt (Pos (Succ zzz49630)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];44462 -> 44533[label="",style="solid", color="black", weight=3]; 130.57/78.22 44463[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];44463 -> 44534[label="",style="solid", color="black", weight=3]; 130.57/78.22 43268 -> 57269[label="",style="dashed", color="red", weight=0]; 130.57/78.22 43268[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpNat (Succ zzz48090) (Succ Zero) == LT)",fontsize=16,color="magenta"];43268 -> 57396[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43268 -> 57397[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43268 -> 57398[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43268 -> 57399[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43268 -> 57400[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43268 -> 57401[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43268 -> 57402[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43268 -> 57403[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43268 -> 57404[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43268 -> 57405[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43268 -> 57406[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43268 -> 57407[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43268 -> 57408[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43268 -> 57409[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43269 -> 57269[label="",style="dashed", color="red", weight=0]; 130.57/78.22 43269[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpNat Zero (Succ Zero) == LT)",fontsize=16,color="magenta"];43269 -> 57410[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43269 -> 57411[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43269 -> 57412[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43269 -> 57413[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43269 -> 57414[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43269 -> 57415[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43269 -> 57416[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43269 -> 57417[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43269 -> 57418[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43269 -> 57419[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43269 -> 57420[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43269 -> 57421[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43269 -> 57422[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43269 -> 57423[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41125[label="primMulNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];41125 -> 41656[label="",style="solid", color="black", weight=3]; 130.57/78.22 58020[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 (Pos zzz6030) zzz6031 zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024 zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029 True",fontsize=16,color="black",shape="box"];58020 -> 58049[label="",style="solid", color="black", weight=3]; 130.57/78.22 63314[label="zzz6020",fontsize=16,color="green",shape="box"];63315 -> 4125[label="",style="dashed", color="red", weight=0]; 130.57/78.22 63315[label="FiniteMap.mkVBalBranch (Pos zzz6030) zzz6031 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47118[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121))) (FiniteMap.mkVBalBranch3Size_l zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121) == LT)",fontsize=16,color="black",shape="box"];47118 -> 47167[label="",style="solid", color="black", weight=3]; 130.57/78.22 41191[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111)) (FiniteMap.mkVBalBranch3Size_l zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111) == LT)",fontsize=16,color="black",shape="box"];41191 -> 41922[label="",style="solid", color="black", weight=3]; 130.57/78.22 41192[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (Pos zzz3748) zzz3749 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747))) (FiniteMap.mkVBalBranch3Size_l zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747) == LT)",fontsize=16,color="black",shape="box"];41192 -> 41923[label="",style="solid", color="black", weight=3]; 130.57/78.22 41193[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg (Succ (Succ (Succ (Succ (Succ Zero))))))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];41193 -> 41924[label="",style="solid", color="black", weight=3]; 130.57/78.22 64407[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Pos (Succ zzz645400)) (Pos (Succ (Succ Zero)) * zzz6455) == LT)",fontsize=16,color="black",shape="box"];64407 -> 64419[label="",style="solid", color="black", weight=3]; 130.57/78.22 64408[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Pos Zero) (Pos (Succ (Succ Zero)) * zzz6455) == LT)",fontsize=16,color="black",shape="box"];64408 -> 64420[label="",style="solid", color="black", weight=3]; 130.57/78.22 64409[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Neg (Succ zzz645400)) (Pos (Succ (Succ Zero)) * zzz6455) == LT)",fontsize=16,color="black",shape="box"];64409 -> 64421[label="",style="solid", color="black", weight=3]; 130.57/78.22 64410[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Neg Zero) (Pos (Succ (Succ Zero)) * zzz6455) == LT)",fontsize=16,color="black",shape="box"];64410 -> 64422[label="",style="solid", color="black", weight=3]; 130.57/78.22 64411[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos (Succ zzz645200)) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos zzz64530)) == GT)",fontsize=16,color="black",shape="box"];64411 -> 64423[label="",style="solid", color="black", weight=3]; 130.57/78.22 64412[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos (Succ zzz645200)) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg zzz64530)) == GT)",fontsize=16,color="black",shape="box"];64412 -> 64424[label="",style="solid", color="black", weight=3]; 130.57/78.22 64413[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos zzz64530)) == GT)",fontsize=16,color="black",shape="box"];64413 -> 64425[label="",style="solid", color="black", weight=3]; 130.57/78.22 64414[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg zzz64530)) == GT)",fontsize=16,color="black",shape="box"];64414 -> 64426[label="",style="solid", color="black", weight=3]; 130.57/78.22 64415[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg (Succ zzz645200)) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos zzz64530)) == GT)",fontsize=16,color="black",shape="box"];64415 -> 64427[label="",style="solid", color="black", weight=3]; 130.57/78.22 64416[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg (Succ zzz645200)) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg zzz64530)) == GT)",fontsize=16,color="black",shape="box"];64416 -> 64428[label="",style="solid", color="black", weight=3]; 130.57/78.22 64417[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos zzz64530)) == GT)",fontsize=16,color="black",shape="box"];64417 -> 64429[label="",style="solid", color="black", weight=3]; 130.57/78.22 64418[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg zzz64530)) == GT)",fontsize=16,color="black",shape="box"];64418 -> 64430[label="",style="solid", color="black", weight=3]; 130.57/78.22 41296[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (LT == LT)",fontsize=16,color="black",shape="box"];41296 -> 42308[label="",style="solid", color="black", weight=3]; 130.57/78.22 41298 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.22 41298[label="FiniteMap.mkBalBranch zzz330 zzz331 zzz333 (FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 zzz334 (FiniteMap.Branch zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264))",fontsize=16,color="magenta"];41298 -> 63326[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41298 -> 63327[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41298 -> 63328[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41298 -> 63329[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 58946[label="Succ (Succ zzz4995)",fontsize=16,color="green",shape="box"];58947[label="zzz4996",fontsize=16,color="green",shape="box"];58948[label="zzz4999",fontsize=16,color="green",shape="box"];58949[label="zzz5002",fontsize=16,color="green",shape="box"];58950[label="Succ zzz4995",fontsize=16,color="green",shape="box"];58951[label="zzz4998",fontsize=16,color="green",shape="box"];58952[label="zzz4993",fontsize=16,color="green",shape="box"];58953[label="zzz5004",fontsize=16,color="green",shape="box"];58954[label="Succ zzz51030",fontsize=16,color="green",shape="box"];58955[label="zzz5003",fontsize=16,color="green",shape="box"];58956[label="zzz5001",fontsize=16,color="green",shape="box"];58957[label="zzz4994",fontsize=16,color="green",shape="box"];58958[label="zzz4997",fontsize=16,color="green",shape="box"];58959[label="zzz5000",fontsize=16,color="green",shape="box"];58960[label="Succ (Succ 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63546[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 63320[label="zzz6123",fontsize=16,color="green",shape="box"];63321[label="zzz6121",fontsize=16,color="green",shape="box"];47569 -> 61744[label="",style="dashed", color="red", weight=0]; 130.57/78.22 47569[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpNat (Succ (Succ zzz5132)) (Succ zzz52440) == LT)",fontsize=16,color="magenta"];47569 -> 61745[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47569 -> 61746[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47569 -> 61747[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47569 -> 61748[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47569 -> 61749[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47569 -> 61750[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47569 -> 61751[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47569 -> 61752[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47569 -> 61753[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47569 -> 61754[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47569 -> 61755[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47569 -> 61756[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47569 -> 61757[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47569 -> 61758[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47570 -> 61744[label="",style="dashed", color="red", weight=0]; 130.57/78.22 47570[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (Neg zzz5140) zzz5141 zzz5130 zzz5131 (Neg (Succ (Succ zzz5132))) zzz5133 zzz5134 zzz5135 zzz5136 (Neg (Succ zzz5137)) zzz5138 zzz5139 (primCmpNat (Succ (Succ zzz5132)) Zero == LT)",fontsize=16,color="magenta"];47570 -> 61759[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47570 -> 61760[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47570 -> 61761[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47570 -> 61762[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47570 -> 61763[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47570 -> 61764[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47570 -> 61765[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47570 -> 61766[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47570 -> 61767[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47570 -> 61768[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47570 -> 61769[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47570 -> 61770[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47570 -> 61771[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47570 -> 61772[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48720 -> 61744[label="",style="dashed", color="red", weight=0]; 130.57/78.22 48720[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpNat (Succ Zero) (Succ zzz53860) == LT)",fontsize=16,color="magenta"];48720 -> 61773[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48720 -> 61774[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48720 -> 61775[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48720 -> 61776[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48720 -> 61777[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48720 -> 61778[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48720 -> 61779[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48720 -> 61780[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48720 -> 61781[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48720 -> 61782[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48720 -> 61783[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48720 -> 61784[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48720 -> 61785[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48720 -> 61786[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48721 -> 61744[label="",style="dashed", color="red", weight=0]; 130.57/78.22 48721[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (Neg zzz5256) zzz5257 zzz5247 zzz5248 (Neg (Succ Zero)) zzz5249 zzz5250 zzz5251 zzz5252 (Neg (Succ zzz5253)) zzz5254 zzz5255 (primCmpNat (Succ Zero) Zero == LT)",fontsize=16,color="magenta"];48721 -> 61787[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48721 -> 61788[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48721 -> 61789[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48721 -> 61790[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48721 -> 61791[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48721 -> 61792[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48721 -> 61793[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48721 -> 61794[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48721 -> 61795[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48721 -> 61796[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48721 -> 61797[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48721 -> 61798[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48721 -> 61799[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 48721 -> 61800[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41672[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ (Succ zzz332000))) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ (Succ zzz5232000))) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ (Succ zzz332000))) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ (Succ zzz5232000))) zzz5233 zzz5234 (primCmpNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) zzz5232000 == LT)",fontsize=16,color="black",shape="box"];41672 -> 43055[label="",style="solid", color="black", weight=3]; 130.57/78.22 41673[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ Zero)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ (Succ zzz5232000))) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ Zero)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ (Succ zzz5232000))) zzz5233 zzz5234 (primCmpNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) Zero) zzz5232000 == LT)",fontsize=16,color="black",shape="box"];41673 -> 43056[label="",style="solid", color="black", weight=3]; 130.57/78.22 41674[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 False",fontsize=16,color="black",shape="box"];41674 -> 43057[label="",style="solid", color="black", weight=3]; 130.57/78.22 41675[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];41675 -> 43058[label="",style="solid", color="black", weight=3]; 130.57/78.22 41676[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];41676 -> 43059[label="",style="solid", color="black", weight=3]; 130.57/78.22 41677[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 False",fontsize=16,color="black",shape="box"];41677 -> 43060[label="",style="solid", color="black", weight=3]; 130.57/78.22 41679[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 False",fontsize=16,color="black",shape="box"];41679 -> 43062[label="",style="solid", color="black", weight=3]; 130.57/78.22 41680[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ (Succ zzz52320000)))) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ (Succ zzz52320000)))) zzz5233 zzz5234 (primCmpNat (Succ zzz52320000) (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200) == LT)",fontsize=16,color="burlywood",shape="box"];65672[label="zzz33200/Succ zzz332000",fontsize=10,color="white",style="solid",shape="box"];41680 -> 65672[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65672 -> 43063[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65673[label="zzz33200/Zero",fontsize=10,color="white",style="solid",shape="box"];41680 -> 65673[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65673 -> 43064[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 41681[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ Zero))) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ Zero))) zzz5233 zzz5234 (primCmpNat Zero (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat zzz33200 zzz33200)) zzz33200)) zzz33200)) zzz33200) == LT)",fontsize=16,color="burlywood",shape="box"];65674[label="zzz33200/Succ zzz332000",fontsize=10,color="white",style="solid",shape="box"];41681 -> 65674[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65674 -> 43065[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65675[label="zzz33200/Zero",fontsize=10,color="white",style="solid",shape="box"];41681 -> 65675[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65675 -> 43066[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 41682[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ Zero)) zzz5233 zzz5234 True",fontsize=16,color="black",shape="box"];41682 -> 43067[label="",style="solid", color="black", weight=3]; 130.57/78.22 63322[label="zzz5230",fontsize=16,color="green",shape="box"];63323[label="zzz5234",fontsize=16,color="green",shape="box"];63324 -> 7670[label="",style="dashed", color="red", weight=0]; 130.57/78.22 63324[label="FiniteMap.mkVBalBranch (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334) zzz5233",fontsize=16,color="magenta"];63324 -> 63547[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63324 -> 63548[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63325[label="zzz5231",fontsize=16,color="green",shape="box"];41687[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 False",fontsize=16,color="black",shape="box"];41687 -> 43070[label="",style="solid", color="black", weight=3]; 130.57/78.22 41689[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 False",fontsize=16,color="black",shape="box"];41689 -> 43072[label="",style="solid", color="black", weight=3]; 130.57/78.22 38739[label="Succ (Succ (primPlusNat (primPlusNat (Succ (Succ zzz6200000)) (Succ (Succ zzz6200000))) zzz6200000))",fontsize=16,color="green",shape="box"];38739 -> 39783[label="",style="dashed", color="green", weight=3]; 130.57/78.22 38740[label="primPlusNat (Succ (primPlusNat zzz3752 (Succ (Succ (Succ zzz375300))))) (Succ zzz375300)",fontsize=16,color="black",shape="box"];38740 -> 39784[label="",style="solid", color="black", weight=3]; 130.57/78.22 38741[label="primPlusNat (Succ (primPlusNat zzz3752 (Succ (Succ Zero)))) Zero",fontsize=16,color="black",shape="box"];38741 -> 39785[label="",style="solid", color="black", weight=3]; 130.57/78.22 38744[label="Succ (Succ (primPlusNat (Succ Zero) (Succ Zero)))",fontsize=16,color="green",shape="box"];38744 -> 39786[label="",style="dashed", color="green", weight=3]; 130.57/78.22 42925 -> 44349[label="",style="dashed", color="red", weight=0]; 130.57/78.22 42925[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz4708))) (FiniteMap.mkVBalBranch3Size_l zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710) == LT)",fontsize=16,color="magenta"];42925 -> 44350[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44375 -> 43358[label="",style="dashed", color="red", weight=0]; 130.57/78.22 44375[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz3882)",fontsize=16,color="magenta"];44375 -> 44402[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44374[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpInt (Pos zzz4958) (FiniteMap.mkVBalBranch3Size_l zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884) == LT)",fontsize=16,color="burlywood",shape="triangle"];65676[label="zzz4958/Succ zzz49580",fontsize=10,color="white",style="solid",shape="box"];44374 -> 65676[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65676 -> 44403[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65677[label="zzz4958/Zero",fontsize=10,color="white",style="solid",shape="box"];44374 -> 65677[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65677 -> 44404[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 43348 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.22 43348[label="primPlusNat (primMulNat (Succ Zero) (Succ (Succ (Succ Zero)))) (Succ (Succ (Succ Zero)))",fontsize=16,color="magenta"];43348 -> 43374[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43348 -> 43375[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43258 -> 40784[label="",style="dashed", color="red", weight=0]; 130.57/78.22 43258[label="primPlusNat zzz48250 (Succ (Succ Zero))",fontsize=16,color="magenta"];43258 -> 43346[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43352[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpInt (Pos (Succ (Succ zzz4827))) (Pos (Succ (Succ zzz2502000))) == LT)",fontsize=16,color="black",shape="box"];43352 -> 43392[label="",style="solid", color="black", weight=3]; 130.57/78.22 41465 -> 40784[label="",style="dashed", color="red", weight=0]; 130.57/78.22 41465[label="primPlusNat (primMulNat (Succ Zero) (Succ (Succ Zero))) (Succ (Succ Zero))",fontsize=16,color="magenta"];41465 -> 41547[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41809 -> 44410[label="",style="dashed", color="red", weight=0]; 130.57/78.22 41809[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ (Succ (Succ (Succ (Succ Zero))))))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344) == LT)",fontsize=16,color="magenta"];41809 -> 44411[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44533[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpInt (Pos (Succ zzz49630)) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];44533 -> 44584[label="",style="solid", color="black", weight=3]; 130.57/78.22 44534[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];44534 -> 44585[label="",style="solid", color="black", weight=3]; 130.57/78.22 57396[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];57397[label="zzz2504",fontsize=16,color="green",shape="box"];57398[label="zzz343",fontsize=16,color="green",shape="box"];57399[label="zzz340",fontsize=16,color="green",shape="box"];57400[label="zzz341",fontsize=16,color="green",shape="box"];57401[label="Succ zzz48090",fontsize=16,color="green",shape="box"];57402[label="Succ Zero",fontsize=16,color="green",shape="box"];57403[label="zzz300",fontsize=16,color="green",shape="box"];57404[label="zzz2501",fontsize=16,color="green",shape="box"];57405[label="zzz344",fontsize=16,color="green",shape="box"];57406[label="Zero",fontsize=16,color="green",shape="box"];57407[label="zzz31",fontsize=16,color="green",shape="box"];57408[label="zzz2503",fontsize=16,color="green",shape="box"];57409[label="zzz2500",fontsize=16,color="green",shape="box"];57410[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];57411[label="zzz2504",fontsize=16,color="green",shape="box"];57412[label="zzz343",fontsize=16,color="green",shape="box"];57413[label="zzz340",fontsize=16,color="green",shape="box"];57414[label="zzz341",fontsize=16,color="green",shape="box"];57415[label="Zero",fontsize=16,color="green",shape="box"];57416[label="Succ Zero",fontsize=16,color="green",shape="box"];57417[label="zzz300",fontsize=16,color="green",shape="box"];57418[label="zzz2501",fontsize=16,color="green",shape="box"];57419[label="zzz344",fontsize=16,color="green",shape="box"];57420[label="Zero",fontsize=16,color="green",shape="box"];57421[label="zzz31",fontsize=16,color="green",shape="box"];57422[label="zzz2503",fontsize=16,color="green",shape="box"];57423[label="zzz2500",fontsize=16,color="green",shape="box"];41656[label="Zero",fontsize=16,color="green",shape="box"];58049 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.22 58049[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Pos zzz6030) zzz6031 (FiniteMap.Branch zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024) (FiniteMap.Branch zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029)",fontsize=16,color="magenta"];58049 -> 60593[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 58049 -> 60594[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 58049 -> 60595[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 58049 -> 60596[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 58049 -> 60597[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63541[label="zzz6024",fontsize=16,color="green",shape="box"];63542[label="zzz6030",fontsize=16,color="green",shape="box"];63543[label="FiniteMap.Branch zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029",fontsize=16,color="green",shape="box"];63544[label="zzz6031",fontsize=16,color="green",shape="box"];41841 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.22 41841[label="FiniteMap.mkBalBranch zzz2500 zzz2501 zzz2503 (FiniteMap.mkVBalBranch (Pos zzz300) zzz31 zzz2504 (FiniteMap.Branch zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344))",fontsize=16,color="magenta"];41841 -> 63330[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41841 -> 63331[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41841 -> 63332[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41841 -> 63333[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47167[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg (Succ zzz5119))) (FiniteMap.mkVBalBranch3Size_l zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121) == LT)",fontsize=16,color="black",shape="box"];47167 -> 47182[label="",style="solid", color="black", weight=3]; 130.57/78.22 41922[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111)) (FiniteMap.mkVBalBranch3Size_l zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111) == LT)",fontsize=16,color="black",shape="box"];41922 -> 43282[label="",style="solid", color="black", weight=3]; 130.57/78.22 41923[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (Pos zzz3748) zzz3749 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg (Succ zzz3745))) (FiniteMap.mkVBalBranch3Size_l zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747) == LT)",fontsize=16,color="black",shape="box"];41923 -> 43283[label="",style="solid", color="black", weight=3]; 130.57/78.22 41924 -> 44482[label="",style="dashed", color="red", weight=0]; 130.57/78.22 41924[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ (Succ (Succ (Succ (Succ Zero))))))) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Neg (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Neg (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344) == LT)",fontsize=16,color="magenta"];41924 -> 44483[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41924 -> 44484[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41924 -> 44485[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41924 -> 44486[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41924 -> 44487[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41924 -> 44488[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41924 -> 44489[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41924 -> 44490[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41924 -> 44491[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41924 -> 44492[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41924 -> 44493[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41924 -> 44494[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64419[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Pos (Succ zzz645400)) (primMulInt (Pos (Succ (Succ Zero))) zzz6455) == LT)",fontsize=16,color="burlywood",shape="box"];65678[label="zzz6455/Pos zzz64550",fontsize=10,color="white",style="solid",shape="box"];64419 -> 65678[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65678 -> 64431[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65679[label="zzz6455/Neg zzz64550",fontsize=10,color="white",style="solid",shape="box"];64419 -> 65679[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65679 -> 64432[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 64420[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Pos Zero) (primMulInt (Pos (Succ (Succ Zero))) zzz6455) == LT)",fontsize=16,color="burlywood",shape="box"];65680[label="zzz6455/Pos zzz64550",fontsize=10,color="white",style="solid",shape="box"];64420 -> 65680[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65680 -> 64433[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65681[label="zzz6455/Neg zzz64550",fontsize=10,color="white",style="solid",shape="box"];64420 -> 65681[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65681 -> 64434[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 64421[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Neg (Succ zzz645400)) (primMulInt (Pos (Succ (Succ Zero))) zzz6455) == LT)",fontsize=16,color="burlywood",shape="box"];65682[label="zzz6455/Pos zzz64550",fontsize=10,color="white",style="solid",shape="box"];64421 -> 65682[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65682 -> 64435[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65683[label="zzz6455/Neg zzz64550",fontsize=10,color="white",style="solid",shape="box"];64421 -> 65683[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65683 -> 64436[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 64422[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Neg Zero) (primMulInt (Pos (Succ (Succ Zero))) zzz6455) == LT)",fontsize=16,color="burlywood",shape="box"];65684[label="zzz6455/Pos zzz64550",fontsize=10,color="white",style="solid",shape="box"];64422 -> 65684[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65684 -> 64437[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65685[label="zzz6455/Neg zzz64550",fontsize=10,color="white",style="solid",shape="box"];64422 -> 65685[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65685 -> 64438[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 64423 -> 64439[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64423[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos (Succ zzz645200)) (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64530)) == GT)",fontsize=16,color="magenta"];64423 -> 64440[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64424 -> 64441[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64424[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos (Succ zzz645200)) (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64530)) == GT)",fontsize=16,color="magenta"];64424 -> 64442[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64425 -> 64443[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64425[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64530)) == GT)",fontsize=16,color="magenta"];64425 -> 64444[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64426 -> 64445[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64426[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64530)) == GT)",fontsize=16,color="magenta"];64426 -> 64446[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64427 -> 64447[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64427[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg (Succ zzz645200)) (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64530)) == GT)",fontsize=16,color="magenta"];64427 -> 64448[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64428 -> 64449[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64428[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg (Succ zzz645200)) (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64530)) == GT)",fontsize=16,color="magenta"];64428 -> 64450[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64429 -> 64451[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64429[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64530)) == GT)",fontsize=16,color="magenta"];64429 -> 64452[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64430 -> 64453[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64430[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64530)) == GT)",fontsize=16,color="magenta"];64430 -> 64454[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 42308[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 (Neg (Succ zzz3000)) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264 True",fontsize=16,color="black",shape="box"];42308 -> 43421[label="",style="solid", color="black", weight=3]; 130.57/78.22 63326[label="zzz330",fontsize=16,color="green",shape="box"];63327 -> 6244[label="",style="dashed", color="red", weight=0]; 130.57/78.22 63327[label="FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 zzz334 (FiniteMap.Branch zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264)",fontsize=16,color="magenta"];63327 -> 63549[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63327 -> 63550[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63328[label="zzz333",fontsize=16,color="green",shape="box"];63329[label="zzz331",fontsize=16,color="green",shape="box"];59568 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.22 59568[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Neg zzz6130) zzz6131 (FiniteMap.Branch zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124) (FiniteMap.Branch zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129)",fontsize=16,color="magenta"];59568 -> 60598[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 59568 -> 60599[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 59568 -> 60600[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 59568 -> 60601[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 59568 -> 60602[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63545[label="FiniteMap.mkVBalBranch (Neg zzz6130) zzz6131 FiniteMap.EmptyFM (FiniteMap.Branch zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129)",fontsize=16,color="black",shape="box"];63545 -> 63588[label="",style="solid", color="black", weight=3]; 130.57/78.22 63546[label="FiniteMap.mkVBalBranch (Neg zzz6130) zzz6131 (FiniteMap.Branch zzz61240 zzz61241 zzz61242 zzz61243 zzz61244) (FiniteMap.Branch zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129)",fontsize=16,color="black",shape="box"];63546 -> 63589[label="",style="solid", color="black", weight=3]; 130.57/78.22 61745[label="zzz5140",fontsize=16,color="green",shape="box"];61746[label="zzz5133",fontsize=16,color="green",shape="box"];61747[label="zzz5135",fontsize=16,color="green",shape="box"];61748[label="zzz5141",fontsize=16,color="green",shape="box"];61749[label="Succ zzz52440",fontsize=16,color="green",shape="box"];61750[label="Succ (Succ zzz5132)",fontsize=16,color="green",shape="box"];61751[label="zzz5138",fontsize=16,color="green",shape="box"];61752[label="zzz5136",fontsize=16,color="green",shape="box"];61753[label="zzz5137",fontsize=16,color="green",shape="box"];61754[label="zzz5130",fontsize=16,color="green",shape="box"];61755[label="zzz5134",fontsize=16,color="green",shape="box"];61756[label="Succ zzz5132",fontsize=16,color="green",shape="box"];61757[label="zzz5139",fontsize=16,color="green",shape="box"];61758[label="zzz5131",fontsize=16,color="green",shape="box"];61744[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (Neg zzz6304) zzz6305 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (primCmpNat zzz6306 zzz6307 == LT)",fontsize=16,color="burlywood",shape="triangle"];65686[label="zzz6306/Succ zzz63060",fontsize=10,color="white",style="solid",shape="box"];61744 -> 65686[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65686 -> 61955[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65687[label="zzz6306/Zero",fontsize=10,color="white",style="solid",shape="box"];61744 -> 65687[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65687 -> 61956[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 61759[label="zzz5140",fontsize=16,color="green",shape="box"];61760[label="zzz5133",fontsize=16,color="green",shape="box"];61761[label="zzz5135",fontsize=16,color="green",shape="box"];61762[label="zzz5141",fontsize=16,color="green",shape="box"];61763[label="Zero",fontsize=16,color="green",shape="box"];61764[label="Succ (Succ zzz5132)",fontsize=16,color="green",shape="box"];61765[label="zzz5138",fontsize=16,color="green",shape="box"];61766[label="zzz5136",fontsize=16,color="green",shape="box"];61767[label="zzz5137",fontsize=16,color="green",shape="box"];61768[label="zzz5130",fontsize=16,color="green",shape="box"];61769[label="zzz5134",fontsize=16,color="green",shape="box"];61770[label="Succ zzz5132",fontsize=16,color="green",shape="box"];61771[label="zzz5139",fontsize=16,color="green",shape="box"];61772[label="zzz5131",fontsize=16,color="green",shape="box"];61773[label="zzz5256",fontsize=16,color="green",shape="box"];61774[label="zzz5249",fontsize=16,color="green",shape="box"];61775[label="zzz5251",fontsize=16,color="green",shape="box"];61776[label="zzz5257",fontsize=16,color="green",shape="box"];61777[label="Succ zzz53860",fontsize=16,color="green",shape="box"];61778[label="Succ Zero",fontsize=16,color="green",shape="box"];61779[label="zzz5254",fontsize=16,color="green",shape="box"];61780[label="zzz5252",fontsize=16,color="green",shape="box"];61781[label="zzz5253",fontsize=16,color="green",shape="box"];61782[label="zzz5247",fontsize=16,color="green",shape="box"];61783[label="zzz5250",fontsize=16,color="green",shape="box"];61784[label="Zero",fontsize=16,color="green",shape="box"];61785[label="zzz5255",fontsize=16,color="green",shape="box"];61786[label="zzz5248",fontsize=16,color="green",shape="box"];61787[label="zzz5256",fontsize=16,color="green",shape="box"];61788[label="zzz5249",fontsize=16,color="green",shape="box"];61789[label="zzz5251",fontsize=16,color="green",shape="box"];61790[label="zzz5257",fontsize=16,color="green",shape="box"];61791[label="Zero",fontsize=16,color="green",shape="box"];61792[label="Succ Zero",fontsize=16,color="green",shape="box"];61793[label="zzz5254",fontsize=16,color="green",shape="box"];61794[label="zzz5252",fontsize=16,color="green",shape="box"];61795[label="zzz5253",fontsize=16,color="green",shape="box"];61796[label="zzz5247",fontsize=16,color="green",shape="box"];61797[label="zzz5250",fontsize=16,color="green",shape="box"];61798[label="Zero",fontsize=16,color="green",shape="box"];61799[label="zzz5255",fontsize=16,color="green",shape="box"];61800[label="zzz5248",fontsize=16,color="green",shape="box"];43055 -> 44629[label="",style="dashed", color="red", weight=0]; 130.57/78.22 43055[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ (Succ zzz332000))) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ (Succ zzz5232000))) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ (Succ zzz332000))) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ (Succ zzz5232000))) zzz5233 zzz5234 (primCmpNat (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) zzz332000))) zzz5232000 == LT)",fontsize=16,color="magenta"];43055 -> 44728[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43055 -> 44729[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43055 -> 44730[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43055 -> 44731[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43055 -> 44732[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43055 -> 44733[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43055 -> 44734[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43055 -> 44735[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43055 -> 44736[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43055 -> 44737[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43055 -> 44738[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43055 -> 44739[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43055 -> 44740[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43055 -> 44741[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43056 -> 45509[label="",style="dashed", color="red", weight=0]; 130.57/78.22 43056[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Pos (Succ Zero)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ (Succ zzz5232000))) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ Zero)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ (Succ zzz5232000))) zzz5233 zzz5234 (primCmpNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) zzz5232000 == LT)",fontsize=16,color="magenta"];43056 -> 45627[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43056 -> 45628[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43056 -> 45629[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43056 -> 45630[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43056 -> 45631[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43056 -> 45632[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43056 -> 45633[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43056 -> 45634[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43056 -> 45635[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43056 -> 45636[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43056 -> 45637[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43056 -> 45638[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43056 -> 45639[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43057[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 < FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];43057 -> 43851[label="",style="solid", color="black", weight=3]; 130.57/78.22 43058[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];43058 -> 43852[label="",style="solid", color="black", weight=3]; 130.57/78.22 43059[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];43059 -> 43853[label="",style="solid", color="black", weight=3]; 130.57/78.22 43060[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 otherwise",fontsize=16,color="black",shape="box"];43060 -> 43854[label="",style="solid", color="black", weight=3]; 130.57/78.22 43062[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 otherwise",fontsize=16,color="black",shape="box"];43062 -> 44093[label="",style="solid", color="black", weight=3]; 130.57/78.22 43063[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ (Succ zzz332000))) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ (Succ zzz52320000)))) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ (Succ zzz332000))) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ (Succ zzz52320000)))) zzz5233 zzz5234 (primCmpNat (Succ zzz52320000) (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) == LT)",fontsize=16,color="black",shape="box"];43063 -> 44094[label="",style="solid", color="black", weight=3]; 130.57/78.22 43064[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ Zero)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ (Succ zzz52320000)))) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ Zero)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ (Succ zzz52320000)))) zzz5233 zzz5234 (primCmpNat (Succ zzz52320000) (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) Zero) == LT)",fontsize=16,color="black",shape="box"];43064 -> 44095[label="",style="solid", color="black", weight=3]; 130.57/78.22 43065[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ (Succ zzz332000))) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ Zero))) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ (Succ zzz332000))) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ Zero))) zzz5233 zzz5234 (primCmpNat Zero (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) == LT)",fontsize=16,color="black",shape="box"];43065 -> 44096[label="",style="solid", color="black", weight=3]; 130.57/78.22 43066[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ Zero)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ Zero))) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ Zero)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ Zero))) zzz5233 zzz5234 (primCmpNat Zero (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) Zero) == LT)",fontsize=16,color="black",shape="box"];43066 -> 44097[label="",style="solid", color="black", weight=3]; 130.57/78.22 43067 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.22 43067[label="FiniteMap.mkBalBranch zzz5230 zzz5231 (FiniteMap.mkVBalBranch (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334) zzz5233) zzz5234",fontsize=16,color="magenta"];43067 -> 63334[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43067 -> 63335[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43067 -> 63336[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43067 -> 63337[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63547[label="Neg (Succ zzz33200)",fontsize=16,color="green",shape="box"];63548[label="zzz5233",fontsize=16,color="green",shape="box"];43070[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 otherwise",fontsize=16,color="black",shape="box"];43070 -> 44102[label="",style="solid", color="black", weight=3]; 130.57/78.22 43072[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 otherwise",fontsize=16,color="black",shape="box"];43072 -> 44348[label="",style="solid", color="black", weight=3]; 130.57/78.22 39783 -> 36060[label="",style="dashed", color="red", weight=0]; 130.57/78.22 39783[label="primPlusNat (primPlusNat (Succ (Succ zzz6200000)) (Succ (Succ zzz6200000))) zzz6200000",fontsize=16,color="magenta"];39783 -> 40781[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 39783 -> 40782[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 39784[label="Succ (Succ (primPlusNat (primPlusNat zzz3752 (Succ (Succ (Succ zzz375300)))) zzz375300))",fontsize=16,color="green",shape="box"];39784 -> 40783[label="",style="dashed", color="green", weight=3]; 130.57/78.22 39785[label="Succ (primPlusNat zzz3752 (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];39785 -> 40784[label="",style="dashed", color="green", weight=3]; 130.57/78.22 39786 -> 38195[label="",style="dashed", color="red", weight=0]; 130.57/78.22 39786[label="primPlusNat (Succ Zero) (Succ Zero)",fontsize=16,color="magenta"];39786 -> 40785[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44350 -> 43358[label="",style="dashed", color="red", weight=0]; 130.57/78.22 44350[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz4708)",fontsize=16,color="magenta"];44350 -> 44371[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44349[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpInt (Pos zzz4956) (FiniteMap.mkVBalBranch3Size_l zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710) == LT)",fontsize=16,color="burlywood",shape="triangle"];65688[label="zzz4956/Succ zzz49560",fontsize=10,color="white",style="solid",shape="box"];44349 -> 65688[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65688 -> 44372[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65689[label="zzz4956/Zero",fontsize=10,color="white",style="solid",shape="box"];44349 -> 65689[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65689 -> 44373[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 44402[label="zzz3882",fontsize=16,color="green",shape="box"];44403[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpInt (Pos (Succ zzz49580)) (FiniteMap.mkVBalBranch3Size_l zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884) == LT)",fontsize=16,color="black",shape="box"];44403 -> 44431[label="",style="solid", color="black", weight=3]; 130.57/78.22 44404[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884) == LT)",fontsize=16,color="black",shape="box"];44404 -> 44432[label="",style="solid", color="black", weight=3]; 130.57/78.22 43374[label="Succ (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];43375[label="primMulNat (Succ Zero) (Succ (Succ (Succ Zero)))",fontsize=16,color="black",shape="box"];43375 -> 43398[label="",style="solid", color="black", weight=3]; 130.57/78.22 43346[label="zzz48250",fontsize=16,color="green",shape="box"];43392 -> 57269[label="",style="dashed", color="red", weight=0]; 130.57/78.22 43392[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ (Succ zzz2502000))) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ Zero)))) zzz343 zzz344 (primCmpNat (Succ (Succ zzz4827)) (Succ (Succ zzz2502000)) == LT)",fontsize=16,color="magenta"];43392 -> 57452[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43392 -> 57453[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43392 -> 57454[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43392 -> 57455[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43392 -> 57456[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43392 -> 57457[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43392 -> 57458[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43392 -> 57459[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43392 -> 57460[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43392 -> 57461[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43392 -> 57462[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43392 -> 57463[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43392 -> 57464[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43392 -> 57465[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41547[label="primMulNat (Succ Zero) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];41547 -> 41572[label="",style="solid", color="black", weight=3]; 130.57/78.22 44411 -> 43358[label="",style="dashed", color="red", weight=0]; 130.57/78.22 44411[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ (Succ (Succ (Succ (Succ Zero)))))",fontsize=16,color="magenta"];44411 -> 44433[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44410[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpInt (Pos zzz4961) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344) == LT)",fontsize=16,color="burlywood",shape="triangle"];65690[label="zzz4961/Succ zzz49610",fontsize=10,color="white",style="solid",shape="box"];44410 -> 65690[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65690 -> 44434[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65691[label="zzz4961/Zero",fontsize=10,color="white",style="solid",shape="box"];44410 -> 65691[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65691 -> 44435[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 44584[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpInt (Pos (Succ zzz49630)) (Pos (Succ Zero)) == LT)",fontsize=16,color="black",shape="box"];44584 -> 44794[label="",style="solid", color="black", weight=3]; 130.57/78.22 44585[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpInt (Pos Zero) (Pos (Succ Zero)) == LT)",fontsize=16,color="black",shape="box"];44585 -> 44795[label="",style="solid", color="black", weight=3]; 130.57/78.22 60593[label="zzz6031",fontsize=16,color="green",shape="box"];60594[label="Pos zzz6030",fontsize=16,color="green",shape="box"];60595[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];60596[label="FiniteMap.Branch zzz6025 zzz6026 (Pos (Succ zzz6027)) zzz6028 zzz6029",fontsize=16,color="green",shape="box"];60597[label="FiniteMap.Branch zzz6020 zzz6021 (Pos (Succ zzz6022)) zzz6023 zzz6024",fontsize=16,color="green",shape="box"];63330[label="zzz2500",fontsize=16,color="green",shape="box"];63331 -> 4125[label="",style="dashed", color="red", weight=0]; 130.57/78.22 63331[label="FiniteMap.mkVBalBranch (Pos zzz300) zzz31 zzz2504 (FiniteMap.Branch zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344)",fontsize=16,color="magenta"];63331 -> 63551[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63331 -> 63552[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63332[label="zzz2503",fontsize=16,color="green",shape="box"];63333[label="zzz2501",fontsize=16,color="green",shape="box"];47182 -> 47208[label="",style="dashed", color="red", weight=0]; 130.57/78.22 47182[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz5119))) (FiniteMap.mkVBalBranch3Size_l zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121) == LT)",fontsize=16,color="magenta"];47182 -> 47209[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43282[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111))) (FiniteMap.mkVBalBranch3Size_l zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111) == LT)",fontsize=16,color="black",shape="box"];43282 -> 44481[label="",style="solid", color="black", weight=3]; 130.57/78.22 43283 -> 44482[label="",style="dashed", color="red", weight=0]; 130.57/78.22 43283[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (Pos zzz3748) zzz3749 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz3745))) (FiniteMap.mkVBalBranch3Size_l zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747) == LT)",fontsize=16,color="magenta"];43283 -> 44495[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44483 -> 43358[label="",style="dashed", color="red", weight=0]; 130.57/78.22 44483[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ (Succ (Succ (Succ (Succ Zero)))))",fontsize=16,color="magenta"];44483 -> 44535[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44484[label="zzz2503",fontsize=16,color="green",shape="box"];44485[label="zzz344",fontsize=16,color="green",shape="box"];44486[label="zzz340",fontsize=16,color="green",shape="box"];44487[label="zzz343",fontsize=16,color="green",shape="box"];44488[label="zzz300",fontsize=16,color="green",shape="box"];44489[label="zzz2504",fontsize=16,color="green",shape="box"];44490[label="Succ (Succ (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];44491[label="zzz2501",fontsize=16,color="green",shape="box"];44492[label="zzz341",fontsize=16,color="green",shape="box"];44493[label="zzz31",fontsize=16,color="green",shape="box"];44494[label="zzz2500",fontsize=16,color="green",shape="box"];44482[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (Pos zzz3748) zzz3749 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (primCmpInt (Neg zzz4968) (FiniteMap.mkVBalBranch3Size_l zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747) == LT)",fontsize=16,color="burlywood",shape="triangle"];65692[label="zzz4968/Succ zzz49680",fontsize=10,color="white",style="solid",shape="box"];44482 -> 65692[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65692 -> 44536[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65693[label="zzz4968/Zero",fontsize=10,color="white",style="solid",shape="box"];44482 -> 65693[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65693 -> 44537[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 64431[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Pos (Succ zzz645400)) (primMulInt (Pos (Succ (Succ Zero))) (Pos zzz64550)) == LT)",fontsize=16,color="black",shape="box"];64431 -> 64455[label="",style="solid", color="black", weight=3]; 130.57/78.22 64432[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Pos (Succ zzz645400)) (primMulInt (Pos (Succ (Succ Zero))) (Neg zzz64550)) == LT)",fontsize=16,color="black",shape="box"];64432 -> 64456[label="",style="solid", color="black", weight=3]; 130.57/78.22 64433[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Pos Zero) (primMulInt (Pos (Succ (Succ Zero))) (Pos zzz64550)) == LT)",fontsize=16,color="black",shape="box"];64433 -> 64457[label="",style="solid", color="black", weight=3]; 130.57/78.22 64434[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Pos Zero) (primMulInt (Pos (Succ (Succ Zero))) (Neg zzz64550)) == LT)",fontsize=16,color="black",shape="box"];64434 -> 64458[label="",style="solid", color="black", weight=3]; 130.57/78.22 64435[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Neg (Succ zzz645400)) (primMulInt (Pos (Succ (Succ Zero))) (Pos zzz64550)) == LT)",fontsize=16,color="black",shape="box"];64435 -> 64459[label="",style="solid", color="black", weight=3]; 130.57/78.22 64436[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Neg (Succ zzz645400)) (primMulInt (Pos (Succ (Succ Zero))) (Neg zzz64550)) == LT)",fontsize=16,color="black",shape="box"];64436 -> 64460[label="",style="solid", color="black", weight=3]; 130.57/78.22 64437[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Neg Zero) (primMulInt (Pos (Succ (Succ Zero))) (Pos zzz64550)) == LT)",fontsize=16,color="black",shape="box"];64437 -> 64461[label="",style="solid", color="black", weight=3]; 130.57/78.22 64438[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Neg Zero) (primMulInt (Pos (Succ (Succ Zero))) (Neg zzz64550)) == LT)",fontsize=16,color="black",shape="box"];64438 -> 64462[label="",style="solid", color="black", weight=3]; 130.57/78.22 64440 -> 62524[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64440[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64530",fontsize=16,color="magenta"];64440 -> 64463[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64439[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos (Succ zzz645200)) (Pos zzz6456) == GT)",fontsize=16,color="black",shape="triangle"];64439 -> 64464[label="",style="solid", color="black", weight=3]; 130.57/78.22 64442 -> 62524[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64442[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64530",fontsize=16,color="magenta"];64442 -> 64465[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64441[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos (Succ zzz645200)) (Neg zzz6457) == GT)",fontsize=16,color="black",shape="triangle"];64441 -> 64466[label="",style="solid", color="black", weight=3]; 130.57/78.22 64444 -> 62524[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64444[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64530",fontsize=16,color="magenta"];64444 -> 64467[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64443[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (Pos zzz6458) == GT)",fontsize=16,color="burlywood",shape="triangle"];65694[label="zzz6458/Succ zzz64580",fontsize=10,color="white",style="solid",shape="box"];64443 -> 65694[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65694 -> 64468[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65695[label="zzz6458/Zero",fontsize=10,color="white",style="solid",shape="box"];64443 -> 65695[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65695 -> 64469[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 64446 -> 62524[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64446[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64530",fontsize=16,color="magenta"];64446 -> 64470[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64445[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (Neg zzz6459) == GT)",fontsize=16,color="burlywood",shape="triangle"];65696[label="zzz6459/Succ zzz64590",fontsize=10,color="white",style="solid",shape="box"];64445 -> 65696[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65696 -> 64471[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65697[label="zzz6459/Zero",fontsize=10,color="white",style="solid",shape="box"];64445 -> 65697[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65697 -> 64472[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 64448 -> 62524[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64448[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64530",fontsize=16,color="magenta"];64448 -> 64473[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64447[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg (Succ zzz645200)) (Pos zzz6460) == GT)",fontsize=16,color="black",shape="triangle"];64447 -> 64474[label="",style="solid", color="black", weight=3]; 130.57/78.22 64450 -> 62524[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64450[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64530",fontsize=16,color="magenta"];64450 -> 64475[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64449[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg (Succ zzz645200)) (Neg zzz6461) == GT)",fontsize=16,color="black",shape="triangle"];64449 -> 64476[label="",style="solid", color="black", weight=3]; 130.57/78.22 64452 -> 62524[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64452[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64530",fontsize=16,color="magenta"];64452 -> 64477[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64451[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (Pos zzz6462) == GT)",fontsize=16,color="burlywood",shape="triangle"];65698[label="zzz6462/Succ zzz64620",fontsize=10,color="white",style="solid",shape="box"];64451 -> 65698[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65698 -> 64478[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65699[label="zzz6462/Zero",fontsize=10,color="white",style="solid",shape="box"];64451 -> 65699[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65699 -> 64479[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 64454 -> 62524[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64454[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) zzz64530",fontsize=16,color="magenta"];64454 -> 64480[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64453[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (Neg zzz6463) == GT)",fontsize=16,color="burlywood",shape="triangle"];65700[label="zzz6463/Succ zzz64630",fontsize=10,color="white",style="solid",shape="box"];64453 -> 65700[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65700 -> 64481[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65701[label="zzz6463/Zero",fontsize=10,color="white",style="solid",shape="box"];64453 -> 65701[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65701 -> 64482[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 43421 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.22 43421[label="FiniteMap.mkBalBranch zzz330 zzz331 zzz333 (FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 zzz334 (FiniteMap.Branch zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264))",fontsize=16,color="magenta"];43421 -> 63338[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43421 -> 63339[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43421 -> 63340[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43421 -> 63341[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63549[label="FiniteMap.Branch zzz4260 zzz4261 (Neg Zero) zzz4263 zzz4264",fontsize=16,color="green",shape="box"];63550[label="zzz334",fontsize=16,color="green",shape="box"];60598[label="zzz6131",fontsize=16,color="green",shape="box"];60599[label="Neg zzz6130",fontsize=16,color="green",shape="box"];60600[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];60601[label="FiniteMap.Branch zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129",fontsize=16,color="green",shape="box"];60602[label="FiniteMap.Branch zzz6120 zzz6121 (Pos (Succ zzz6122)) zzz6123 zzz6124",fontsize=16,color="green",shape="box"];63588[label="FiniteMap.mkVBalBranch5 (Neg zzz6130) zzz6131 FiniteMap.EmptyFM (FiniteMap.Branch zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129)",fontsize=16,color="black",shape="box"];63588 -> 63628[label="",style="solid", color="black", weight=3]; 130.57/78.22 63589 -> 11068[label="",style="dashed", color="red", weight=0]; 130.57/78.22 63589[label="FiniteMap.mkVBalBranch3 (Neg zzz6130) zzz6131 (FiniteMap.Branch zzz61240 zzz61241 zzz61242 zzz61243 zzz61244) (FiniteMap.Branch zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129)",fontsize=16,color="magenta"];63589 -> 63629[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63589 -> 63630[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63589 -> 63631[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63589 -> 63632[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63589 -> 63633[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63589 -> 63634[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63589 -> 63635[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63589 -> 63636[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63589 -> 63637[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63589 -> 63638[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63589 -> 63639[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63589 -> 63640[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 61955[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (Neg zzz6304) zzz6305 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (primCmpNat (Succ zzz63060) zzz6307 == LT)",fontsize=16,color="burlywood",shape="box"];65702[label="zzz6307/Succ zzz63070",fontsize=10,color="white",style="solid",shape="box"];61955 -> 65702[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65702 -> 62003[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65703[label="zzz6307/Zero",fontsize=10,color="white",style="solid",shape="box"];61955 -> 65703[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65703 -> 62004[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 61956[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (Neg zzz6304) zzz6305 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (primCmpNat Zero zzz6307 == LT)",fontsize=16,color="burlywood",shape="box"];65704[label="zzz6307/Succ zzz63070",fontsize=10,color="white",style="solid",shape="box"];61956 -> 65704[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65704 -> 62005[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65705[label="zzz6307/Zero",fontsize=10,color="white",style="solid",shape="box"];61956 -> 65705[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65705 -> 62006[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 44728[label="zzz332000",fontsize=16,color="green",shape="box"];44729[label="zzz31",fontsize=16,color="green",shape="box"];44730[label="Succ zzz5232000",fontsize=16,color="green",shape="box"];44731[label="zzz5234",fontsize=16,color="green",shape="box"];44732[label="zzz334",fontsize=16,color="green",shape="box"];44733[label="zzz5231",fontsize=16,color="green",shape="box"];44734[label="zzz333",fontsize=16,color="green",shape="box"];44735[label="zzz5233",fontsize=16,color="green",shape="box"];44736[label="Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) zzz332000))",fontsize=16,color="green",shape="box"];44736 -> 45430[label="",style="dashed", color="green", weight=3]; 130.57/78.22 44737[label="zzz5230",fontsize=16,color="green",shape="box"];44738[label="zzz5232000",fontsize=16,color="green",shape="box"];44739[label="zzz330",fontsize=16,color="green",shape="box"];44740[label="zzz331",fontsize=16,color="green",shape="box"];44741[label="zzz300",fontsize=16,color="green",shape="box"];45627[label="zzz5234",fontsize=16,color="green",shape="box"];45628[label="zzz333",fontsize=16,color="green",shape="box"];45629[label="zzz334",fontsize=16,color="green",shape="box"];45630[label="Succ zzz5232000",fontsize=16,color="green",shape="box"];45631[label="zzz331",fontsize=16,color="green",shape="box"];45632[label="zzz300",fontsize=16,color="green",shape="box"];45633[label="zzz5230",fontsize=16,color="green",shape="box"];45634[label="zzz5231",fontsize=16,color="green",shape="box"];45635[label="zzz5233",fontsize=16,color="green",shape="box"];45636[label="zzz5232000",fontsize=16,color="green",shape="box"];45637[label="zzz31",fontsize=16,color="green",shape="box"];45638[label="Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)",fontsize=16,color="green",shape="box"];45638 -> 45693[label="",style="dashed", color="green", weight=3]; 130.57/78.22 45639[label="zzz330",fontsize=16,color="green",shape="box"];43851[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (compare (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];43851 -> 45433[label="",style="solid", color="black", weight=3]; 130.57/78.22 43852[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];43852 -> 45434[label="",style="solid", color="black", weight=3]; 130.57/78.22 43853[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];43853 -> 45435[label="",style="solid", color="black", weight=3]; 130.57/78.22 43854[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 True",fontsize=16,color="black",shape="box"];43854 -> 45436[label="",style="solid", color="black", weight=3]; 130.57/78.22 44093[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 True",fontsize=16,color="black",shape="box"];44093 -> 45437[label="",style="solid", color="black", weight=3]; 130.57/78.22 44094 -> 46205[label="",style="dashed", color="red", weight=0]; 130.57/78.22 44094[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ (Succ zzz332000))) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ (Succ zzz52320000)))) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ (Succ zzz332000))) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ (Succ zzz52320000)))) zzz5233 zzz5234 (primCmpNat (Succ zzz52320000) (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) zzz332000))) == LT)",fontsize=16,color="magenta"];44094 -> 46346[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44094 -> 46347[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44094 -> 46348[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44094 -> 46349[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44094 -> 46350[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44094 -> 46351[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44094 -> 46352[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44094 -> 46353[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44094 -> 46354[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44094 -> 46355[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44094 -> 46356[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44094 -> 46357[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44094 -> 46358[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44094 -> 46359[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44095 -> 47219[label="",style="dashed", color="red", weight=0]; 130.57/78.22 44095[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ Zero)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ (Succ zzz52320000)))) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ Zero)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ (Succ zzz52320000)))) zzz5233 zzz5234 (primCmpNat (Succ zzz52320000) (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) == LT)",fontsize=16,color="magenta"];44095 -> 47389[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44095 -> 47390[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44095 -> 47391[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44095 -> 47392[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44095 -> 47393[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44095 -> 47394[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44095 -> 47395[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44095 -> 47396[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44095 -> 47397[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44095 -> 47398[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44095 -> 47399[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44095 -> 47400[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44095 -> 47401[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44096 -> 46205[label="",style="dashed", color="red", weight=0]; 130.57/78.22 44096[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ (Succ zzz332000))) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ Zero))) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ (Succ zzz332000))) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ Zero))) zzz5233 zzz5234 (primCmpNat Zero (Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) zzz332000))) == LT)",fontsize=16,color="magenta"];44096 -> 46360[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44096 -> 46361[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44096 -> 46362[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44096 -> 46363[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44096 -> 46364[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44096 -> 46365[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44096 -> 46366[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44096 -> 46367[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44096 -> 46368[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44096 -> 46369[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44096 -> 46370[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44096 -> 46371[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44096 -> 46372[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44096 -> 46373[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44097 -> 47219[label="",style="dashed", color="red", weight=0]; 130.57/78.22 44097[label="FiniteMap.mkVBalBranch3MkVBalBranch2 zzz330 zzz331 (Neg (Succ Zero)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ Zero))) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg (Succ Zero)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ (Succ Zero))) zzz5233 zzz5234 (primCmpNat Zero (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)) == LT)",fontsize=16,color="magenta"];44097 -> 47402[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44097 -> 47403[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44097 -> 47404[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44097 -> 47405[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44097 -> 47406[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44097 -> 47407[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44097 -> 47408[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44097 -> 47409[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44097 -> 47410[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44097 -> 47411[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44097 -> 47412[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44097 -> 47413[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44097 -> 47414[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63334[label="zzz5230",fontsize=16,color="green",shape="box"];63335[label="zzz5234",fontsize=16,color="green",shape="box"];63336 -> 7670[label="",style="dashed", color="red", weight=0]; 130.57/78.22 63336[label="FiniteMap.mkVBalBranch (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg (Succ zzz33200)) zzz333 zzz334) zzz5233",fontsize=16,color="magenta"];63336 -> 63553[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63336 -> 63554[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63337[label="zzz5231",fontsize=16,color="green",shape="box"];44102[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 True",fontsize=16,color="black",shape="box"];44102 -> 45801[label="",style="solid", color="black", weight=3]; 130.57/78.22 44348[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Neg Zero) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 True",fontsize=16,color="black",shape="box"];44348 -> 45802[label="",style="solid", color="black", weight=3]; 130.57/78.22 40781[label="zzz6200000",fontsize=16,color="green",shape="box"];40782[label="Succ zzz6200000",fontsize=16,color="green",shape="box"];40783[label="primPlusNat (primPlusNat zzz3752 (Succ (Succ (Succ zzz375300)))) zzz375300",fontsize=16,color="burlywood",shape="box"];65706[label="zzz3752/Succ zzz37520",fontsize=10,color="white",style="solid",shape="box"];40783 -> 65706[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65706 -> 41194[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65707[label="zzz3752/Zero",fontsize=10,color="white",style="solid",shape="box"];40783 -> 65707[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65707 -> 41195[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 40785[label="Succ Zero",fontsize=16,color="green",shape="box"];44371[label="zzz4708",fontsize=16,color="green",shape="box"];44372[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpInt (Pos (Succ zzz49560)) (FiniteMap.mkVBalBranch3Size_l zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710) == LT)",fontsize=16,color="black",shape="box"];44372 -> 45803[label="",style="solid", color="black", weight=3]; 130.57/78.22 44373[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710) == LT)",fontsize=16,color="black",shape="box"];44373 -> 45804[label="",style="solid", color="black", weight=3]; 130.57/78.22 44431[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpInt (Pos (Succ zzz49580)) (FiniteMap.sizeFM (FiniteMap.Branch zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879)) == LT)",fontsize=16,color="black",shape="box"];44431 -> 45805[label="",style="solid", color="black", weight=3]; 130.57/78.22 44432[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879)) == LT)",fontsize=16,color="black",shape="box"];44432 -> 45806[label="",style="solid", color="black", weight=3]; 130.57/78.22 43398 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.22 43398[label="primPlusNat (primMulNat Zero (Succ (Succ (Succ Zero)))) (Succ (Succ (Succ Zero)))",fontsize=16,color="magenta"];43398 -> 44796[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 43398 -> 44797[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 57452[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];57453[label="zzz2504",fontsize=16,color="green",shape="box"];57454[label="zzz343",fontsize=16,color="green",shape="box"];57455[label="zzz340",fontsize=16,color="green",shape="box"];57456[label="zzz341",fontsize=16,color="green",shape="box"];57457[label="Succ (Succ zzz4827)",fontsize=16,color="green",shape="box"];57458[label="Succ (Succ zzz2502000)",fontsize=16,color="green",shape="box"];57459[label="zzz300",fontsize=16,color="green",shape="box"];57460[label="zzz2501",fontsize=16,color="green",shape="box"];57461[label="zzz344",fontsize=16,color="green",shape="box"];57462[label="Succ zzz2502000",fontsize=16,color="green",shape="box"];57463[label="zzz31",fontsize=16,color="green",shape="box"];57464[label="zzz2503",fontsize=16,color="green",shape="box"];57465[label="zzz2500",fontsize=16,color="green",shape="box"];41572 -> 40784[label="",style="dashed", color="red", weight=0]; 130.57/78.22 41572[label="primPlusNat (primMulNat Zero (Succ (Succ Zero))) (Succ (Succ Zero))",fontsize=16,color="magenta"];41572 -> 41596[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44433[label="Succ (Succ (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];44434[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpInt (Pos (Succ zzz49610)) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];44434 -> 45813[label="",style="solid", color="black", weight=3]; 130.57/78.22 44435[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344) == LT)",fontsize=16,color="black",shape="box"];44435 -> 45814[label="",style="solid", color="black", weight=3]; 130.57/78.22 44794 -> 57269[label="",style="dashed", color="red", weight=0]; 130.57/78.22 44794[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpNat (Succ zzz49630) (Succ Zero) == LT)",fontsize=16,color="magenta"];44794 -> 57480[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44794 -> 57481[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44794 -> 57482[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44794 -> 57483[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44794 -> 57484[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44794 -> 57485[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44794 -> 57486[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44794 -> 57487[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44794 -> 57488[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44794 -> 57489[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44794 -> 57490[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44794 -> 57491[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44794 -> 57492[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44794 -> 57493[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44795 -> 57269[label="",style="dashed", color="red", weight=0]; 130.57/78.22 44795[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ Zero))))) zzz343 zzz344 (primCmpNat Zero (Succ Zero) == LT)",fontsize=16,color="magenta"];44795 -> 57494[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44795 -> 57495[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44795 -> 57496[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44795 -> 57497[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44795 -> 57498[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44795 -> 57499[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44795 -> 57500[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44795 -> 57501[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44795 -> 57502[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44795 -> 57503[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44795 -> 57504[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44795 -> 57505[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44795 -> 57506[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44795 -> 57507[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63551[label="zzz2504",fontsize=16,color="green",shape="box"];63552[label="FiniteMap.Branch zzz340 zzz341 (Neg (Succ zzz34200)) zzz343 zzz344",fontsize=16,color="green",shape="box"];47209 -> 43358[label="",style="dashed", color="red", weight=0]; 130.57/78.22 47209[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz5119)",fontsize=16,color="magenta"];47209 -> 47423[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 47208[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpInt (Neg zzz5245) (FiniteMap.mkVBalBranch3Size_l zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121) == LT)",fontsize=16,color="burlywood",shape="triangle"];65708[label="zzz5245/Succ zzz52450",fontsize=10,color="white",style="solid",shape="box"];47208 -> 65708[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65708 -> 47424[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65709[label="zzz5245/Zero",fontsize=10,color="white",style="solid",shape="box"];47208 -> 65709[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65709 -> 47425[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 44481[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg (Succ zzz4109))) (FiniteMap.mkVBalBranch3Size_l zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111) == LT)",fontsize=16,color="black",shape="box"];44481 -> 45988[label="",style="solid", color="black", weight=3]; 130.57/78.22 44495 -> 43358[label="",style="dashed", color="red", weight=0]; 130.57/78.22 44495[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz3745)",fontsize=16,color="magenta"];44495 -> 45989[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 44535[label="Succ (Succ (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];44536[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (Pos zzz3748) zzz3749 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (primCmpInt (Neg (Succ zzz49680)) (FiniteMap.mkVBalBranch3Size_l zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747) == LT)",fontsize=16,color="black",shape="box"];44536 -> 45990[label="",style="solid", color="black", weight=3]; 130.57/78.22 44537[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (Pos zzz3748) zzz3749 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747) == LT)",fontsize=16,color="black",shape="box"];44537 -> 45991[label="",style="solid", color="black", weight=3]; 130.57/78.22 64455[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Pos (Succ zzz645400)) (Pos (primMulNat (Succ (Succ Zero)) zzz64550)) == LT)",fontsize=16,color="black",shape="box"];64455 -> 64483[label="",style="solid", color="black", weight=3]; 130.57/78.22 64456[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Pos (Succ zzz645400)) (Neg (primMulNat (Succ (Succ Zero)) zzz64550)) == LT)",fontsize=16,color="black",shape="box"];64456 -> 64484[label="",style="solid", color="black", weight=3]; 130.57/78.22 64457 -> 64537[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64457[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Pos Zero) (Pos (primMulNat (Succ (Succ Zero)) zzz64550)) == LT)",fontsize=16,color="magenta"];64457 -> 64538[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64458 -> 64545[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64458[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Pos Zero) (Neg (primMulNat (Succ (Succ Zero)) zzz64550)) == LT)",fontsize=16,color="magenta"];64458 -> 64546[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64459[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Neg (Succ zzz645400)) (Pos (primMulNat (Succ (Succ Zero)) zzz64550)) == LT)",fontsize=16,color="black",shape="box"];64459 -> 64489[label="",style="solid", color="black", weight=3]; 130.57/78.22 64460[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Neg (Succ zzz645400)) (Neg (primMulNat (Succ (Succ Zero)) zzz64550)) == LT)",fontsize=16,color="black",shape="box"];64460 -> 64490[label="",style="solid", color="black", weight=3]; 130.57/78.22 64461 -> 64559[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64461[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Neg Zero) (Pos (primMulNat (Succ (Succ Zero)) zzz64550)) == LT)",fontsize=16,color="magenta"];64461 -> 64560[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64462 -> 64567[label="",style="dashed", color="red", weight=0]; 130.57/78.22 64462[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Neg Zero) (Neg (primMulNat (Succ (Succ Zero)) zzz64550)) == LT)",fontsize=16,color="magenta"];64462 -> 64568[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 64463[label="zzz64530",fontsize=16,color="green",shape="box"];64464[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat (Succ zzz645200) zzz6456 == GT)",fontsize=16,color="burlywood",shape="triangle"];65710[label="zzz6456/Succ zzz64560",fontsize=10,color="white",style="solid",shape="box"];64464 -> 65710[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65710 -> 64495[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65711[label="zzz6456/Zero",fontsize=10,color="white",style="solid",shape="box"];64464 -> 65711[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65711 -> 64496[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 64465[label="zzz64530",fontsize=16,color="green",shape="box"];64466[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (GT == GT)",fontsize=16,color="black",shape="triangle"];64466 -> 64497[label="",style="solid", color="black", weight=3]; 130.57/78.22 64467[label="zzz64530",fontsize=16,color="green",shape="box"];64468[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (Pos (Succ zzz64580)) == GT)",fontsize=16,color="black",shape="box"];64468 -> 64498[label="",style="solid", color="black", weight=3]; 130.57/78.22 64469[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];64469 -> 64499[label="",style="solid", color="black", weight=3]; 130.57/78.22 64470[label="zzz64530",fontsize=16,color="green",shape="box"];64471[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (Neg (Succ zzz64590)) == GT)",fontsize=16,color="black",shape="box"];64471 -> 64500[label="",style="solid", color="black", weight=3]; 130.57/78.22 64472[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Pos Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];64472 -> 64501[label="",style="solid", color="black", weight=3]; 130.57/78.22 64473[label="zzz64530",fontsize=16,color="green",shape="box"];64474[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (LT == GT)",fontsize=16,color="black",shape="triangle"];64474 -> 64502[label="",style="solid", color="black", weight=3]; 130.57/78.22 64475[label="zzz64530",fontsize=16,color="green",shape="box"];64476[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat zzz6461 (Succ zzz645200) == GT)",fontsize=16,color="burlywood",shape="triangle"];65712[label="zzz6461/Succ zzz64610",fontsize=10,color="white",style="solid",shape="box"];64476 -> 65712[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65712 -> 64503[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 65713[label="zzz6461/Zero",fontsize=10,color="white",style="solid",shape="box"];64476 -> 65713[label="",style="solid", color="burlywood", weight=9]; 130.57/78.22 65713 -> 64504[label="",style="solid", color="burlywood", weight=3]; 130.57/78.22 64477[label="zzz64530",fontsize=16,color="green",shape="box"];64478[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (Pos (Succ zzz64620)) == GT)",fontsize=16,color="black",shape="box"];64478 -> 64505[label="",style="solid", color="black", weight=3]; 130.57/78.22 64479[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];64479 -> 64506[label="",style="solid", color="black", weight=3]; 130.57/78.22 64480[label="zzz64530",fontsize=16,color="green",shape="box"];64481[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (Neg (Succ zzz64630)) == GT)",fontsize=16,color="black",shape="box"];64481 -> 64507[label="",style="solid", color="black", weight=3]; 130.57/78.22 64482[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpInt (Neg Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];64482 -> 64508[label="",style="solid", color="black", weight=3]; 130.57/78.22 63338[label="zzz330",fontsize=16,color="green",shape="box"];63339 -> 6244[label="",style="dashed", color="red", weight=0]; 130.57/78.22 63339[label="FiniteMap.mkVBalBranch (Neg (Succ zzz3000)) zzz31 zzz334 (FiniteMap.Branch zzz4260 zzz4261 (Pos Zero) zzz4263 zzz4264)",fontsize=16,color="magenta"];63339 -> 63555[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63339 -> 63556[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63340[label="zzz333",fontsize=16,color="green",shape="box"];63341[label="zzz331",fontsize=16,color="green",shape="box"];63628 -> 12428[label="",style="dashed", color="red", weight=0]; 130.57/78.22 63628[label="FiniteMap.addToFM (FiniteMap.Branch zzz6125 zzz6126 (Pos (Succ zzz6127)) zzz6128 zzz6129) (Neg zzz6130) zzz6131",fontsize=16,color="magenta"];63628 -> 63685[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63628 -> 63686[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63628 -> 63687[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63628 -> 63688[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63628 -> 63689[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63628 -> 63690[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63628 -> 63691[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 63629[label="zzz61242",fontsize=16,color="green",shape="box"];63630[label="zzz6125",fontsize=16,color="green",shape="box"];63631[label="zzz6130",fontsize=16,color="green",shape="box"];63632[label="zzz61244",fontsize=16,color="green",shape="box"];63633[label="zzz6128",fontsize=16,color="green",shape="box"];63634[label="Pos (Succ zzz6127)",fontsize=16,color="green",shape="box"];63635[label="zzz61240",fontsize=16,color="green",shape="box"];63636[label="zzz6126",fontsize=16,color="green",shape="box"];63637[label="zzz61243",fontsize=16,color="green",shape="box"];63638[label="zzz6131",fontsize=16,color="green",shape="box"];63639[label="zzz61241",fontsize=16,color="green",shape="box"];63640[label="zzz6129",fontsize=16,color="green",shape="box"];62003[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (Neg zzz6304) zzz6305 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (primCmpNat (Succ zzz63060) (Succ zzz63070) == LT)",fontsize=16,color="black",shape="box"];62003 -> 62031[label="",style="solid", color="black", weight=3]; 130.57/78.22 62004[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (Neg zzz6304) zzz6305 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (primCmpNat (Succ zzz63060) Zero == LT)",fontsize=16,color="black",shape="box"];62004 -> 62032[label="",style="solid", color="black", weight=3]; 130.57/78.22 62005[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (Neg zzz6304) zzz6305 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (primCmpNat Zero (Succ zzz63070) == LT)",fontsize=16,color="black",shape="box"];62005 -> 62033[label="",style="solid", color="black", weight=3]; 130.57/78.22 62006[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (Neg zzz6304) zzz6305 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];62006 -> 62034[label="",style="solid", color="black", weight=3]; 130.57/78.22 45430 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.22 45430[label="primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) zzz332000",fontsize=16,color="magenta"];45430 -> 46518[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45430 -> 46519[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45693 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.22 45693[label="primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero",fontsize=16,color="magenta"];45693 -> 46520[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45693 -> 46521[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45433[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (primCmpInt (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];45433 -> 46522[label="",style="solid", color="black", weight=3]; 130.57/78.22 45434[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];45434 -> 46523[label="",style="solid", color="black", weight=3]; 130.57/78.22 45435[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg zzz52320)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg zzz52320) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];45435 -> 46524[label="",style="solid", color="black", weight=3]; 130.57/78.22 45436 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.22 45436[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 (Pos Zero) zzz333 zzz334) (FiniteMap.Branch zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234)",fontsize=16,color="magenta"];45436 -> 60613[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45436 -> 60614[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45436 -> 60615[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45436 -> 60616[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45436 -> 60617[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45437 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.22 45437[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 (Pos Zero) zzz333 zzz334) (FiniteMap.Branch zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234)",fontsize=16,color="magenta"];45437 -> 60618[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45437 -> 60619[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45437 -> 60620[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45437 -> 60621[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45437 -> 60622[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 46346[label="zzz5231",fontsize=16,color="green",shape="box"];46347[label="zzz334",fontsize=16,color="green",shape="box"];46348[label="zzz5234",fontsize=16,color="green",shape="box"];46349[label="zzz300",fontsize=16,color="green",shape="box"];46350[label="zzz31",fontsize=16,color="green",shape="box"];46351[label="zzz330",fontsize=16,color="green",shape="box"];46352[label="zzz333",fontsize=16,color="green",shape="box"];46353[label="zzz5230",fontsize=16,color="green",shape="box"];46354[label="Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) zzz332000))",fontsize=16,color="green",shape="box"];46354 -> 46778[label="",style="dashed", color="green", weight=3]; 130.57/78.22 46355[label="Succ zzz52320000",fontsize=16,color="green",shape="box"];46356[label="zzz331",fontsize=16,color="green",shape="box"];46357[label="zzz5233",fontsize=16,color="green",shape="box"];46358[label="zzz332000",fontsize=16,color="green",shape="box"];46359[label="Succ (Succ zzz52320000)",fontsize=16,color="green",shape="box"];47389[label="Succ (Succ zzz52320000)",fontsize=16,color="green",shape="box"];47390[label="Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)",fontsize=16,color="green",shape="box"];47390 -> 47435[label="",style="dashed", color="green", weight=3]; 130.57/78.22 47391[label="zzz330",fontsize=16,color="green",shape="box"];47392[label="zzz5234",fontsize=16,color="green",shape="box"];47393[label="zzz300",fontsize=16,color="green",shape="box"];47394[label="zzz5233",fontsize=16,color="green",shape="box"];47395[label="zzz31",fontsize=16,color="green",shape="box"];47396[label="zzz333",fontsize=16,color="green",shape="box"];47397[label="zzz5231",fontsize=16,color="green",shape="box"];47398[label="zzz334",fontsize=16,color="green",shape="box"];47399[label="Succ zzz52320000",fontsize=16,color="green",shape="box"];47400[label="zzz331",fontsize=16,color="green",shape="box"];47401[label="zzz5230",fontsize=16,color="green",shape="box"];46360[label="zzz5231",fontsize=16,color="green",shape="box"];46361[label="zzz334",fontsize=16,color="green",shape="box"];46362[label="zzz5234",fontsize=16,color="green",shape="box"];46363[label="zzz300",fontsize=16,color="green",shape="box"];46364[label="zzz31",fontsize=16,color="green",shape="box"];46365[label="zzz330",fontsize=16,color="green",shape="box"];46366[label="zzz333",fontsize=16,color="green",shape="box"];46367[label="zzz5230",fontsize=16,color="green",shape="box"];46368[label="Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)) zzz332000))",fontsize=16,color="green",shape="box"];46368 -> 46781[label="",style="dashed", color="green", weight=3]; 130.57/78.22 46369[label="Zero",fontsize=16,color="green",shape="box"];46370[label="zzz331",fontsize=16,color="green",shape="box"];46371[label="zzz5233",fontsize=16,color="green",shape="box"];46372[label="zzz332000",fontsize=16,color="green",shape="box"];46373[label="Succ Zero",fontsize=16,color="green",shape="box"];47402[label="Succ Zero",fontsize=16,color="green",shape="box"];47403[label="Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero)",fontsize=16,color="green",shape="box"];47403 -> 47436[label="",style="dashed", color="green", weight=3]; 130.57/78.22 47404[label="zzz330",fontsize=16,color="green",shape="box"];47405[label="zzz5234",fontsize=16,color="green",shape="box"];47406[label="zzz300",fontsize=16,color="green",shape="box"];47407[label="zzz5233",fontsize=16,color="green",shape="box"];47408[label="zzz31",fontsize=16,color="green",shape="box"];47409[label="zzz333",fontsize=16,color="green",shape="box"];47410[label="zzz5231",fontsize=16,color="green",shape="box"];47411[label="zzz334",fontsize=16,color="green",shape="box"];47412[label="Zero",fontsize=16,color="green",shape="box"];47413[label="zzz331",fontsize=16,color="green",shape="box"];47414[label="zzz5230",fontsize=16,color="green",shape="box"];63553[label="Neg (Succ zzz33200)",fontsize=16,color="green",shape="box"];63554[label="zzz5233",fontsize=16,color="green",shape="box"];45801 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.22 45801[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334) (FiniteMap.Branch zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234)",fontsize=16,color="magenta"];45801 -> 60623[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45801 -> 60624[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45801 -> 60625[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45801 -> 60626[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45801 -> 60627[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45802 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.22 45802[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Neg zzz300) zzz31 (FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334) (FiniteMap.Branch zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234)",fontsize=16,color="magenta"];45802 -> 60628[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45802 -> 60629[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45802 -> 60630[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45802 -> 60631[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 45802 -> 60632[label="",style="dashed", color="magenta", weight=3]; 130.57/78.22 41194[label="primPlusNat (primPlusNat (Succ zzz37520) (Succ (Succ (Succ zzz375300)))) zzz375300",fontsize=16,color="black",shape="box"];41194 -> 41925[label="",style="solid", color="black", weight=3]; 130.57/78.22 41195[label="primPlusNat (primPlusNat Zero (Succ (Succ (Succ zzz375300)))) zzz375300",fontsize=16,color="black",shape="box"];41195 -> 41926[label="",style="solid", color="black", weight=3]; 130.57/78.22 45803[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpInt (Pos (Succ zzz49560)) (FiniteMap.sizeFM (FiniteMap.Branch zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705)) == LT)",fontsize=16,color="black",shape="box"];45803 -> 47075[label="",style="solid", color="black", weight=3]; 130.57/78.22 45804[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705)) == LT)",fontsize=16,color="black",shape="box"];45804 -> 47076[label="",style="solid", color="black", weight=3]; 130.57/78.22 45805[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpInt (Pos (Succ zzz49580)) (Pos (Succ (Succ Zero))) == LT)",fontsize=16,color="black",shape="box"];45805 -> 47077[label="",style="solid", color="black", weight=3]; 130.57/78.22 45806[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpInt (Pos Zero) (Pos (Succ (Succ Zero))) == LT)",fontsize=16,color="black",shape="box"];45806 -> 47078[label="",style="solid", color="black", weight=3]; 130.57/78.22 44796[label="Succ (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];44797 -> 44418[label="",style="dashed", color="red", weight=0]; 130.57/78.22 44797[label="primMulNat Zero (Succ (Succ (Succ Zero)))",fontsize=16,color="magenta"];44797 -> 46095[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 41596[label="primMulNat Zero (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];41596 -> 42073[label="",style="solid", color="black", weight=3]; 130.57/78.23 45813[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpInt (Pos (Succ zzz49610)) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];45813 -> 47086[label="",style="solid", color="black", weight=3]; 130.57/78.23 45814[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504)) == LT)",fontsize=16,color="black",shape="box"];45814 -> 47087[label="",style="solid", color="black", weight=3]; 130.57/78.23 57480[label="Succ (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];57481[label="zzz2504",fontsize=16,color="green",shape="box"];57482[label="zzz343",fontsize=16,color="green",shape="box"];57483[label="zzz340",fontsize=16,color="green",shape="box"];57484[label="zzz341",fontsize=16,color="green",shape="box"];57485[label="Succ zzz49630",fontsize=16,color="green",shape="box"];57486[label="Succ Zero",fontsize=16,color="green",shape="box"];57487[label="zzz300",fontsize=16,color="green",shape="box"];57488[label="zzz2501",fontsize=16,color="green",shape="box"];57489[label="zzz344",fontsize=16,color="green",shape="box"];57490[label="Zero",fontsize=16,color="green",shape="box"];57491[label="zzz31",fontsize=16,color="green",shape="box"];57492[label="zzz2503",fontsize=16,color="green",shape="box"];57493[label="zzz2500",fontsize=16,color="green",shape="box"];57494[label="Succ (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];57495[label="zzz2504",fontsize=16,color="green",shape="box"];57496[label="zzz343",fontsize=16,color="green",shape="box"];57497[label="zzz340",fontsize=16,color="green",shape="box"];57498[label="zzz341",fontsize=16,color="green",shape="box"];57499[label="Zero",fontsize=16,color="green",shape="box"];57500[label="Succ Zero",fontsize=16,color="green",shape="box"];57501[label="zzz300",fontsize=16,color="green",shape="box"];57502[label="zzz2501",fontsize=16,color="green",shape="box"];57503[label="zzz344",fontsize=16,color="green",shape="box"];57504[label="Zero",fontsize=16,color="green",shape="box"];57505[label="zzz31",fontsize=16,color="green",shape="box"];57506[label="zzz2503",fontsize=16,color="green",shape="box"];57507[label="zzz2500",fontsize=16,color="green",shape="box"];47423[label="zzz5119",fontsize=16,color="green",shape="box"];47424[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpInt (Neg (Succ zzz52450)) (FiniteMap.mkVBalBranch3Size_l zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121) == LT)",fontsize=16,color="black",shape="box"];47424 -> 47571[label="",style="solid", color="black", weight=3]; 130.57/78.23 47425[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121) == LT)",fontsize=16,color="black",shape="box"];47425 -> 47572[label="",style="solid", color="black", weight=3]; 130.57/78.23 45988 -> 47178[label="",style="dashed", color="red", weight=0]; 130.57/78.23 45988[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz4109))) (FiniteMap.mkVBalBranch3Size_l zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111) == LT)",fontsize=16,color="magenta"];45988 -> 47179[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 45989[label="zzz3745",fontsize=16,color="green",shape="box"];45990[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (Pos zzz3748) zzz3749 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (primCmpInt (Neg (Succ zzz49680)) (FiniteMap.sizeFM (FiniteMap.Branch zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742)) == LT)",fontsize=16,color="black",shape="box"];45990 -> 47192[label="",style="solid", color="black", weight=3]; 130.57/78.23 45991[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (Pos zzz3748) zzz3749 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742)) == LT)",fontsize=16,color="black",shape="box"];45991 -> 47193[label="",style="solid", color="black", weight=3]; 130.57/78.23 64483 -> 64583[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64483[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpNat (Succ zzz645400) (primMulNat (Succ (Succ Zero)) zzz64550) == LT)",fontsize=16,color="magenta"];64483 -> 64584[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64484[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (GT == LT)",fontsize=16,color="black",shape="triangle"];64484 -> 64511[label="",style="solid", color="black", weight=3]; 130.57/78.23 64538[label="primMulNat (Succ (Succ Zero)) zzz64550",fontsize=16,color="burlywood",shape="triangle"];65714[label="zzz64550/Succ zzz645500",fontsize=10,color="white",style="solid",shape="box"];64538 -> 65714[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65714 -> 64541[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65715[label="zzz64550/Zero",fontsize=10,color="white",style="solid",shape="box"];64538 -> 65715[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65715 -> 64542[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64537[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Pos Zero) (Pos zzz6464) == LT)",fontsize=16,color="burlywood",shape="triangle"];65716[label="zzz6464/Succ zzz64640",fontsize=10,color="white",style="solid",shape="box"];64537 -> 65716[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65716 -> 64543[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65717[label="zzz6464/Zero",fontsize=10,color="white",style="solid",shape="box"];64537 -> 65717[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65717 -> 64544[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64546 -> 64538[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64546[label="primMulNat (Succ (Succ Zero)) zzz64550",fontsize=16,color="magenta"];64546 -> 64549[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64545[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Pos Zero) (Neg zzz6466) == LT)",fontsize=16,color="burlywood",shape="triangle"];65718[label="zzz6466/Succ zzz64660",fontsize=10,color="white",style="solid",shape="box"];64545 -> 65718[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65718 -> 64550[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65719[label="zzz6466/Zero",fontsize=10,color="white",style="solid",shape="box"];64545 -> 65719[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65719 -> 64551[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64489[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (LT == LT)",fontsize=16,color="black",shape="triangle"];64489 -> 64516[label="",style="solid", color="black", weight=3]; 130.57/78.23 64490 -> 64597[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64490[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpNat (primMulNat (Succ (Succ Zero)) zzz64550) (Succ zzz645400) == LT)",fontsize=16,color="magenta"];64490 -> 64598[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64560 -> 64538[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64560[label="primMulNat (Succ (Succ Zero)) zzz64550",fontsize=16,color="magenta"];64559[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Neg Zero) (Pos zzz6468) == LT)",fontsize=16,color="burlywood",shape="triangle"];65720[label="zzz6468/Succ zzz64680",fontsize=10,color="white",style="solid",shape="box"];64559 -> 65720[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65720 -> 64563[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65721[label="zzz6468/Zero",fontsize=10,color="white",style="solid",shape="box"];64559 -> 65721[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65721 -> 64564[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64568 -> 64538[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64568[label="primMulNat (Succ (Succ Zero)) zzz64550",fontsize=16,color="magenta"];64568 -> 64571[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64567[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Neg Zero) (Neg zzz6470) == LT)",fontsize=16,color="burlywood",shape="triangle"];65722[label="zzz6470/Succ zzz64700",fontsize=10,color="white",style="solid",shape="box"];64567 -> 65722[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65722 -> 64572[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65723[label="zzz6470/Zero",fontsize=10,color="white",style="solid",shape="box"];64567 -> 65723[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65723 -> 64573[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64495[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat (Succ zzz645200) (Succ zzz64560) == GT)",fontsize=16,color="black",shape="box"];64495 -> 64523[label="",style="solid", color="black", weight=3]; 130.57/78.23 64496[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat (Succ zzz645200) Zero == GT)",fontsize=16,color="black",shape="box"];64496 -> 64524[label="",style="solid", color="black", weight=3]; 130.57/78.23 64497[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 True",fontsize=16,color="black",shape="box"];64497 -> 64525[label="",style="solid", color="black", weight=3]; 130.57/78.23 64498 -> 64476[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64498[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat Zero (Succ zzz64580) == GT)",fontsize=16,color="magenta"];64498 -> 64526[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64498 -> 64527[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64499[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (EQ == GT)",fontsize=16,color="black",shape="triangle"];64499 -> 64528[label="",style="solid", color="black", weight=3]; 130.57/78.23 64500 -> 64466[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64500[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (GT == GT)",fontsize=16,color="magenta"];64501 -> 64499[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64501[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (EQ == GT)",fontsize=16,color="magenta"];64502[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 False",fontsize=16,color="black",shape="triangle"];64502 -> 64529[label="",style="solid", color="black", weight=3]; 130.57/78.23 64503[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat (Succ zzz64610) (Succ zzz645200) == GT)",fontsize=16,color="black",shape="box"];64503 -> 64530[label="",style="solid", color="black", weight=3]; 130.57/78.23 64504[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat Zero (Succ zzz645200) == GT)",fontsize=16,color="black",shape="box"];64504 -> 64531[label="",style="solid", color="black", weight=3]; 130.57/78.23 64505 -> 64474[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64505[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (LT == GT)",fontsize=16,color="magenta"];64506 -> 64499[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64506[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (EQ == GT)",fontsize=16,color="magenta"];64507 -> 64464[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64507[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat (Succ zzz64630) Zero 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130.57/78.23 62032[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (Neg zzz6304) zzz6305 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (GT == LT)",fontsize=16,color="black",shape="box"];62032 -> 62046[label="",style="solid", color="black", weight=3]; 130.57/78.23 62033[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (Neg zzz6304) zzz6305 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (LT == LT)",fontsize=16,color="black",shape="box"];62033 -> 62047[label="",style="solid", color="black", weight=3]; 130.57/78.23 62034[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (Neg 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46522[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (primCmpInt (primMulInt FiniteMap.sIZE_RATIO (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];46522 -> 48392[label="",style="solid", color="black", weight=3]; 130.57/78.23 46523[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ 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65724[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65724 -> 48394[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65725[label="zzz52320/Zero",fontsize=10,color="white",style="solid",shape="box"];46524 -> 65725[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65725 -> 48395[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 60613[label="zzz31",fontsize=16,color="green",shape="box"];60614[label="Neg zzz300",fontsize=16,color="green",shape="box"];60615[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];60616[label="FiniteMap.Branch zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234",fontsize=16,color="green",shape="box"];60617[label="FiniteMap.Branch zzz330 zzz331 (Pos Zero) zzz333 zzz334",fontsize=16,color="green",shape="box"];60618[label="zzz31",fontsize=16,color="green",shape="box"];60619[label="Neg 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60623[label="zzz31",fontsize=16,color="green",shape="box"];60624[label="Neg zzz300",fontsize=16,color="green",shape="box"];60625[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];60626[label="FiniteMap.Branch zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234",fontsize=16,color="green",shape="box"];60627[label="FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334",fontsize=16,color="green",shape="box"];60628[label="zzz31",fontsize=16,color="green",shape="box"];60629[label="Neg zzz300",fontsize=16,color="green",shape="box"];60630[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];60631[label="FiniteMap.Branch zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234",fontsize=16,color="green",shape="box"];60632[label="FiniteMap.Branch zzz330 zzz331 (Neg Zero) zzz333 zzz334",fontsize=16,color="green",shape="box"];41925 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.23 41925[label="primPlusNat (Succ (Succ (primPlusNat zzz37520 (Succ (Succ zzz375300))))) zzz375300",fontsize=16,color="magenta"];41925 -> 44538[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 41925 -> 44539[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 41926 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.23 41926[label="primPlusNat (Succ (Succ (Succ zzz375300))) zzz375300",fontsize=16,color="magenta"];41926 -> 44540[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 41926 -> 44541[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 47075[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpInt (Pos (Succ zzz49560)) (Pos (Succ (Succ (Succ zzz4703)))) == LT)",fontsize=16,color="black",shape="box"];47075 -> 48404[label="",style="solid", color="black", weight=3]; 130.57/78.23 47076[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpInt (Pos Zero) (Pos (Succ (Succ (Succ zzz4703)))) == LT)",fontsize=16,color="black",shape="box"];47076 -> 48405[label="",style="solid", color="black", weight=3]; 130.57/78.23 47077 -> 57269[label="",style="dashed", color="red", weight=0]; 130.57/78.23 47077[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) 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57546[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 47077 -> 57547[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 47077 -> 57548[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 47077 -> 57549[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 47078 -> 57269[label="",style="dashed", color="red", weight=0]; 130.57/78.23 47078[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (Pos zzz3885) zzz3886 zzz3876 zzz3877 (Pos (Succ (Succ Zero))) zzz3878 zzz3879 zzz3880 zzz3881 (Pos (Succ zzz3882)) zzz3883 zzz3884 (primCmpNat Zero (Succ (Succ Zero)) == LT)",fontsize=16,color="magenta"];47078 -> 57550[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 47078 -> 57551[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 47078 -> 57552[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 47078 -> 57553[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 47078 -> 57554[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 47078 -> 57555[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 47078 -> 57556[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 47078 -> 57557[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 47078 -> 57558[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 47078 -> 57559[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 47078 -> 57560[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 47078 -> 57561[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 47078 -> 57562[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 47078 -> 57563[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 46095[label="Succ (Succ 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zzz5120 zzz5121 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116)) == LT)",fontsize=16,color="black",shape="box"];47572 -> 48432[label="",style="solid", color="black", weight=3]; 130.57/78.23 47179 -> 43358[label="",style="dashed", color="red", weight=0]; 130.57/78.23 47179[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz4109)",fontsize=16,color="magenta"];47179 -> 48433[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 47178[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpInt (Neg zzz5242) (FiniteMap.mkVBalBranch3Size_l zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111) == 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130.57/78.23 47193[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (Pos zzz3748) zzz3749 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (primCmpInt (Neg Zero) (Neg (Succ Zero)) == LT)",fontsize=16,color="black",shape="box"];47193 -> 48437[label="",style="solid", color="black", weight=3]; 130.57/78.23 64584 -> 64538[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64584[label="primMulNat (Succ (Succ Zero)) zzz64550",fontsize=16,color="magenta"];64583[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpNat (Succ zzz645400) zzz6472 == LT)",fontsize=16,color="burlywood",shape="triangle"];65728[label="zzz6472/Succ zzz64720",fontsize=10,color="white",style="solid",shape="box"];64583 -> 65728[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65728 -> 64587[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65729[label="zzz6472/Zero",fontsize=10,color="white",style="solid",shape="box"];64583 -> 65729[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65729 -> 64588[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64511[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 False",fontsize=16,color="black",shape="triangle"];64511 -> 64536[label="",style="solid", color="black", weight=3]; 130.57/78.23 64541[label="primMulNat (Succ (Succ Zero)) (Succ zzz645500)",fontsize=16,color="black",shape="box"];64541 -> 64552[label="",style="solid", color="black", weight=3]; 130.57/78.23 64542[label="primMulNat (Succ (Succ Zero)) Zero",fontsize=16,color="black",shape="box"];64542 -> 64553[label="",style="solid", color="black", weight=3]; 130.57/78.23 64543[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Pos Zero) (Pos (Succ zzz64640)) == LT)",fontsize=16,color="black",shape="box"];64543 -> 64554[label="",style="solid", color="black", weight=3]; 130.57/78.23 64544[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];64544 -> 64555[label="",style="solid", color="black", weight=3]; 130.57/78.23 64549[label="zzz64550",fontsize=16,color="green",shape="box"];64550[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Pos Zero) (Neg (Succ zzz64660)) == LT)",fontsize=16,color="black",shape="box"];64550 -> 64565[label="",style="solid", color="black", weight=3]; 130.57/78.23 64551[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];64551 -> 64566[label="",style="solid", color="black", weight=3]; 130.57/78.23 64516[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 True",fontsize=16,color="black",shape="box"];64516 -> 64556[label="",style="solid", color="black", weight=3]; 130.57/78.23 64598 -> 64538[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64598[label="primMulNat (Succ (Succ Zero)) zzz64550",fontsize=16,color="magenta"];64598 -> 64603[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64597[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpNat zzz6474 (Succ zzz645400) == LT)",fontsize=16,color="burlywood",shape="triangle"];65730[label="zzz6474/Succ zzz64740",fontsize=10,color="white",style="solid",shape="box"];64597 -> 65730[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65730 -> 64604[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65731[label="zzz6474/Zero",fontsize=10,color="white",style="solid",shape="box"];64597 -> 65731[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65731 -> 64605[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64563[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Neg Zero) (Pos (Succ zzz64680)) == LT)",fontsize=16,color="black",shape="box"];64563 -> 64574[label="",style="solid", color="black", weight=3]; 130.57/78.23 64564[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];64564 -> 64575[label="",style="solid", color="black", weight=3]; 130.57/78.23 64571[label="zzz64550",fontsize=16,color="green",shape="box"];64572[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Neg Zero) (Neg (Succ zzz64700)) == LT)",fontsize=16,color="black",shape="box"];64572 -> 64589[label="",style="solid", color="black", weight=3]; 130.57/78.23 64573[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];64573 -> 64590[label="",style="solid", color="black", weight=3]; 130.57/78.23 64523[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat zzz645200 zzz64560 == GT)",fontsize=16,color="burlywood",shape="triangle"];65732[label="zzz645200/Succ zzz6452000",fontsize=10,color="white",style="solid",shape="box"];64523 -> 65732[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65732 -> 64576[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65733[label="zzz645200/Zero",fontsize=10,color="white",style="solid",shape="box"];64523 -> 65733[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65733 -> 64577[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64524 -> 64466[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64524[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (GT == GT)",fontsize=16,color="magenta"];64525[label="FiniteMap.mkBalBranch6MkBalBranch1 zzz474034 zzz474030 zzz474031 zzz6373 zzz6373 zzz474034 zzz6373",fontsize=16,color="burlywood",shape="box"];65734[label="zzz6373/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];64525 -> 65734[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65734 -> 64578[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65735[label="zzz6373/FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734",fontsize=10,color="white",style="solid",shape="box"];64525 -> 65735[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65735 -> 64579[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64526[label="zzz64580",fontsize=16,color="green",shape="box"];64527[label="Zero",fontsize=16,color="green",shape="box"];64528 -> 64502[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64528[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 False",fontsize=16,color="magenta"];64529[label="FiniteMap.mkBalBranch6MkBalBranch2 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 otherwise",fontsize=16,color="black",shape="box"];64529 -> 64580[label="",style="solid", color="black", weight=3]; 130.57/78.23 64530 -> 64523[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64530[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat zzz64610 zzz645200 == GT)",fontsize=16,color="magenta"];64530 -> 64581[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64530 -> 64582[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64531 -> 64474[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64531[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (LT == GT)",fontsize=16,color="magenta"];64532[label="zzz64630",fontsize=16,color="green",shape="box"];64533[label="Zero",fontsize=16,color="green",shape="box"];62044[label="zzz63070",fontsize=16,color="green",shape="box"];62045[label="zzz63060",fontsize=16,color="green",shape="box"];62046[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (Neg zzz6304) zzz6305 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 False",fontsize=16,color="black",shape="triangle"];62046 -> 62071[label="",style="solid", color="black", weight=3]; 130.57/78.23 62047[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (Neg zzz6304) zzz6305 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 True",fontsize=16,color="black",shape="box"];62047 -> 62072[label="",style="solid", color="black", weight=3]; 130.57/78.23 62048 -> 62046[label="",style="dashed", color="red", weight=0]; 130.57/78.23 62048[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (Neg zzz6304) zzz6305 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ 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(Succ (Succ Zero)))))) (FiniteMap.mkVBalBranch3Size_r zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];48392 -> 48818[label="",style="solid", color="black", weight=3]; 130.57/78.23 48393[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];48393 -> 48819[label="",style="solid", color="black", weight=3]; 130.57/78.23 48394[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ zzz523200))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];48394 -> 48820[label="",style="solid", color="black", weight=3]; 130.57/78.23 48395[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];48395 -> 48821[label="",style="solid", color="black", weight=3]; 130.57/78.23 48396[label="zzz332000",fontsize=16,color="green",shape="box"];48397 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.23 48397[label="primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)",fontsize=16,color="magenta"];48397 -> 48822[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48397 -> 48823[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48398[label="Zero",fontsize=16,color="green",shape="box"];48399[label="Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)",fontsize=16,color="green",shape="box"];48399 -> 48824[label="",style="dashed", color="green", weight=3]; 130.57/78.23 48400[label="zzz332000",fontsize=16,color="green",shape="box"];48401 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.23 48401[label="primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))) (Succ zzz332000)",fontsize=16,color="magenta"];48401 -> 48825[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48401 -> 48826[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48402[label="Zero",fontsize=16,color="green",shape="box"];48403[label="Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)",fontsize=16,color="green",shape="box"];48403 -> 48827[label="",style="dashed", color="green", weight=3]; 130.57/78.23 44538[label="zzz375300",fontsize=16,color="green",shape="box"];44539[label="Succ (Succ (primPlusNat zzz37520 (Succ (Succ zzz375300))))",fontsize=16,color="green",shape="box"];44539 -> 45992[label="",style="dashed", color="green", weight=3]; 130.57/78.23 44540[label="zzz375300",fontsize=16,color="green",shape="box"];44541[label="Succ (Succ (Succ zzz375300))",fontsize=16,color="green",shape="box"];48404 -> 57269[label="",style="dashed", color="red", weight=0]; 130.57/78.23 48404[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpNat (Succ zzz49560) (Succ (Succ (Succ zzz4703))) == LT)",fontsize=16,color="magenta"];48404 -> 57564[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48404 -> 57565[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48404 -> 57566[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48404 -> 57567[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48404 -> 57568[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48404 -> 57569[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48404 -> 57570[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48404 -> 57571[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48404 -> 57572[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48404 -> 57573[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48404 -> 57574[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48404 -> 57575[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48404 -> 57576[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48404 -> 57577[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48405 -> 57269[label="",style="dashed", color="red", weight=0]; 130.57/78.23 48405[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (Pos zzz4711) zzz4712 zzz4701 zzz4702 (Pos (Succ (Succ (Succ zzz4703)))) zzz4704 zzz4705 zzz4706 zzz4707 (Pos (Succ zzz4708)) zzz4709 zzz4710 (primCmpNat Zero (Succ (Succ (Succ zzz4703))) == LT)",fontsize=16,color="magenta"];48405 -> 57578[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48405 -> 57579[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48405 -> 57580[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48405 -> 57581[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48405 -> 57582[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48405 -> 57583[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48405 -> 57584[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48405 -> 57585[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48405 -> 57586[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48405 -> 57587[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48405 -> 57588[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48405 -> 57589[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48405 -> 57590[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48405 -> 57591[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 57536[label="zzz3882",fontsize=16,color="green",shape="box"];57537[label="zzz3879",fontsize=16,color="green",shape="box"];57538[label="zzz3883",fontsize=16,color="green",shape="box"];57539[label="zzz3880",fontsize=16,color="green",shape="box"];57540[label="zzz3881",fontsize=16,color="green",shape="box"];57541[label="Succ zzz49580",fontsize=16,color="green",shape="box"];57542[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];57543[label="zzz3885",fontsize=16,color="green",shape="box"];57544[label="zzz3877",fontsize=16,color="green",shape="box"];57545[label="zzz3884",fontsize=16,color="green",shape="box"];57546[label="Succ Zero",fontsize=16,color="green",shape="box"];57547[label="zzz3886",fontsize=16,color="green",shape="box"];57548[label="zzz3878",fontsize=16,color="green",shape="box"];57549[label="zzz3876",fontsize=16,color="green",shape="box"];57550[label="zzz3882",fontsize=16,color="green",shape="box"];57551[label="zzz3879",fontsize=16,color="green",shape="box"];57552[label="zzz3883",fontsize=16,color="green",shape="box"];57553[label="zzz3880",fontsize=16,color="green",shape="box"];57554[label="zzz3881",fontsize=16,color="green",shape="box"];57555[label="Zero",fontsize=16,color="green",shape="box"];57556[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];57557[label="zzz3885",fontsize=16,color="green",shape="box"];57558[label="zzz3877",fontsize=16,color="green",shape="box"];57559[label="zzz3884",fontsize=16,color="green",shape="box"];57560[label="Succ Zero",fontsize=16,color="green",shape="box"];57561[label="zzz3886",fontsize=16,color="green",shape="box"];57562[label="zzz3878",fontsize=16,color="green",shape="box"];57563[label="zzz3876",fontsize=16,color="green",shape="box"];48417 -> 57269[label="",style="dashed", color="red", weight=0]; 130.57/78.23 48417[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpNat (Succ zzz49610) (Succ Zero) == LT)",fontsize=16,color="magenta"];48417 -> 57606[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48417 -> 57607[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48417 -> 57608[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48417 -> 57609[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48417 -> 57610[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48417 -> 57611[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48417 -> 57612[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48417 -> 57613[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48417 -> 57614[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48417 -> 57615[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48417 -> 57616[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48417 -> 57617[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48417 -> 57618[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48417 -> 57619[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48418 -> 57269[label="",style="dashed", color="red", weight=0]; 130.57/78.23 48418[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (Pos zzz300) zzz31 zzz2500 zzz2501 (Pos (Succ Zero)) zzz2503 zzz2504 zzz340 zzz341 (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz343 zzz344 (primCmpNat Zero (Succ Zero) == LT)",fontsize=16,color="magenta"];48418 -> 57620[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48418 -> 57621[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48418 -> 57622[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48418 -> 57623[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48418 -> 57624[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48418 -> 57625[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48418 -> 57626[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48418 -> 57627[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48418 -> 57628[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48418 -> 57629[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48418 -> 57630[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48418 -> 57631[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48418 -> 57632[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48418 -> 57633[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48431[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpInt (Neg (Succ zzz52450)) (Neg (Succ (Succ (Succ zzz5114)))) == LT)",fontsize=16,color="black",shape="box"];48431 -> 48861[label="",style="solid", color="black", weight=3]; 130.57/78.23 48432[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpInt (Neg Zero) (Neg (Succ (Succ (Succ zzz5114)))) == LT)",fontsize=16,color="black",shape="box"];48432 -> 48862[label="",style="solid", color="black", weight=3]; 130.57/78.23 48433[label="zzz4109",fontsize=16,color="green",shape="box"];48434[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpInt (Neg (Succ zzz52420)) (FiniteMap.mkVBalBranch3Size_l zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111) == LT)",fontsize=16,color="black",shape="box"];48434 -> 48863[label="",style="solid", color="black", weight=3]; 130.57/78.23 48435[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111) == LT)",fontsize=16,color="black",shape="box"];48435 -> 48864[label="",style="solid", color="black", weight=3]; 130.57/78.23 48436 -> 62196[label="",style="dashed", color="red", weight=0]; 130.57/78.23 48436[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (Pos zzz3748) zzz3749 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (primCmpNat (Succ Zero) (Succ zzz49680) == LT)",fontsize=16,color="magenta"];48436 -> 62197[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48436 -> 62198[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48436 -> 62199[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48436 -> 62200[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48436 -> 62201[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48436 -> 62202[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48436 -> 62203[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48436 -> 62204[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48436 -> 62205[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48436 -> 62206[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48436 -> 62207[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48436 -> 62208[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48436 -> 62209[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48436 -> 62210[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48437 -> 62196[label="",style="dashed", color="red", weight=0]; 130.57/78.23 48437[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (Pos zzz3748) zzz3749 zzz3739 zzz3740 (Neg (Succ Zero)) zzz3741 zzz3742 zzz3743 zzz3744 (Neg (Succ zzz3745)) zzz3746 zzz3747 (primCmpNat (Succ Zero) Zero == LT)",fontsize=16,color="magenta"];48437 -> 62211[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48437 -> 62212[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48437 -> 62213[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48437 -> 62214[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48437 -> 62215[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48437 -> 62216[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48437 -> 62217[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48437 -> 62218[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48437 -> 62219[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48437 -> 62220[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48437 -> 62221[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48437 -> 62222[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48437 -> 62223[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48437 -> 62224[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64587[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpNat (Succ zzz645400) (Succ zzz64720) == LT)",fontsize=16,color="black",shape="box"];64587 -> 64606[label="",style="solid", color="black", weight=3]; 130.57/78.23 64588[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpNat (Succ zzz645400) Zero == LT)",fontsize=16,color="black",shape="box"];64588 -> 64607[label="",style="solid", color="black", weight=3]; 130.57/78.23 64536[label="FiniteMap.mkBalBranch6MkBalBranch00 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 otherwise",fontsize=16,color="black",shape="box"];64536 -> 64591[label="",style="solid", color="black", weight=3]; 130.57/78.23 64552 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64552[label="primPlusNat (primMulNat (Succ Zero) (Succ zzz645500)) (Succ zzz645500)",fontsize=16,color="magenta"];64552 -> 64592[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64552 -> 64593[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64553[label="Zero",fontsize=16,color="green",shape="box"];64554 -> 64597[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64554[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpNat Zero (Succ zzz64640) == LT)",fontsize=16,color="magenta"];64554 -> 64599[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64554 -> 64600[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64555[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (EQ == LT)",fontsize=16,color="black",shape="triangle"];64555 -> 64595[label="",style="solid", color="black", weight=3]; 130.57/78.23 64565 -> 64484[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64565[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (GT == LT)",fontsize=16,color="magenta"];64566 -> 64555[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64566[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (EQ == LT)",fontsize=16,color="magenta"];64556[label="FiniteMap.mkBalBranch6Single_L (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344)",fontsize=16,color="black",shape="box"];64556 -> 64596[label="",style="solid", color="black", weight=3]; 130.57/78.23 64603[label="zzz64550",fontsize=16,color="green",shape="box"];64604[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpNat (Succ zzz64740) (Succ zzz645400) == LT)",fontsize=16,color="black",shape="box"];64604 -> 64624[label="",style="solid", color="black", weight=3]; 130.57/78.23 64605[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpNat Zero (Succ zzz645400) == LT)",fontsize=16,color="black",shape="box"];64605 -> 64625[label="",style="solid", color="black", weight=3]; 130.57/78.23 64574 -> 64489[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64574[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (LT == LT)",fontsize=16,color="magenta"];64575 -> 64555[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64575[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (EQ == LT)",fontsize=16,color="magenta"];64589 -> 64583[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64589[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpNat (Succ zzz64700) Zero == LT)",fontsize=16,color="magenta"];64589 -> 64608[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64589 -> 64609[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64590 -> 64555[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64590[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (EQ == LT)",fontsize=16,color="magenta"];64576[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat (Succ zzz6452000) zzz64560 == GT)",fontsize=16,color="burlywood",shape="box"];65736[label="zzz64560/Succ zzz645600",fontsize=10,color="white",style="solid",shape="box"];64576 -> 65736[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65736 -> 64610[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65737[label="zzz64560/Zero",fontsize=10,color="white",style="solid",shape="box"];64576 -> 65737[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65737 -> 64611[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64577[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat Zero zzz64560 == GT)",fontsize=16,color="burlywood",shape="box"];65738[label="zzz64560/Succ zzz645600",fontsize=10,color="white",style="solid",shape="box"];64577 -> 65738[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65738 -> 64612[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65739[label="zzz64560/Zero",fontsize=10,color="white",style="solid",shape="box"];64577 -> 65739[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65739 -> 64613[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64578[label="FiniteMap.mkBalBranch6MkBalBranch1 zzz474034 zzz474030 zzz474031 FiniteMap.EmptyFM FiniteMap.EmptyFM zzz474034 FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];64578 -> 64614[label="",style="solid", color="black", weight=3]; 130.57/78.23 64579[label="FiniteMap.mkBalBranch6MkBalBranch1 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734)",fontsize=16,color="black",shape="box"];64579 -> 64615[label="",style="solid", color="black", weight=3]; 130.57/78.23 64580[label="FiniteMap.mkBalBranch6MkBalBranch2 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 True",fontsize=16,color="black",shape="box"];64580 -> 64616[label="",style="solid", color="black", weight=3]; 130.57/78.23 64581[label="zzz64610",fontsize=16,color="green",shape="box"];64582[label="zzz645200",fontsize=16,color="green",shape="box"];62071[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (Neg zzz6304) zzz6305 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 otherwise",fontsize=16,color="black",shape="box"];62071 -> 62103[label="",style="solid", color="black", weight=3]; 130.57/78.23 62072 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.23 62072[label="FiniteMap.mkBalBranch zzz6294 zzz6295 zzz6297 (FiniteMap.mkVBalBranch (Neg zzz6304) zzz6305 zzz6298 (FiniteMap.Branch zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303))",fontsize=16,color="magenta"];62072 -> 63342[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62072 -> 63343[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62072 -> 63344[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62072 -> 63345[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48815 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.23 48815[label="primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000)",fontsize=16,color="magenta"];48815 -> 49573[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48815 -> 49574[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48816[label="Zero",fontsize=16,color="green",shape="box"];48817[label="Succ (primPlusNat Zero Zero)",fontsize=16,color="green",shape="box"];48817 -> 49575[label="",style="dashed", color="green", weight=3]; 130.57/78.23 48818[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (FiniteMap.sizeFM (FiniteMap.Branch zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];48818 -> 49576[label="",style="solid", color="black", weight=3]; 130.57/78.23 48819[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero)) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];48819 -> 49577[label="",style="solid", color="black", weight=3]; 130.57/78.23 48820 -> 49578[label="",style="dashed", color="red", weight=0]; 130.57/78.23 48820[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234 (primCmpInt (Neg (primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz523200)) (Succ zzz523200))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg (Succ zzz523200)) zzz5233 zzz5234) == LT)",fontsize=16,color="magenta"];48820 -> 49725[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48821[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (Neg Zero) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];48821 -> 49774[label="",style="solid", color="black", weight=3]; 130.57/78.23 48822[label="Succ zzz332000",fontsize=16,color="green",shape="box"];48823[label="Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))",fontsize=16,color="green",shape="box"];48823 -> 49775[label="",style="dashed", color="green", weight=3]; 130.57/78.23 48824 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.23 48824[label="primPlusNat (Succ (primPlusNat Zero Zero)) Zero",fontsize=16,color="magenta"];48824 -> 49776[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48824 -> 49777[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48825[label="Succ zzz332000",fontsize=16,color="green",shape="box"];48826[label="Succ (primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000))",fontsize=16,color="green",shape="box"];48826 -> 49778[label="",style="dashed", color="green", weight=3]; 130.57/78.23 48827 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.23 48827[label="primPlusNat (Succ (primPlusNat Zero Zero)) Zero",fontsize=16,color="magenta"];48827 -> 49779[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48827 -> 49780[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 45992 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.23 45992[label="primPlusNat zzz37520 (Succ (Succ zzz375300))",fontsize=16,color="magenta"];45992 -> 47194[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 45992 -> 47195[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 57564[label="zzz4708",fontsize=16,color="green",shape="box"];57565[label="zzz4705",fontsize=16,color="green",shape="box"];57566[label="zzz4709",fontsize=16,color="green",shape="box"];57567[label="zzz4706",fontsize=16,color="green",shape="box"];57568[label="zzz4707",fontsize=16,color="green",shape="box"];57569[label="Succ zzz49560",fontsize=16,color="green",shape="box"];57570[label="Succ (Succ (Succ zzz4703))",fontsize=16,color="green",shape="box"];57571[label="zzz4711",fontsize=16,color="green",shape="box"];57572[label="zzz4702",fontsize=16,color="green",shape="box"];57573[label="zzz4710",fontsize=16,color="green",shape="box"];57574[label="Succ (Succ zzz4703)",fontsize=16,color="green",shape="box"];57575[label="zzz4712",fontsize=16,color="green",shape="box"];57576[label="zzz4704",fontsize=16,color="green",shape="box"];57577[label="zzz4701",fontsize=16,color="green",shape="box"];57578[label="zzz4708",fontsize=16,color="green",shape="box"];57579[label="zzz4705",fontsize=16,color="green",shape="box"];57580[label="zzz4709",fontsize=16,color="green",shape="box"];57581[label="zzz4706",fontsize=16,color="green",shape="box"];57582[label="zzz4707",fontsize=16,color="green",shape="box"];57583[label="Zero",fontsize=16,color="green",shape="box"];57584[label="Succ (Succ (Succ zzz4703))",fontsize=16,color="green",shape="box"];57585[label="zzz4711",fontsize=16,color="green",shape="box"];57586[label="zzz4702",fontsize=16,color="green",shape="box"];57587[label="zzz4710",fontsize=16,color="green",shape="box"];57588[label="Succ (Succ zzz4703)",fontsize=16,color="green",shape="box"];57589[label="zzz4712",fontsize=16,color="green",shape="box"];57590[label="zzz4704",fontsize=16,color="green",shape="box"];57591[label="zzz4701",fontsize=16,color="green",shape="box"];57606[label="Succ (Succ (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];57607[label="zzz2504",fontsize=16,color="green",shape="box"];57608[label="zzz343",fontsize=16,color="green",shape="box"];57609[label="zzz340",fontsize=16,color="green",shape="box"];57610[label="zzz341",fontsize=16,color="green",shape="box"];57611[label="Succ zzz49610",fontsize=16,color="green",shape="box"];57612[label="Succ Zero",fontsize=16,color="green",shape="box"];57613[label="zzz300",fontsize=16,color="green",shape="box"];57614[label="zzz2501",fontsize=16,color="green",shape="box"];57615[label="zzz344",fontsize=16,color="green",shape="box"];57616[label="Zero",fontsize=16,color="green",shape="box"];57617[label="zzz31",fontsize=16,color="green",shape="box"];57618[label="zzz2503",fontsize=16,color="green",shape="box"];57619[label="zzz2500",fontsize=16,color="green",shape="box"];57620[label="Succ (Succ (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];57621[label="zzz2504",fontsize=16,color="green",shape="box"];57622[label="zzz343",fontsize=16,color="green",shape="box"];57623[label="zzz340",fontsize=16,color="green",shape="box"];57624[label="zzz341",fontsize=16,color="green",shape="box"];57625[label="Zero",fontsize=16,color="green",shape="box"];57626[label="Succ Zero",fontsize=16,color="green",shape="box"];57627[label="zzz300",fontsize=16,color="green",shape="box"];57628[label="zzz2501",fontsize=16,color="green",shape="box"];57629[label="zzz344",fontsize=16,color="green",shape="box"];57630[label="Zero",fontsize=16,color="green",shape="box"];57631[label="zzz31",fontsize=16,color="green",shape="box"];57632[label="zzz2503",fontsize=16,color="green",shape="box"];57633[label="zzz2500",fontsize=16,color="green",shape="box"];48861 -> 62196[label="",style="dashed", color="red", weight=0]; 130.57/78.23 48861[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpNat (Succ (Succ (Succ zzz5114))) (Succ zzz52450) == LT)",fontsize=16,color="magenta"];48861 -> 62225[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48861 -> 62226[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48861 -> 62227[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48861 -> 62228[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48861 -> 62229[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48861 -> 62230[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48861 -> 62231[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48861 -> 62232[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48861 -> 62233[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48861 -> 62234[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48861 -> 62235[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48861 -> 62236[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48861 -> 62237[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48861 -> 62238[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48862 -> 62196[label="",style="dashed", color="red", weight=0]; 130.57/78.23 48862[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (Pos zzz5122) zzz5123 zzz5112 zzz5113 (Neg (Succ (Succ (Succ zzz5114)))) zzz5115 zzz5116 zzz5117 zzz5118 (Neg (Succ zzz5119)) zzz5120 zzz5121 (primCmpNat (Succ (Succ (Succ zzz5114))) Zero == LT)",fontsize=16,color="magenta"];48862 -> 62239[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48862 -> 62240[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48862 -> 62241[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48862 -> 62242[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48862 -> 62243[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48862 -> 62244[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48862 -> 62245[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48862 -> 62246[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48862 -> 62247[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48862 -> 62248[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48862 -> 62249[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48862 -> 62250[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48862 -> 62251[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48862 -> 62252[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 48863[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpInt (Neg (Succ zzz52420)) (FiniteMap.sizeFM (FiniteMap.Branch zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106)) == LT)",fontsize=16,color="black",shape="box"];48863 -> 49900[label="",style="solid", color="black", weight=3]; 130.57/78.23 48864[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106)) == LT)",fontsize=16,color="black",shape="box"];48864 -> 49901[label="",style="solid", color="black", weight=3]; 130.57/78.23 62197[label="zzz3749",fontsize=16,color="green",shape="box"];62198[label="Succ Zero",fontsize=16,color="green",shape="box"];62199[label="Succ zzz49680",fontsize=16,color="green",shape="box"];62200[label="zzz3742",fontsize=16,color="green",shape="box"];62201[label="zzz3747",fontsize=16,color="green",shape="box"];62202[label="zzz3739",fontsize=16,color="green",shape="box"];62203[label="zzz3748",fontsize=16,color="green",shape="box"];62204[label="zzz3740",fontsize=16,color="green",shape="box"];62205[label="zzz3746",fontsize=16,color="green",shape="box"];62206[label="Zero",fontsize=16,color="green",shape="box"];62207[label="zzz3744",fontsize=16,color="green",shape="box"];62208[label="zzz3745",fontsize=16,color="green",shape="box"];62209[label="zzz3741",fontsize=16,color="green",shape="box"];62210[label="zzz3743",fontsize=16,color="green",shape="box"];62196[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (Pos zzz6333) zzz6334 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (primCmpNat zzz6335 zzz6336 == LT)",fontsize=16,color="burlywood",shape="triangle"];65740[label="zzz6335/Succ zzz63350",fontsize=10,color="white",style="solid",shape="box"];62196 -> 65740[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65740 -> 62456[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65741[label="zzz6335/Zero",fontsize=10,color="white",style="solid",shape="box"];62196 -> 65741[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65741 -> 62457[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 62211[label="zzz3749",fontsize=16,color="green",shape="box"];62212[label="Succ Zero",fontsize=16,color="green",shape="box"];62213[label="Zero",fontsize=16,color="green",shape="box"];62214[label="zzz3742",fontsize=16,color="green",shape="box"];62215[label="zzz3747",fontsize=16,color="green",shape="box"];62216[label="zzz3739",fontsize=16,color="green",shape="box"];62217[label="zzz3748",fontsize=16,color="green",shape="box"];62218[label="zzz3740",fontsize=16,color="green",shape="box"];62219[label="zzz3746",fontsize=16,color="green",shape="box"];62220[label="Zero",fontsize=16,color="green",shape="box"];62221[label="zzz3744",fontsize=16,color="green",shape="box"];62222[label="zzz3745",fontsize=16,color="green",shape="box"];62223[label="zzz3741",fontsize=16,color="green",shape="box"];62224[label="zzz3743",fontsize=16,color="green",shape="box"];64606[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpNat zzz645400 zzz64720 == LT)",fontsize=16,color="burlywood",shape="triangle"];65742[label="zzz645400/Succ zzz6454000",fontsize=10,color="white",style="solid",shape="box"];64606 -> 65742[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65742 -> 64626[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65743[label="zzz645400/Zero",fontsize=10,color="white",style="solid",shape="box"];64606 -> 65743[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65743 -> 64627[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64607 -> 64484[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64607[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (GT == LT)",fontsize=16,color="magenta"];64591[label="FiniteMap.mkBalBranch6MkBalBranch00 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 True",fontsize=16,color="black",shape="box"];64591 -> 64617[label="",style="solid", color="black", weight=3]; 130.57/78.23 64592[label="Succ zzz645500",fontsize=16,color="green",shape="box"];64593 -> 44357[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64593[label="primMulNat (Succ Zero) (Succ zzz645500)",fontsize=16,color="magenta"];64593 -> 64618[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64599[label="Zero",fontsize=16,color="green",shape="box"];64600[label="zzz64640",fontsize=16,color="green",shape="box"];64595 -> 64511[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64595[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 False",fontsize=16,color="magenta"];64596 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64596[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ Zero)))) zzz4740340 zzz4740341 (FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ Zero))))) zzz474030 zzz474031 zzz6373 zzz4740343) zzz4740344",fontsize=16,color="magenta"];64596 -> 64619[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64596 -> 64620[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64596 -> 64621[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64596 -> 64622[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64596 -> 64623[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64624 -> 64606[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64624[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpNat zzz64740 zzz645400 == LT)",fontsize=16,color="magenta"];64624 -> 64645[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64624 -> 64646[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64625 -> 64489[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64625[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (LT == LT)",fontsize=16,color="magenta"];64608[label="zzz64700",fontsize=16,color="green",shape="box"];64609[label="Zero",fontsize=16,color="green",shape="box"];64610[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat (Succ zzz6452000) (Succ zzz645600) == GT)",fontsize=16,color="black",shape="box"];64610 -> 64628[label="",style="solid", color="black", weight=3]; 130.57/78.23 64611[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat (Succ zzz6452000) Zero == GT)",fontsize=16,color="black",shape="box"];64611 -> 64629[label="",style="solid", color="black", weight=3]; 130.57/78.23 64612[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat Zero (Succ zzz645600) == GT)",fontsize=16,color="black",shape="box"];64612 -> 64630[label="",style="solid", color="black", weight=3]; 130.57/78.23 64613[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];64613 -> 64631[label="",style="solid", color="black", weight=3]; 130.57/78.23 64614[label="error []",fontsize=16,color="red",shape="box"];64615[label="FiniteMap.mkBalBranch6MkBalBranch12 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734)",fontsize=16,color="black",shape="box"];64615 -> 64632[label="",style="solid", color="black", weight=3]; 130.57/78.23 64616 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64616[label="FiniteMap.mkBranch (Pos (Succ (Succ Zero))) zzz474030 zzz474031 zzz6373 zzz474034",fontsize=16,color="magenta"];64616 -> 64633[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64616 -> 64634[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64616 -> 64635[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64616 -> 64636[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64616 -> 64637[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62103[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 (Neg zzz6304) zzz6305 zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298 zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303 True",fontsize=16,color="black",shape="box"];62103 -> 62142[label="",style="solid", color="black", weight=3]; 130.57/78.23 63342[label="zzz6294",fontsize=16,color="green",shape="box"];63343 -> 63190[label="",style="dashed", color="red", weight=0]; 130.57/78.23 63343[label="FiniteMap.mkVBalBranch (Neg zzz6304) zzz6305 zzz6298 (FiniteMap.Branch zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303)",fontsize=16,color="magenta"];63343 -> 63557[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63343 -> 63558[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63343 -> 63559[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63343 -> 63560[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63343 -> 63561[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63343 -> 63562[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63343 -> 63563[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63343 -> 63564[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63344[label="zzz6297",fontsize=16,color="green",shape="box"];63345[label="zzz6295",fontsize=16,color="green",shape="box"];49573[label="Succ zzz332000",fontsize=16,color="green",shape="box"];49574[label="Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))",fontsize=16,color="green",shape="box"];49574 -> 50590[label="",style="dashed", color="green", weight=3]; 130.57/78.23 49575 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.23 49575[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];49575 -> 50591[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 49575 -> 50592[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 49576[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (primCmpInt (primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos (Succ Zero))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];49576 -> 50593[label="",style="solid", color="black", weight=3]; 130.57/78.23 49577[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (Pos Zero) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) == LT)",fontsize=16,color="black",shape="box"];49577 -> 50594[label="",style="solid", color="black", weight=3]; 130.57/78.23 49725 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.23 49725[label="primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz523200)) (Succ zzz523200)",fontsize=16,color="magenta"];49725 -> 50595[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 49725 -> 50596[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 49774[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (Neg Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];49774 -> 50597[label="",style="solid", color="black", weight=3]; 130.57/78.23 49775 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.23 49775[label="primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000)",fontsize=16,color="magenta"];49775 -> 50598[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 49775 -> 50599[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 49776[label="Zero",fontsize=16,color="green",shape="box"];49777[label="Succ (primPlusNat Zero Zero)",fontsize=16,color="green",shape="box"];49777 -> 50600[label="",style="dashed", color="green", weight=3]; 130.57/78.23 49778 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.23 49778[label="primPlusNat (Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))) (Succ zzz332000)",fontsize=16,color="magenta"];49778 -> 50601[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 49778 -> 50602[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 49779[label="Zero",fontsize=16,color="green",shape="box"];49780[label="Succ (primPlusNat Zero Zero)",fontsize=16,color="green",shape="box"];49780 -> 50603[label="",style="dashed", color="green", weight=3]; 130.57/78.23 47194[label="Succ (Succ zzz375300)",fontsize=16,color="green",shape="box"];47195[label="zzz37520",fontsize=16,color="green",shape="box"];62225[label="zzz5123",fontsize=16,color="green",shape="box"];62226[label="Succ (Succ (Succ zzz5114))",fontsize=16,color="green",shape="box"];62227[label="Succ zzz52450",fontsize=16,color="green",shape="box"];62228[label="zzz5116",fontsize=16,color="green",shape="box"];62229[label="zzz5121",fontsize=16,color="green",shape="box"];62230[label="zzz5112",fontsize=16,color="green",shape="box"];62231[label="zzz5122",fontsize=16,color="green",shape="box"];62232[label="zzz5113",fontsize=16,color="green",shape="box"];62233[label="zzz5120",fontsize=16,color="green",shape="box"];62234[label="Succ (Succ zzz5114)",fontsize=16,color="green",shape="box"];62235[label="zzz5118",fontsize=16,color="green",shape="box"];62236[label="zzz5119",fontsize=16,color="green",shape="box"];62237[label="zzz5115",fontsize=16,color="green",shape="box"];62238[label="zzz5117",fontsize=16,color="green",shape="box"];62239[label="zzz5123",fontsize=16,color="green",shape="box"];62240[label="Succ (Succ (Succ zzz5114))",fontsize=16,color="green",shape="box"];62241[label="Zero",fontsize=16,color="green",shape="box"];62242[label="zzz5116",fontsize=16,color="green",shape="box"];62243[label="zzz5121",fontsize=16,color="green",shape="box"];62244[label="zzz5112",fontsize=16,color="green",shape="box"];62245[label="zzz5122",fontsize=16,color="green",shape="box"];62246[label="zzz5113",fontsize=16,color="green",shape="box"];62247[label="zzz5120",fontsize=16,color="green",shape="box"];62248[label="Succ (Succ zzz5114)",fontsize=16,color="green",shape="box"];62249[label="zzz5118",fontsize=16,color="green",shape="box"];62250[label="zzz5119",fontsize=16,color="green",shape="box"];62251[label="zzz5115",fontsize=16,color="green",shape="box"];62252[label="zzz5117",fontsize=16,color="green",shape="box"];49900[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpInt (Neg (Succ zzz52420)) (Neg (Succ (Succ Zero))) == LT)",fontsize=16,color="black",shape="box"];49900 -> 50641[label="",style="solid", color="black", weight=3]; 130.57/78.23 49901[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpInt (Neg Zero) (Neg (Succ (Succ Zero))) == LT)",fontsize=16,color="black",shape="box"];49901 -> 50642[label="",style="solid", color="black", weight=3]; 130.57/78.23 62456[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (Pos zzz6333) zzz6334 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (primCmpNat (Succ zzz63350) zzz6336 == LT)",fontsize=16,color="burlywood",shape="box"];65744[label="zzz6336/Succ zzz63360",fontsize=10,color="white",style="solid",shape="box"];62456 -> 65744[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65744 -> 62465[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65745[label="zzz6336/Zero",fontsize=10,color="white",style="solid",shape="box"];62456 -> 65745[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65745 -> 62466[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 62457[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (Pos zzz6333) zzz6334 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (primCmpNat Zero zzz6336 == LT)",fontsize=16,color="burlywood",shape="box"];65746[label="zzz6336/Succ zzz63360",fontsize=10,color="white",style="solid",shape="box"];62457 -> 65746[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65746 -> 62467[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65747[label="zzz6336/Zero",fontsize=10,color="white",style="solid",shape="box"];62457 -> 65747[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65747 -> 62468[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64626[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpNat (Succ zzz6454000) zzz64720 == LT)",fontsize=16,color="burlywood",shape="box"];65748[label="zzz64720/Succ zzz647200",fontsize=10,color="white",style="solid",shape="box"];64626 -> 65748[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65748 -> 64647[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65749[label="zzz64720/Zero",fontsize=10,color="white",style="solid",shape="box"];64626 -> 65749[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65749 -> 64648[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64627[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpNat Zero zzz64720 == LT)",fontsize=16,color="burlywood",shape="box"];65750[label="zzz64720/Succ zzz647200",fontsize=10,color="white",style="solid",shape="box"];64627 -> 65750[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65750 -> 64649[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65751[label="zzz64720/Zero",fontsize=10,color="white",style="solid",shape="box"];64627 -> 65751[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65751 -> 64650[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64617[label="FiniteMap.mkBalBranch6Double_L (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344)",fontsize=16,color="burlywood",shape="box"];65752[label="zzz4740343/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];64617 -> 65752[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65752 -> 64638[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65753[label="zzz4740343/FiniteMap.Branch zzz47403430 zzz47403431 zzz47403432 zzz47403433 zzz47403434",fontsize=10,color="white",style="solid",shape="box"];64617 -> 65753[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65753 -> 64639[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64618[label="zzz645500",fontsize=16,color="green",shape="box"];64619[label="zzz4740341",fontsize=16,color="green",shape="box"];64620[label="zzz4740340",fontsize=16,color="green",shape="box"];64621[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];64622[label="zzz4740344",fontsize=16,color="green",shape="box"];64623 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64623[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ Zero))))) zzz474030 zzz474031 zzz6373 zzz4740343",fontsize=16,color="magenta"];64623 -> 64640[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64623 -> 64641[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64623 -> 64642[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64623 -> 64643[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64623 -> 64644[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64645[label="zzz645400",fontsize=16,color="green",shape="box"];64646[label="zzz64740",fontsize=16,color="green",shape="box"];64628 -> 64523[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64628[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (primCmpNat zzz6452000 zzz645600 == GT)",fontsize=16,color="magenta"];64628 -> 64651[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64628 -> 64652[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64629 -> 64466[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64629[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (GT == GT)",fontsize=16,color="magenta"];64630 -> 64474[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64630[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (LT == GT)",fontsize=16,color="magenta"];64631 -> 64499[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64631[label="FiniteMap.mkBalBranch6MkBalBranch3 zzz474034 zzz474030 zzz474031 zzz6373 zzz474030 zzz474031 zzz6373 zzz474034 (EQ == GT)",fontsize=16,color="magenta"];64632 -> 64653[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64632[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (FiniteMap.sizeFM zzz63734 < Pos (Succ (Succ Zero)) * FiniteMap.sizeFM zzz63733)",fontsize=16,color="magenta"];64632 -> 64654[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64632 -> 64655[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64633[label="zzz474031",fontsize=16,color="green",shape="box"];64634[label="zzz474030",fontsize=16,color="green",shape="box"];64635[label="Succ Zero",fontsize=16,color="green",shape="box"];64636[label="zzz474034",fontsize=16,color="green",shape="box"];64637[label="zzz6373",fontsize=16,color="green",shape="box"];62142 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.23 62142[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Neg zzz6304) zzz6305 (FiniteMap.Branch zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298) (FiniteMap.Branch zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303)",fontsize=16,color="magenta"];62142 -> 62176[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62142 -> 62177[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62142 -> 62178[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62142 -> 62179[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62142 -> 62180[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63557[label="zzz6299",fontsize=16,color="green",shape="box"];63558[label="zzz6304",fontsize=16,color="green",shape="box"];63559[label="zzz6298",fontsize=16,color="green",shape="box"];63560[label="zzz6302",fontsize=16,color="green",shape="box"];63561[label="zzz6301",fontsize=16,color="green",shape="box"];63562[label="zzz6300",fontsize=16,color="green",shape="box"];63563[label="zzz6305",fontsize=16,color="green",shape="box"];63564[label="zzz6303",fontsize=16,color="green",shape="box"];50590 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.23 50590[label="primPlusNat (Succ zzz332000) (Succ zzz332000)",fontsize=16,color="magenta"];50590 -> 50852[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50590 -> 50853[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50591[label="Zero",fontsize=16,color="green",shape="box"];50592[label="Zero",fontsize=16,color="green",shape="box"];50593 -> 50854[label="",style="dashed", color="red", weight=0]; 130.57/78.23 50593[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234 (primCmpInt (Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ Zero))) (FiniteMap.mkVBalBranch3Size_l zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos (Succ Zero)) zzz5233 zzz5234) == LT)",fontsize=16,color="magenta"];50593 -> 50889[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50594[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (Pos Zero) (FiniteMap.sizeFM (FiniteMap.Branch zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334)) == LT)",fontsize=16,color="black",shape="box"];50594 -> 50902[label="",style="solid", color="black", weight=3]; 130.57/78.23 50595[label="Succ zzz523200",fontsize=16,color="green",shape="box"];50596 -> 43384[label="",style="dashed", color="red", weight=0]; 130.57/78.23 50596[label="primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ zzz523200)",fontsize=16,color="magenta"];50596 -> 50903[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50597[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (primCmpInt (Neg Zero) (Pos (Succ zzz33200)) == LT)",fontsize=16,color="black",shape="box"];50597 -> 50904[label="",style="solid", color="black", weight=3]; 130.57/78.23 50598[label="Succ zzz332000",fontsize=16,color="green",shape="box"];50599[label="Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))",fontsize=16,color="green",shape="box"];50599 -> 50905[label="",style="dashed", color="green", weight=3]; 130.57/78.23 50600 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.23 50600[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];50600 -> 50906[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50600 -> 50907[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50601[label="Succ zzz332000",fontsize=16,color="green",shape="box"];50602[label="Succ (primPlusNat (Succ zzz332000) (Succ zzz332000))",fontsize=16,color="green",shape="box"];50602 -> 50908[label="",style="dashed", color="green", weight=3]; 130.57/78.23 50603 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.23 50603[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];50603 -> 50909[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50603 -> 50910[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50641 -> 62196[label="",style="dashed", color="red", weight=0]; 130.57/78.23 50641[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpNat (Succ (Succ Zero)) (Succ zzz52420) == LT)",fontsize=16,color="magenta"];50641 -> 62281[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50641 -> 62282[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50641 -> 62283[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50641 -> 62284[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50641 -> 62285[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50641 -> 62286[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50641 -> 62287[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50641 -> 62288[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50641 -> 62289[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50641 -> 62290[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50641 -> 62291[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50641 -> 62292[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50641 -> 62293[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50641 -> 62294[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50642 -> 62196[label="",style="dashed", color="red", weight=0]; 130.57/78.23 50642[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (Pos zzz4112) zzz4113 zzz4103 zzz4104 (Neg (Succ (Succ Zero))) zzz4105 zzz4106 zzz4107 zzz4108 (Neg (Succ zzz4109)) zzz4110 zzz4111 (primCmpNat (Succ (Succ Zero)) Zero == LT)",fontsize=16,color="magenta"];50642 -> 62295[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50642 -> 62296[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50642 -> 62297[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50642 -> 62298[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50642 -> 62299[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50642 -> 62300[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50642 -> 62301[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50642 -> 62302[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50642 -> 62303[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50642 -> 62304[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50642 -> 62305[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50642 -> 62306[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50642 -> 62307[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50642 -> 62308[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62465[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (Pos zzz6333) zzz6334 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (primCmpNat (Succ zzz63350) (Succ zzz63360) == LT)",fontsize=16,color="black",shape="box"];62465 -> 62482[label="",style="solid", color="black", weight=3]; 130.57/78.23 62466[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (Pos zzz6333) zzz6334 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (primCmpNat (Succ zzz63350) Zero == LT)",fontsize=16,color="black",shape="box"];62466 -> 62483[label="",style="solid", color="black", weight=3]; 130.57/78.23 62467[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (Pos zzz6333) zzz6334 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (primCmpNat Zero (Succ zzz63360) == LT)",fontsize=16,color="black",shape="box"];62467 -> 62484[label="",style="solid", color="black", weight=3]; 130.57/78.23 62468[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (Pos zzz6333) zzz6334 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];62468 -> 62485[label="",style="solid", color="black", weight=3]; 130.57/78.23 64647[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpNat (Succ zzz6454000) (Succ zzz647200) == LT)",fontsize=16,color="black",shape="box"];64647 -> 64656[label="",style="solid", color="black", weight=3]; 130.57/78.23 64648[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpNat (Succ zzz6454000) Zero == LT)",fontsize=16,color="black",shape="box"];64648 -> 64657[label="",style="solid", color="black", weight=3]; 130.57/78.23 64649[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpNat Zero (Succ zzz647200) == LT)",fontsize=16,color="black",shape="box"];64649 -> 64658[label="",style="solid", color="black", weight=3]; 130.57/78.23 64650[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];64650 -> 64659[label="",style="solid", color="black", weight=3]; 130.57/78.23 64638[label="FiniteMap.mkBalBranch6Double_L (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 FiniteMap.EmptyFM zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 FiniteMap.EmptyFM zzz4740344)",fontsize=16,color="black",shape="box"];64638 -> 64660[label="",style="solid", color="black", weight=3]; 130.57/78.23 64639[label="FiniteMap.mkBalBranch6Double_L (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 (FiniteMap.Branch zzz47403430 zzz47403431 zzz47403432 zzz47403433 zzz47403434) zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 (FiniteMap.Branch zzz47403430 zzz47403431 zzz47403432 zzz47403433 zzz47403434) zzz4740344)",fontsize=16,color="black",shape="box"];64639 -> 64661[label="",style="solid", color="black", weight=3]; 130.57/78.23 64640[label="zzz474031",fontsize=16,color="green",shape="box"];64641[label="zzz474030",fontsize=16,color="green",shape="box"];64642[label="Succ (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];64643[label="zzz4740343",fontsize=16,color="green",shape="box"];64644[label="zzz6373",fontsize=16,color="green",shape="box"];64651[label="zzz6452000",fontsize=16,color="green",shape="box"];64652[label="zzz645600",fontsize=16,color="green",shape="box"];64654 -> 54589[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64654[label="FiniteMap.sizeFM zzz63733",fontsize=16,color="magenta"];64654 -> 64662[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64655 -> 54589[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64655[label="FiniteMap.sizeFM zzz63734",fontsize=16,color="magenta"];64655 -> 64663[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64653[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (zzz6476 < Pos (Succ (Succ Zero)) * zzz6477)",fontsize=16,color="black",shape="triangle"];64653 -> 64664[label="",style="solid", color="black", weight=3]; 130.57/78.23 62176[label="zzz6305",fontsize=16,color="green",shape="box"];62177[label="Neg zzz6304",fontsize=16,color="green",shape="box"];62178[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];62179[label="FiniteMap.Branch zzz6299 zzz6300 (Neg (Succ zzz6301)) zzz6302 zzz6303",fontsize=16,color="green",shape="box"];62180[label="FiniteMap.Branch zzz6294 zzz6295 (Neg (Succ zzz6296)) zzz6297 zzz6298",fontsize=16,color="green",shape="box"];50852[label="Succ zzz332000",fontsize=16,color="green",shape="box"];50853[label="Succ zzz332000",fontsize=16,color="green",shape="box"];50889 -> 43358[label="",style="dashed", color="red", weight=0]; 130.57/78.23 50889[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ Zero)",fontsize=16,color="magenta"];50889 -> 51536[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50902[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpInt (Pos Zero) (Pos (Succ zzz33200)) == LT)",fontsize=16,color="black",shape="box"];50902 -> 51537[label="",style="solid", color="black", weight=3]; 130.57/78.23 50903[label="zzz523200",fontsize=16,color="green",shape="box"];50904[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (LT == LT)",fontsize=16,color="black",shape="box"];50904 -> 51538[label="",style="solid", color="black", weight=3]; 130.57/78.23 50905 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.23 50905[label="primPlusNat (Succ zzz332000) (Succ zzz332000)",fontsize=16,color="magenta"];50905 -> 51539[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50905 -> 51540[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50906[label="Zero",fontsize=16,color="green",shape="box"];50907[label="Zero",fontsize=16,color="green",shape="box"];50908 -> 42929[label="",style="dashed", color="red", weight=0]; 130.57/78.23 50908[label="primPlusNat (Succ zzz332000) (Succ zzz332000)",fontsize=16,color="magenta"];50908 -> 51541[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50908 -> 51542[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 50909[label="Zero",fontsize=16,color="green",shape="box"];50910[label="Zero",fontsize=16,color="green",shape="box"];62281[label="zzz4113",fontsize=16,color="green",shape="box"];62282[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];62283[label="Succ zzz52420",fontsize=16,color="green",shape="box"];62284[label="zzz4106",fontsize=16,color="green",shape="box"];62285[label="zzz4111",fontsize=16,color="green",shape="box"];62286[label="zzz4103",fontsize=16,color="green",shape="box"];62287[label="zzz4112",fontsize=16,color="green",shape="box"];62288[label="zzz4104",fontsize=16,color="green",shape="box"];62289[label="zzz4110",fontsize=16,color="green",shape="box"];62290[label="Succ Zero",fontsize=16,color="green",shape="box"];62291[label="zzz4108",fontsize=16,color="green",shape="box"];62292[label="zzz4109",fontsize=16,color="green",shape="box"];62293[label="zzz4105",fontsize=16,color="green",shape="box"];62294[label="zzz4107",fontsize=16,color="green",shape="box"];62295[label="zzz4113",fontsize=16,color="green",shape="box"];62296[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];62297[label="Zero",fontsize=16,color="green",shape="box"];62298[label="zzz4106",fontsize=16,color="green",shape="box"];62299[label="zzz4111",fontsize=16,color="green",shape="box"];62300[label="zzz4103",fontsize=16,color="green",shape="box"];62301[label="zzz4112",fontsize=16,color="green",shape="box"];62302[label="zzz4104",fontsize=16,color="green",shape="box"];62303[label="zzz4110",fontsize=16,color="green",shape="box"];62304[label="Succ Zero",fontsize=16,color="green",shape="box"];62305[label="zzz4108",fontsize=16,color="green",shape="box"];62306[label="zzz4109",fontsize=16,color="green",shape="box"];62307[label="zzz4105",fontsize=16,color="green",shape="box"];62308[label="zzz4107",fontsize=16,color="green",shape="box"];62482 -> 62196[label="",style="dashed", color="red", weight=0]; 130.57/78.23 62482[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (Pos zzz6333) zzz6334 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (primCmpNat zzz63350 zzz63360 == LT)",fontsize=16,color="magenta"];62482 -> 62494[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62482 -> 62495[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62483[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (Pos zzz6333) zzz6334 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (GT == LT)",fontsize=16,color="black",shape="box"];62483 -> 62496[label="",style="solid", color="black", weight=3]; 130.57/78.23 62484[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (Pos zzz6333) zzz6334 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (LT == LT)",fontsize=16,color="black",shape="box"];62484 -> 62497[label="",style="solid", color="black", weight=3]; 130.57/78.23 62485[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (Pos zzz6333) zzz6334 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (EQ == LT)",fontsize=16,color="black",shape="box"];62485 -> 62498[label="",style="solid", color="black", weight=3]; 130.57/78.23 64656 -> 64606[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64656[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (primCmpNat zzz6454000 zzz647200 == LT)",fontsize=16,color="magenta"];64656 -> 64665[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64656 -> 64666[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64657 -> 64484[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64657[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (GT == LT)",fontsize=16,color="magenta"];64658 -> 64489[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64658[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (LT == LT)",fontsize=16,color="magenta"];64659 -> 64555[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64659[label="FiniteMap.mkBalBranch6MkBalBranch01 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz474030 zzz474031 zzz6373 zzz6373 (FiniteMap.Branch zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344) zzz4740340 zzz4740341 zzz4740342 zzz4740343 zzz4740344 (EQ == LT)",fontsize=16,color="magenta"];64660[label="error []",fontsize=16,color="red",shape="box"];64661 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64661[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) zzz47403430 zzz47403431 (FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) zzz474030 zzz474031 zzz6373 zzz47403433) (FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) zzz4740340 zzz4740341 zzz47403434 zzz4740344)",fontsize=16,color="magenta"];64661 -> 64667[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64661 -> 64668[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64661 -> 64669[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64661 -> 64670[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64661 -> 64671[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64662[label="zzz63733",fontsize=16,color="green",shape="box"];64663[label="zzz63734",fontsize=16,color="green",shape="box"];64664[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (compare zzz6476 (Pos (Succ (Succ Zero)) * zzz6477) == LT)",fontsize=16,color="black",shape="box"];64664 -> 64672[label="",style="solid", color="black", weight=3]; 130.57/78.23 51536[label="Zero",fontsize=16,color="green",shape="box"];51537[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (primCmpNat Zero (Succ zzz33200) == LT)",fontsize=16,color="black",shape="box"];51537 -> 51898[label="",style="solid", color="black", weight=3]; 130.57/78.23 51538[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234 True",fontsize=16,color="black",shape="box"];51538 -> 51899[label="",style="solid", color="black", weight=3]; 130.57/78.23 51539[label="Succ zzz332000",fontsize=16,color="green",shape="box"];51540[label="Succ zzz332000",fontsize=16,color="green",shape="box"];51541[label="Succ zzz332000",fontsize=16,color="green",shape="box"];51542[label="Succ zzz332000",fontsize=16,color="green",shape="box"];62494[label="zzz63350",fontsize=16,color="green",shape="box"];62495[label="zzz63360",fontsize=16,color="green",shape="box"];62496[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (Pos zzz6333) zzz6334 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 False",fontsize=16,color="black",shape="triangle"];62496 -> 62510[label="",style="solid", color="black", weight=3]; 130.57/78.23 62497[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (Pos zzz6333) zzz6334 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 True",fontsize=16,color="black",shape="box"];62497 -> 62511[label="",style="solid", color="black", weight=3]; 130.57/78.23 62498 -> 62496[label="",style="dashed", color="red", weight=0]; 130.57/78.23 62498[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (Pos zzz6333) zzz6334 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 False",fontsize=16,color="magenta"];64665[label="zzz647200",fontsize=16,color="green",shape="box"];64666[label="zzz6454000",fontsize=16,color="green",shape="box"];64667[label="zzz47403431",fontsize=16,color="green",shape="box"];64668[label="zzz47403430",fontsize=16,color="green",shape="box"];64669[label="Succ (Succ (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];64670 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64670[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ 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64681[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64671 -> 64682[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64672[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt zzz6476 (Pos (Succ (Succ Zero)) * zzz6477) == LT)",fontsize=16,color="burlywood",shape="box"];65754[label="zzz6476/Pos zzz64760",fontsize=10,color="white",style="solid",shape="box"];64672 -> 65754[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65754 -> 64683[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65755[label="zzz6476/Neg zzz64760",fontsize=10,color="white",style="solid",shape="box"];64672 -> 65755[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65755 -> 64684[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 51898[label="FiniteMap.mkVBalBranch3MkVBalBranch1 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (Neg zzz300) zzz31 zzz330 zzz331 (Pos (Succ zzz33200)) zzz333 zzz334 zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234 (LT == LT)",fontsize=16,color="black",shape="box"];51898 -> 52627[label="",style="solid", color="black", weight=3]; 130.57/78.23 51899 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.23 51899[label="FiniteMap.mkBalBranch zzz330 zzz331 zzz333 (FiniteMap.mkVBalBranch (Neg zzz300) zzz31 zzz334 (FiniteMap.Branch zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234))",fontsize=16,color="magenta"];51899 -> 63346[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 51899 -> 63347[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 51899 -> 63348[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 51899 -> 63349[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62510[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (Pos zzz6333) zzz6334 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 otherwise",fontsize=16,color="black",shape="box"];62510 -> 62518[label="",style="solid", color="black", weight=3]; 130.57/78.23 62511 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.23 62511[label="FiniteMap.mkBalBranch zzz6323 zzz6324 zzz6326 (FiniteMap.mkVBalBranch (Pos zzz6333) zzz6334 zzz6327 (FiniteMap.Branch zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332))",fontsize=16,color="magenta"];62511 -> 63350[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62511 -> 63351[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62511 -> 63352[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62511 -> 63353[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64673[label="zzz4740341",fontsize=16,color="green",shape="box"];64674[label="zzz4740340",fontsize=16,color="green",shape="box"];64675[label="Succ (Succ (Succ (Succ (Succ (Succ Zero)))))",fontsize=16,color="green",shape="box"];64676[label="zzz4740344",fontsize=16,color="green",shape="box"];64677[label="zzz47403434",fontsize=16,color="green",shape="box"];64678[label="zzz474031",fontsize=16,color="green",shape="box"];64679[label="zzz474030",fontsize=16,color="green",shape="box"];64680[label="Succ (Succ (Succ (Succ (Succ Zero))))",fontsize=16,color="green",shape="box"];64681[label="zzz47403433",fontsize=16,color="green",shape="box"];64682[label="zzz6373",fontsize=16,color="green",shape="box"];64683[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos zzz64760) (Pos (Succ (Succ Zero)) * zzz6477) == LT)",fontsize=16,color="burlywood",shape="box"];65756[label="zzz64760/Succ zzz647600",fontsize=10,color="white",style="solid",shape="box"];64683 -> 65756[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65756 -> 64685[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65757[label="zzz64760/Zero",fontsize=10,color="white",style="solid",shape="box"];64683 -> 65757[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65757 -> 64686[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64684[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg zzz64760) (Pos (Succ (Succ Zero)) * zzz6477) == 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63346[label="zzz330",fontsize=16,color="green",shape="box"];63347[label="FiniteMap.mkVBalBranch (Neg zzz300) zzz31 zzz334 (FiniteMap.Branch zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234)",fontsize=16,color="burlywood",shape="box"];65760[label="zzz334/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];63347 -> 65760[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65760 -> 63565[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65761[label="zzz334/FiniteMap.Branch zzz3340 zzz3341 zzz3342 zzz3343 zzz3344",fontsize=10,color="white",style="solid",shape="box"];63347 -> 65761[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65761 -> 63566[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 63348[label="zzz333",fontsize=16,color="green",shape="box"];63349[label="zzz331",fontsize=16,color="green",shape="box"];62518[label="FiniteMap.mkVBalBranch3MkVBalBranch0 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 (Pos zzz6333) zzz6334 zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327 zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332 True",fontsize=16,color="black",shape="box"];62518 -> 62546[label="",style="solid", color="black", weight=3]; 130.57/78.23 63350[label="zzz6323",fontsize=16,color="green",shape="box"];63351 -> 4125[label="",style="dashed", color="red", weight=0]; 130.57/78.23 63351[label="FiniteMap.mkVBalBranch (Pos zzz6333) zzz6334 zzz6327 (FiniteMap.Branch zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332)",fontsize=16,color="magenta"];63351 -> 63567[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63351 -> 63568[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63351 -> 63569[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63351 -> 63570[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63352[label="zzz6326",fontsize=16,color="green",shape="box"];63353[label="zzz6324",fontsize=16,color="green",shape="box"];64685[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos (Succ zzz647600)) (Pos (Succ (Succ Zero)) * zzz6477) == LT)",fontsize=16,color="black",shape="box"];64685 -> 64689[label="",style="solid", color="black", weight=3]; 130.57/78.23 64686[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos Zero) (Pos (Succ (Succ Zero)) * zzz6477) == LT)",fontsize=16,color="black",shape="box"];64686 -> 64690[label="",style="solid", color="black", weight=3]; 130.57/78.23 64687[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg (Succ zzz647600)) (Pos (Succ (Succ Zero)) * zzz6477) == LT)",fontsize=16,color="black",shape="box"];64687 -> 64691[label="",style="solid", color="black", weight=3]; 130.57/78.23 64688[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg Zero) (Pos (Succ (Succ Zero)) * zzz6477) == LT)",fontsize=16,color="black",shape="box"];64688 -> 64692[label="",style="solid", color="black", weight=3]; 130.57/78.23 53060 -> 63083[label="",style="dashed", color="red", weight=0]; 130.57/78.23 53060[label="FiniteMap.mkBalBranch zzz330 zzz331 zzz333 (FiniteMap.mkVBalBranch (Neg zzz300) zzz31 zzz334 (FiniteMap.Branch zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234))",fontsize=16,color="magenta"];53060 -> 63354[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 53060 -> 63355[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 53060 -> 63356[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 53060 -> 63357[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63565[label="FiniteMap.mkVBalBranch (Neg zzz300) zzz31 FiniteMap.EmptyFM (FiniteMap.Branch zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];63565 -> 63590[label="",style="solid", color="black", weight=3]; 130.57/78.23 63566[label="FiniteMap.mkVBalBranch (Neg zzz300) zzz31 (FiniteMap.Branch zzz3340 zzz3341 zzz3342 zzz3343 zzz3344) (FiniteMap.Branch zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];63566 -> 63591[label="",style="solid", color="black", weight=3]; 130.57/78.23 62546 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.23 62546[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) (Pos zzz6333) zzz6334 (FiniteMap.Branch zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327) (FiniteMap.Branch zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332)",fontsize=16,color="magenta"];62546 -> 62565[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62546 -> 62566[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62546 -> 62567[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62546 -> 62568[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62546 -> 62569[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63567[label="zzz6327",fontsize=16,color="green",shape="box"];63568[label="zzz6333",fontsize=16,color="green",shape="box"];63569[label="FiniteMap.Branch zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332",fontsize=16,color="green",shape="box"];63570[label="zzz6334",fontsize=16,color="green",shape="box"];64689[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos (Succ zzz647600)) (primMulInt (Pos (Succ (Succ Zero))) zzz6477) == LT)",fontsize=16,color="burlywood",shape="box"];65762[label="zzz6477/Pos zzz64770",fontsize=10,color="white",style="solid",shape="box"];64689 -> 65762[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65762 -> 64693[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65763[label="zzz6477/Neg zzz64770",fontsize=10,color="white",style="solid",shape="box"];64689 -> 65763[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65763 -> 64694[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64690[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos Zero) (primMulInt (Pos (Succ (Succ Zero))) zzz6477) == LT)",fontsize=16,color="burlywood",shape="box"];65764[label="zzz6477/Pos zzz64770",fontsize=10,color="white",style="solid",shape="box"];64690 -> 65764[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65764 -> 64695[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65765[label="zzz6477/Neg zzz64770",fontsize=10,color="white",style="solid",shape="box"];64690 -> 65765[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65765 -> 64696[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64691[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg (Succ zzz647600)) (primMulInt (Pos (Succ (Succ Zero))) zzz6477) == LT)",fontsize=16,color="burlywood",shape="box"];65766[label="zzz6477/Pos zzz64770",fontsize=10,color="white",style="solid",shape="box"];64691 -> 65766[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65766 -> 64697[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65767[label="zzz6477/Neg zzz64770",fontsize=10,color="white",style="solid",shape="box"];64691 -> 65767[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65767 -> 64698[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64692[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg Zero) (primMulInt (Pos (Succ (Succ Zero))) zzz6477) == LT)",fontsize=16,color="burlywood",shape="box"];65768[label="zzz6477/Pos zzz64770",fontsize=10,color="white",style="solid",shape="box"];64692 -> 65768[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65768 -> 64699[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65769[label="zzz6477/Neg zzz64770",fontsize=10,color="white",style="solid",shape="box"];64692 -> 65769[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65769 -> 64700[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 63354[label="zzz330",fontsize=16,color="green",shape="box"];63355[label="FiniteMap.mkVBalBranch (Neg zzz300) zzz31 zzz334 (FiniteMap.Branch zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234)",fontsize=16,color="burlywood",shape="box"];65770[label="zzz334/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];63355 -> 65770[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65770 -> 63571[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65771[label="zzz334/FiniteMap.Branch zzz3340 zzz3341 zzz3342 zzz3343 zzz3344",fontsize=10,color="white",style="solid",shape="box"];63355 -> 65771[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65771 -> 63572[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 63356[label="zzz333",fontsize=16,color="green",shape="box"];63357[label="zzz331",fontsize=16,color="green",shape="box"];63590[label="FiniteMap.mkVBalBranch5 (Neg zzz300) zzz31 FiniteMap.EmptyFM (FiniteMap.Branch zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];63590 -> 63641[label="",style="solid", color="black", weight=3]; 130.57/78.23 63591 -> 11068[label="",style="dashed", color="red", weight=0]; 130.57/78.23 63591[label="FiniteMap.mkVBalBranch3 (Neg zzz300) zzz31 (FiniteMap.Branch zzz3340 zzz3341 zzz3342 zzz3343 zzz3344) (FiniteMap.Branch zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234)",fontsize=16,color="magenta"];63591 -> 63642[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63591 -> 63643[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63591 -> 63644[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63591 -> 63645[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63591 -> 63646[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63591 -> 63647[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 62565[label="zzz6334",fontsize=16,color="green",shape="box"];62566[label="Pos zzz6333",fontsize=16,color="green",shape="box"];62567[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];62568[label="FiniteMap.Branch zzz6328 zzz6329 (Neg (Succ zzz6330)) zzz6331 zzz6332",fontsize=16,color="green",shape="box"];62569[label="FiniteMap.Branch zzz6323 zzz6324 (Neg (Succ zzz6325)) zzz6326 zzz6327",fontsize=16,color="green",shape="box"];64693[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos (Succ zzz647600)) (primMulInt (Pos (Succ (Succ Zero))) (Pos zzz64770)) == LT)",fontsize=16,color="black",shape="box"];64693 -> 64701[label="",style="solid", color="black", weight=3]; 130.57/78.23 64694[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos (Succ zzz647600)) (primMulInt (Pos (Succ (Succ Zero))) (Neg zzz64770)) == LT)",fontsize=16,color="black",shape="box"];64694 -> 64702[label="",style="solid", color="black", weight=3]; 130.57/78.23 64695[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos Zero) (primMulInt (Pos (Succ (Succ Zero))) (Pos zzz64770)) == LT)",fontsize=16,color="black",shape="box"];64695 -> 64703[label="",style="solid", color="black", weight=3]; 130.57/78.23 64696[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos Zero) (primMulInt (Pos (Succ (Succ Zero))) (Neg zzz64770)) == LT)",fontsize=16,color="black",shape="box"];64696 -> 64704[label="",style="solid", color="black", weight=3]; 130.57/78.23 64697[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg (Succ zzz647600)) (primMulInt (Pos (Succ (Succ Zero))) (Pos zzz64770)) == LT)",fontsize=16,color="black",shape="box"];64697 -> 64705[label="",style="solid", color="black", weight=3]; 130.57/78.23 64698[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg (Succ zzz647600)) (primMulInt (Pos (Succ (Succ Zero))) (Neg zzz64770)) == LT)",fontsize=16,color="black",shape="box"];64698 -> 64706[label="",style="solid", color="black", weight=3]; 130.57/78.23 64699[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg Zero) (primMulInt (Pos (Succ (Succ Zero))) (Pos zzz64770)) == LT)",fontsize=16,color="black",shape="box"];64699 -> 64707[label="",style="solid", color="black", weight=3]; 130.57/78.23 64700[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg Zero) (primMulInt (Pos (Succ (Succ Zero))) (Neg zzz64770)) == LT)",fontsize=16,color="black",shape="box"];64700 -> 64708[label="",style="solid", color="black", weight=3]; 130.57/78.23 63571[label="FiniteMap.mkVBalBranch (Neg zzz300) zzz31 FiniteMap.EmptyFM (FiniteMap.Branch zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];63571 -> 63592[label="",style="solid", color="black", weight=3]; 130.57/78.23 63572[label="FiniteMap.mkVBalBranch (Neg zzz300) zzz31 (FiniteMap.Branch zzz3340 zzz3341 zzz3342 zzz3343 zzz3344) (FiniteMap.Branch zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];63572 -> 63593[label="",style="solid", color="black", weight=3]; 130.57/78.23 63641 -> 12428[label="",style="dashed", color="red", weight=0]; 130.57/78.23 63641[label="FiniteMap.addToFM (FiniteMap.Branch zzz5230 zzz5231 (Neg Zero) zzz5233 zzz5234) (Neg zzz300) zzz31",fontsize=16,color="magenta"];63641 -> 63692[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63641 -> 63693[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63641 -> 63694[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63641 -> 63695[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63641 -> 63696[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63642[label="zzz3342",fontsize=16,color="green",shape="box"];63643[label="zzz3344",fontsize=16,color="green",shape="box"];63644[label="Neg Zero",fontsize=16,color="green",shape="box"];63645[label="zzz3340",fontsize=16,color="green",shape="box"];63646[label="zzz3343",fontsize=16,color="green",shape="box"];63647[label="zzz3341",fontsize=16,color="green",shape="box"];64701 -> 64709[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64701[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos (Succ zzz647600)) (Pos (primMulNat (Succ (Succ Zero)) zzz64770)) == LT)",fontsize=16,color="magenta"];64701 -> 64710[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64702 -> 64711[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64702[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos (Succ zzz647600)) (Neg (primMulNat (Succ (Succ Zero)) zzz64770)) == LT)",fontsize=16,color="magenta"];64702 -> 64712[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64703 -> 64713[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64703[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos Zero) (Pos (primMulNat (Succ (Succ Zero)) zzz64770)) == LT)",fontsize=16,color="magenta"];64703 -> 64714[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64704 -> 64715[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64704[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos Zero) (Neg (primMulNat (Succ (Succ Zero)) zzz64770)) == LT)",fontsize=16,color="magenta"];64704 -> 64716[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64705 -> 64717[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64705[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg (Succ zzz647600)) (Pos (primMulNat (Succ (Succ Zero)) zzz64770)) == LT)",fontsize=16,color="magenta"];64705 -> 64718[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64706 -> 64719[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64706[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg (Succ zzz647600)) (Neg (primMulNat (Succ (Succ Zero)) zzz64770)) == LT)",fontsize=16,color="magenta"];64706 -> 64720[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64707 -> 64721[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64707[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg Zero) (Pos (primMulNat (Succ (Succ Zero)) zzz64770)) == LT)",fontsize=16,color="magenta"];64707 -> 64722[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64708 -> 64723[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64708[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg Zero) (Neg (primMulNat (Succ (Succ Zero)) zzz64770)) == LT)",fontsize=16,color="magenta"];64708 -> 64724[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63592[label="FiniteMap.mkVBalBranch5 (Neg zzz300) zzz31 FiniteMap.EmptyFM (FiniteMap.Branch zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234)",fontsize=16,color="black",shape="box"];63592 -> 63648[label="",style="solid", color="black", weight=3]; 130.57/78.23 63593 -> 11068[label="",style="dashed", color="red", weight=0]; 130.57/78.23 63593[label="FiniteMap.mkVBalBranch3 (Neg zzz300) zzz31 (FiniteMap.Branch zzz3340 zzz3341 zzz3342 zzz3343 zzz3344) (FiniteMap.Branch zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234)",fontsize=16,color="magenta"];63593 -> 63649[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63593 -> 63650[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63593 -> 63651[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63593 -> 63652[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63593 -> 63653[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63593 -> 63654[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63692[label="Neg Zero",fontsize=16,color="green",shape="box"];63693[label="zzz5234",fontsize=16,color="green",shape="box"];63694[label="zzz5230",fontsize=16,color="green",shape="box"];63695[label="zzz5233",fontsize=16,color="green",shape="box"];63696[label="zzz5231",fontsize=16,color="green",shape="box"];64710 -> 64538[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64710[label="primMulNat (Succ (Succ Zero)) zzz64770",fontsize=16,color="magenta"];64710 -> 64725[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64709[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos (Succ zzz647600)) (Pos zzz6478) == LT)",fontsize=16,color="black",shape="triangle"];64709 -> 64726[label="",style="solid", color="black", weight=3]; 130.57/78.23 64712 -> 64538[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64712[label="primMulNat (Succ (Succ Zero)) zzz64770",fontsize=16,color="magenta"];64712 -> 64727[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64711[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos (Succ zzz647600)) (Neg zzz6479) == LT)",fontsize=16,color="black",shape="triangle"];64711 -> 64728[label="",style="solid", color="black", weight=3]; 130.57/78.23 64714 -> 64538[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64714[label="primMulNat (Succ (Succ Zero)) zzz64770",fontsize=16,color="magenta"];64714 -> 64729[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64713[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos Zero) (Pos zzz6480) == LT)",fontsize=16,color="burlywood",shape="triangle"];65772[label="zzz6480/Succ zzz64800",fontsize=10,color="white",style="solid",shape="box"];64713 -> 65772[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65772 -> 64730[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65773[label="zzz6480/Zero",fontsize=10,color="white",style="solid",shape="box"];64713 -> 65773[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65773 -> 64731[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64716 -> 64538[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64716[label="primMulNat (Succ (Succ Zero)) zzz64770",fontsize=16,color="magenta"];64716 -> 64732[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64715[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos Zero) (Neg zzz6481) == LT)",fontsize=16,color="burlywood",shape="triangle"];65774[label="zzz6481/Succ zzz64810",fontsize=10,color="white",style="solid",shape="box"];64715 -> 65774[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65774 -> 64733[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65775[label="zzz6481/Zero",fontsize=10,color="white",style="solid",shape="box"];64715 -> 65775[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65775 -> 64734[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64718 -> 64538[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64718[label="primMulNat (Succ (Succ Zero)) zzz64770",fontsize=16,color="magenta"];64718 -> 64735[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64717[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg (Succ zzz647600)) (Pos zzz6482) == LT)",fontsize=16,color="black",shape="triangle"];64717 -> 64736[label="",style="solid", color="black", weight=3]; 130.57/78.23 64720 -> 64538[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64720[label="primMulNat (Succ (Succ Zero)) zzz64770",fontsize=16,color="magenta"];64720 -> 64737[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64719[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg (Succ zzz647600)) (Neg zzz6483) == LT)",fontsize=16,color="black",shape="triangle"];64719 -> 64738[label="",style="solid", color="black", weight=3]; 130.57/78.23 64722 -> 64538[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64722[label="primMulNat (Succ (Succ Zero)) zzz64770",fontsize=16,color="magenta"];64722 -> 64739[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64721[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg Zero) (Pos zzz6484) == LT)",fontsize=16,color="burlywood",shape="triangle"];65776[label="zzz6484/Succ zzz64840",fontsize=10,color="white",style="solid",shape="box"];64721 -> 65776[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65776 -> 64740[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65777[label="zzz6484/Zero",fontsize=10,color="white",style="solid",shape="box"];64721 -> 65777[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65777 -> 64741[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64724 -> 64538[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64724[label="primMulNat (Succ (Succ Zero)) zzz64770",fontsize=16,color="magenta"];64724 -> 64742[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64723[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg Zero) (Neg zzz6485) == LT)",fontsize=16,color="burlywood",shape="triangle"];65778[label="zzz6485/Succ zzz64850",fontsize=10,color="white",style="solid",shape="box"];64723 -> 65778[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65778 -> 64743[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65779[label="zzz6485/Zero",fontsize=10,color="white",style="solid",shape="box"];64723 -> 65779[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65779 -> 64744[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 63648 -> 12428[label="",style="dashed", color="red", weight=0]; 130.57/78.23 63648[label="FiniteMap.addToFM (FiniteMap.Branch zzz5230 zzz5231 (Pos Zero) zzz5233 zzz5234) (Neg zzz300) zzz31",fontsize=16,color="magenta"];63648 -> 63697[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63648 -> 63698[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63648 -> 63699[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63648 -> 63700[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63648 -> 63701[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 63649[label="zzz3342",fontsize=16,color="green",shape="box"];63650[label="zzz3344",fontsize=16,color="green",shape="box"];63651[label="Pos Zero",fontsize=16,color="green",shape="box"];63652[label="zzz3340",fontsize=16,color="green",shape="box"];63653[label="zzz3343",fontsize=16,color="green",shape="box"];63654[label="zzz3341",fontsize=16,color="green",shape="box"];64725[label="zzz64770",fontsize=16,color="green",shape="box"];64726[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpNat (Succ zzz647600) zzz6478 == LT)",fontsize=16,color="burlywood",shape="triangle"];65780[label="zzz6478/Succ zzz64780",fontsize=10,color="white",style="solid",shape="box"];64726 -> 65780[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65780 -> 64745[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65781[label="zzz6478/Zero",fontsize=10,color="white",style="solid",shape="box"];64726 -> 65781[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65781 -> 64746[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64727[label="zzz64770",fontsize=16,color="green",shape="box"];64728[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (GT == LT)",fontsize=16,color="black",shape="triangle"];64728 -> 64747[label="",style="solid", color="black", weight=3]; 130.57/78.23 64729[label="zzz64770",fontsize=16,color="green",shape="box"];64730[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos Zero) (Pos (Succ zzz64800)) == LT)",fontsize=16,color="black",shape="box"];64730 -> 64748[label="",style="solid", color="black", weight=3]; 130.57/78.23 64731[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];64731 -> 64749[label="",style="solid", color="black", weight=3]; 130.57/78.23 64732[label="zzz64770",fontsize=16,color="green",shape="box"];64733[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos Zero) (Neg (Succ zzz64810)) == LT)",fontsize=16,color="black",shape="box"];64733 -> 64750[label="",style="solid", color="black", weight=3]; 130.57/78.23 64734[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];64734 -> 64751[label="",style="solid", color="black", weight=3]; 130.57/78.23 64735[label="zzz64770",fontsize=16,color="green",shape="box"];64736[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (LT == LT)",fontsize=16,color="black",shape="triangle"];64736 -> 64752[label="",style="solid", color="black", weight=3]; 130.57/78.23 64737[label="zzz64770",fontsize=16,color="green",shape="box"];64738[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpNat zzz6483 (Succ zzz647600) == LT)",fontsize=16,color="burlywood",shape="triangle"];65782[label="zzz6483/Succ zzz64830",fontsize=10,color="white",style="solid",shape="box"];64738 -> 65782[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65782 -> 64753[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65783[label="zzz6483/Zero",fontsize=10,color="white",style="solid",shape="box"];64738 -> 65783[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65783 -> 64754[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64739[label="zzz64770",fontsize=16,color="green",shape="box"];64740[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg Zero) (Pos (Succ zzz64840)) == LT)",fontsize=16,color="black",shape="box"];64740 -> 64755[label="",style="solid", color="black", weight=3]; 130.57/78.23 64741[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];64741 -> 64756[label="",style="solid", color="black", weight=3]; 130.57/78.23 64742[label="zzz64770",fontsize=16,color="green",shape="box"];64743[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg Zero) (Neg (Succ zzz64850)) == LT)",fontsize=16,color="black",shape="box"];64743 -> 64757[label="",style="solid", color="black", weight=3]; 130.57/78.23 64744[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];64744 -> 64758[label="",style="solid", color="black", weight=3]; 130.57/78.23 63697[label="Pos Zero",fontsize=16,color="green",shape="box"];63698[label="zzz5234",fontsize=16,color="green",shape="box"];63699[label="zzz5230",fontsize=16,color="green",shape="box"];63700[label="zzz5233",fontsize=16,color="green",shape="box"];63701[label="zzz5231",fontsize=16,color="green",shape="box"];64745[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpNat (Succ zzz647600) (Succ zzz64780) == LT)",fontsize=16,color="black",shape="box"];64745 -> 64759[label="",style="solid", color="black", weight=3]; 130.57/78.23 64746[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpNat (Succ zzz647600) Zero == LT)",fontsize=16,color="black",shape="box"];64746 -> 64760[label="",style="solid", color="black", weight=3]; 130.57/78.23 64747[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 False",fontsize=16,color="black",shape="triangle"];64747 -> 64761[label="",style="solid", color="black", weight=3]; 130.57/78.23 64748 -> 64738[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64748[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpNat Zero (Succ zzz64800) == LT)",fontsize=16,color="magenta"];64748 -> 64762[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64748 -> 64763[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64749[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (EQ == LT)",fontsize=16,color="black",shape="triangle"];64749 -> 64764[label="",style="solid", color="black", weight=3]; 130.57/78.23 64750 -> 64728[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64750[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (GT == LT)",fontsize=16,color="magenta"];64751 -> 64749[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64751[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (EQ == LT)",fontsize=16,color="magenta"];64752[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 True",fontsize=16,color="black",shape="box"];64752 -> 64765[label="",style="solid", color="black", weight=3]; 130.57/78.23 64753[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpNat (Succ zzz64830) (Succ zzz647600) == LT)",fontsize=16,color="black",shape="box"];64753 -> 64766[label="",style="solid", color="black", weight=3]; 130.57/78.23 64754[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpNat Zero (Succ zzz647600) == LT)",fontsize=16,color="black",shape="box"];64754 -> 64767[label="",style="solid", color="black", weight=3]; 130.57/78.23 64755 -> 64736[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64755[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (LT == LT)",fontsize=16,color="magenta"];64756 -> 64749[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64756[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (EQ == LT)",fontsize=16,color="magenta"];64757 -> 64726[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64757[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpNat (Succ zzz64850) Zero == LT)",fontsize=16,color="magenta"];64757 -> 64768[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64757 -> 64769[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64758 -> 64749[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64758[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (EQ == LT)",fontsize=16,color="magenta"];64759[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpNat zzz647600 zzz64780 == LT)",fontsize=16,color="burlywood",shape="triangle"];65784[label="zzz647600/Succ zzz6476000",fontsize=10,color="white",style="solid",shape="box"];64759 -> 65784[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65784 -> 64770[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65785[label="zzz647600/Zero",fontsize=10,color="white",style="solid",shape="box"];64759 -> 65785[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65785 -> 64771[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64760 -> 64728[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64760[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (GT == LT)",fontsize=16,color="magenta"];64761[label="FiniteMap.mkBalBranch6MkBalBranch10 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 otherwise",fontsize=16,color="black",shape="box"];64761 -> 64772[label="",style="solid", color="black", weight=3]; 130.57/78.23 64762[label="Zero",fontsize=16,color="green",shape="box"];64763[label="zzz64800",fontsize=16,color="green",shape="box"];64764 -> 64747[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64764[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 False",fontsize=16,color="magenta"];64765[label="FiniteMap.mkBalBranch6Single_R zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034",fontsize=16,color="black",shape="box"];64765 -> 64773[label="",style="solid", color="black", weight=3]; 130.57/78.23 64766 -> 64759[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64766[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpNat zzz64830 zzz647600 == LT)",fontsize=16,color="magenta"];64766 -> 64774[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64766 -> 64775[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64767 -> 64736[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64767[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (LT == LT)",fontsize=16,color="magenta"];64768[label="Zero",fontsize=16,color="green",shape="box"];64769[label="zzz64850",fontsize=16,color="green",shape="box"];64770[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpNat (Succ zzz6476000) zzz64780 == LT)",fontsize=16,color="burlywood",shape="box"];65786[label="zzz64780/Succ zzz647800",fontsize=10,color="white",style="solid",shape="box"];64770 -> 65786[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65786 -> 64776[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65787[label="zzz64780/Zero",fontsize=10,color="white",style="solid",shape="box"];64770 -> 65787[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65787 -> 64777[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64771[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpNat Zero zzz64780 == LT)",fontsize=16,color="burlywood",shape="box"];65788[label="zzz64780/Succ zzz647800",fontsize=10,color="white",style="solid",shape="box"];64771 -> 65788[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65788 -> 64778[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65789[label="zzz64780/Zero",fontsize=10,color="white",style="solid",shape="box"];64771 -> 65789[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65789 -> 64779[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64772[label="FiniteMap.mkBalBranch6MkBalBranch10 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 True",fontsize=16,color="black",shape="box"];64772 -> 64780[label="",style="solid", color="black", weight=3]; 130.57/78.23 64773 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64773[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))) zzz63730 zzz63731 zzz63733 (FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))) zzz474030 zzz474031 zzz63734 zzz474034)",fontsize=16,color="magenta"];64773 -> 64781[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64773 -> 64782[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64773 -> 64783[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64773 -> 64784[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64773 -> 64785[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64774[label="zzz64830",fontsize=16,color="green",shape="box"];64775[label="zzz647600",fontsize=16,color="green",shape="box"];64776[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpNat (Succ zzz6476000) (Succ zzz647800) == LT)",fontsize=16,color="black",shape="box"];64776 -> 64786[label="",style="solid", color="black", weight=3]; 130.57/78.23 64777[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpNat (Succ zzz6476000) Zero == LT)",fontsize=16,color="black",shape="box"];64777 -> 64787[label="",style="solid", color="black", weight=3]; 130.57/78.23 64778[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpNat Zero (Succ zzz647800) == LT)",fontsize=16,color="black",shape="box"];64778 -> 64788[label="",style="solid", color="black", weight=3]; 130.57/78.23 64779[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];64779 -> 64789[label="",style="solid", color="black", weight=3]; 130.57/78.23 64780[label="FiniteMap.mkBalBranch6Double_R zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034",fontsize=16,color="burlywood",shape="box"];65790[label="zzz63734/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];64780 -> 65790[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65790 -> 64790[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 65791[label="zzz63734/FiniteMap.Branch zzz637340 zzz637341 zzz637342 zzz637343 zzz637344",fontsize=10,color="white",style="solid",shape="box"];64780 -> 65791[label="",style="solid", color="burlywood", weight=9]; 130.57/78.23 65791 -> 64791[label="",style="solid", color="burlywood", weight=3]; 130.57/78.23 64781[label="zzz63731",fontsize=16,color="green",shape="box"];64782[label="zzz63730",fontsize=16,color="green",shape="box"];64783[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))",fontsize=16,color="green",shape="box"];64784 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64784[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))) zzz474030 zzz474031 zzz63734 zzz474034",fontsize=16,color="magenta"];64784 -> 64792[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64784 -> 64793[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64784 -> 64794[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64784 -> 64795[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64784 -> 64796[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64785[label="zzz63733",fontsize=16,color="green",shape="box"];64786 -> 64759[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64786[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (primCmpNat zzz6476000 zzz647800 == LT)",fontsize=16,color="magenta"];64786 -> 64797[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64786 -> 64798[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64787 -> 64728[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64787[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (GT == LT)",fontsize=16,color="magenta"];64788 -> 64736[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64788[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (LT == LT)",fontsize=16,color="magenta"];64789 -> 64749[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64789[label="FiniteMap.mkBalBranch6MkBalBranch11 zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 zzz63734) zzz474034 zzz63730 zzz63731 zzz63732 zzz63733 zzz63734 (EQ == LT)",fontsize=16,color="magenta"];64790[label="FiniteMap.mkBalBranch6Double_R zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 FiniteMap.EmptyFM) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 FiniteMap.EmptyFM) zzz474034",fontsize=16,color="black",shape="box"];64790 -> 64799[label="",style="solid", color="black", weight=3]; 130.57/78.23 64791[label="FiniteMap.mkBalBranch6Double_R zzz474034 zzz474030 zzz474031 (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 (FiniteMap.Branch zzz637340 zzz637341 zzz637342 zzz637343 zzz637344)) (FiniteMap.Branch zzz63730 zzz63731 zzz63732 zzz63733 (FiniteMap.Branch zzz637340 zzz637341 zzz637342 zzz637343 zzz637344)) zzz474034",fontsize=16,color="black",shape="box"];64791 -> 64800[label="",style="solid", color="black", weight=3]; 130.57/78.23 64792[label="zzz474031",fontsize=16,color="green",shape="box"];64793[label="zzz474030",fontsize=16,color="green",shape="box"];64794[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))",fontsize=16,color="green",shape="box"];64795[label="zzz474034",fontsize=16,color="green",shape="box"];64796[label="zzz63734",fontsize=16,color="green",shape="box"];64797[label="zzz6476000",fontsize=16,color="green",shape="box"];64798[label="zzz647800",fontsize=16,color="green",shape="box"];64799[label="error []",fontsize=16,color="red",shape="box"];64800 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64800[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) zzz637340 zzz637341 (FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))) zzz63730 zzz63731 zzz63733 zzz637343) (FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) zzz474030 zzz474031 zzz637344 zzz474034)",fontsize=16,color="magenta"];64800 -> 64801[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64800 -> 64802[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64800 -> 64803[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64800 -> 64804[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64800 -> 64805[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64801[label="zzz637341",fontsize=16,color="green",shape="box"];64802[label="zzz637340",fontsize=16,color="green",shape="box"];64803[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];64804 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64804[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) zzz474030 zzz474031 zzz637344 zzz474034",fontsize=16,color="magenta"];64804 -> 64806[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64804 -> 64807[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64804 -> 64808[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64804 -> 64809[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64804 -> 64810[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64805 -> 60457[label="",style="dashed", color="red", weight=0]; 130.57/78.23 64805[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))) zzz63730 zzz63731 zzz63733 zzz637343",fontsize=16,color="magenta"];64805 -> 64811[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64805 -> 64812[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64805 -> 64813[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64805 -> 64814[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64805 -> 64815[label="",style="dashed", color="magenta", weight=3]; 130.57/78.23 64806[label="zzz474031",fontsize=16,color="green",shape="box"];64807[label="zzz474030",fontsize=16,color="green",shape="box"];64808[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="green",shape="box"];64809[label="zzz474034",fontsize=16,color="green",shape="box"];64810[label="zzz637344",fontsize=16,color="green",shape="box"];64811[label="zzz63731",fontsize=16,color="green",shape="box"];64812[label="zzz63730",fontsize=16,color="green",shape="box"];64813[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))",fontsize=16,color="green",shape="box"];64814[label="zzz637343",fontsize=16,color="green",shape="box"];64815[label="zzz63733",fontsize=16,color="green",shape="box"];} 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (16) 130.57/78.23 Complex Obligation (AND) 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (17) 130.57/78.23 Obligation: 130.57/78.23 Q DP problem: 130.57/78.23 The TRS P consists of the following rules: 130.57/78.23 130.57/78.23 new_glueBal2GlueBal1(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz6355000), Succ(zzz6354000), h, ba) -> new_glueBal2GlueBal1(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz6355000, zzz6354000, h, ba) 130.57/78.23 130.57/78.23 R is empty. 130.57/78.23 Q is empty. 130.57/78.23 We have to consider all minimal (P,Q,R)-chains. 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (18) QDPSizeChangeProof (EQUIVALENT) 130.57/78.23 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. 130.57/78.23 130.57/78.23 From the DPs we obtained the following set of size-change graphs: 130.57/78.23 *new_glueBal2GlueBal1(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz6355000), Succ(zzz6354000), h, ba) -> new_glueBal2GlueBal1(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz6355000, zzz6354000, h, ba) 130.57/78.23 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 > 11, 12 > 12, 13 >= 13, 14 >= 14 130.57/78.23 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (19) 130.57/78.23 YES 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (20) 130.57/78.23 Obligation: 130.57/78.23 Q DP problem: 130.57/78.23 The TRS P consists of the following rules: 130.57/78.23 130.57/78.23 new_primMinusNat(Succ(zzz482800), Succ(zzz47700)) -> new_primMinusNat(zzz482800, zzz47700) 130.57/78.23 130.57/78.23 R is empty. 130.57/78.23 Q is empty. 130.57/78.23 We have to consider all minimal (P,Q,R)-chains. 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (21) QDPSizeChangeProof (EQUIVALENT) 130.57/78.23 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. 130.57/78.23 130.57/78.23 From the DPs we obtained the following set of size-change graphs: 130.57/78.23 *new_primMinusNat(Succ(zzz482800), Succ(zzz47700)) -> new_primMinusNat(zzz482800, zzz47700) 130.57/78.23 The graph contains the following edges 1 > 1, 2 > 2 130.57/78.23 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (22) 130.57/78.23 YES 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (23) 130.57/78.23 Obligation: 130.57/78.23 Q DP problem: 130.57/78.23 The TRS P consists of the following rules: 130.57/78.23 130.57/78.23 new_primPlusNat(Succ(zzz50920000), Succ(zzz542000)) -> new_primPlusNat(zzz50920000, zzz542000) 130.57/78.23 130.57/78.23 R is empty. 130.57/78.23 Q is empty. 130.57/78.23 We have to consider all minimal (P,Q,R)-chains. 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (24) QDPSizeChangeProof (EQUIVALENT) 130.57/78.23 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. 130.57/78.23 130.57/78.23 From the DPs we obtained the following set of size-change graphs: 130.57/78.23 *new_primPlusNat(Succ(zzz50920000), Succ(zzz542000)) -> new_primPlusNat(zzz50920000, zzz542000) 130.57/78.23 The graph contains the following edges 1 > 1, 2 > 2 130.57/78.23 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (25) 130.57/78.23 YES 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (26) 130.57/78.23 Obligation: 130.57/78.23 Q DP problem: 130.57/78.23 The TRS P consists of the following rules: 130.57/78.23 130.57/78.23 new_mkBalBranch6MkBalBranch11(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Succ(zzz6476000), Succ(zzz647800), h, ba) -> new_mkBalBranch6MkBalBranch11(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz6476000, zzz647800, h, ba) 130.57/78.23 130.57/78.23 R is empty. 130.57/78.23 Q is empty. 130.57/78.23 We have to consider all minimal (P,Q,R)-chains. 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (27) QDPSizeChangeProof (EQUIVALENT) 130.57/78.23 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. 130.57/78.23 130.57/78.23 From the DPs we obtained the following set of size-change graphs: 130.57/78.23 *new_mkBalBranch6MkBalBranch11(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Succ(zzz6476000), Succ(zzz647800), h, ba) -> new_mkBalBranch6MkBalBranch11(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz6476000, zzz647800, h, ba) 130.57/78.23 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 > 9, 10 > 10, 11 >= 11, 12 >= 12 130.57/78.23 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (28) 130.57/78.23 YES 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (29) 130.57/78.23 Obligation: 130.57/78.23 Q DP problem: 130.57/78.23 The TRS P consists of the following rules: 130.57/78.23 130.57/78.23 new_glueBal2Mid_elt20(zzz6395, zzz6396, zzz6397, zzz6398, zzz6399, zzz6400, zzz6401, zzz6402, zzz6403, zzz6404, zzz6405, zzz6406, zzz6407, Branch(zzz64080, zzz64081, zzz64082, zzz64083, zzz64084), zzz6409, h, ba) -> new_glueBal2Mid_elt20(zzz6395, zzz6396, zzz6397, zzz6398, zzz6399, zzz6400, zzz6401, zzz6402, zzz6403, zzz6404, zzz64080, zzz64081, zzz64082, zzz64083, zzz64084, h, ba) 130.57/78.23 130.57/78.23 R is empty. 130.57/78.23 Q is empty. 130.57/78.23 We have to consider all minimal (P,Q,R)-chains. 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (30) QDPSizeChangeProof (EQUIVALENT) 130.57/78.23 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. 130.57/78.23 130.57/78.23 From the DPs we obtained the following set of size-change graphs: 130.57/78.23 *new_glueBal2Mid_elt20(zzz6395, zzz6396, zzz6397, zzz6398, zzz6399, zzz6400, zzz6401, zzz6402, zzz6403, zzz6404, zzz6405, zzz6406, zzz6407, Branch(zzz64080, zzz64081, zzz64082, zzz64083, zzz64084), zzz6409, h, ba) -> new_glueBal2Mid_elt20(zzz6395, zzz6396, zzz6397, zzz6398, zzz6399, zzz6400, zzz6401, zzz6402, zzz6403, zzz6404, zzz64080, zzz64081, zzz64082, zzz64083, zzz64084, h, ba) 130.57/78.23 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 14 > 11, 14 > 12, 14 > 13, 14 > 14, 14 > 15, 16 >= 16, 17 >= 17 130.57/78.23 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (31) 130.57/78.23 YES 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (32) 130.57/78.23 Obligation: 130.57/78.23 Q DP problem: 130.57/78.23 The TRS P consists of the following rules: 130.57/78.23 130.57/78.23 new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), h) -> new_mkVBalBranch2(zzz3000, zzz31, zzz334, Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), h) 130.57/78.23 new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Zero), zzz4263, zzz4264), h) -> new_mkVBalBranch2(zzz3000, zzz31, zzz334, Branch(zzz4260, zzz4261, Pos(Zero), zzz4263, zzz4264), h) 130.57/78.23 130.57/78.23 R is empty. 130.57/78.23 Q is empty. 130.57/78.23 We have to consider all minimal (P,Q,R)-chains. 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (33) DependencyGraphProof (EQUIVALENT) 130.57/78.23 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (34) 130.57/78.23 Complex Obligation (AND) 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (35) 130.57/78.23 Obligation: 130.57/78.23 Q DP problem: 130.57/78.23 The TRS P consists of the following rules: 130.57/78.23 130.57/78.23 new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Zero), zzz4263, zzz4264), h) -> new_mkVBalBranch2(zzz3000, zzz31, zzz334, Branch(zzz4260, zzz4261, Pos(Zero), zzz4263, zzz4264), h) 130.57/78.23 130.57/78.23 R is empty. 130.57/78.23 Q is empty. 130.57/78.23 We have to consider all minimal (P,Q,R)-chains. 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (36) QDPSizeChangeProof (EQUIVALENT) 130.57/78.23 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. 130.57/78.23 130.57/78.23 From the DPs we obtained the following set of size-change graphs: 130.57/78.23 *new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Zero), zzz4263, zzz4264), h) -> new_mkVBalBranch2(zzz3000, zzz31, zzz334, Branch(zzz4260, zzz4261, Pos(Zero), zzz4263, zzz4264), h) 130.57/78.23 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5 130.57/78.23 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (37) 130.57/78.23 YES 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (38) 130.57/78.23 Obligation: 130.57/78.23 Q DP problem: 130.57/78.23 The TRS P consists of the following rules: 130.57/78.23 130.57/78.23 new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), h) -> new_mkVBalBranch2(zzz3000, zzz31, zzz334, Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), h) 130.57/78.23 130.57/78.23 R is empty. 130.57/78.23 Q is empty. 130.57/78.23 We have to consider all minimal (P,Q,R)-chains. 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (39) QDPSizeChangeProof (EQUIVALENT) 130.57/78.23 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. 130.57/78.23 130.57/78.23 From the DPs we obtained the following set of size-change graphs: 130.57/78.23 *new_mkVBalBranch2(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), h) -> new_mkVBalBranch2(zzz3000, zzz31, zzz334, Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), h) 130.57/78.23 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5 130.57/78.23 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (40) 130.57/78.23 YES 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (41) 130.57/78.23 Obligation: 130.57/78.23 Q DP problem: 130.57/78.23 The TRS P consists of the following rules: 130.57/78.23 130.57/78.23 new_deleteMax(zzz47460, zzz47461, zzz47462, zzz47463, Branch(zzz474640, zzz474641, zzz474642, zzz474643, zzz474644), h, ba) -> new_deleteMax(zzz474640, zzz474641, zzz474642, zzz474643, zzz474644, h, ba) 130.57/78.23 130.57/78.23 R is empty. 130.57/78.23 Q is empty. 130.57/78.23 We have to consider all minimal (P,Q,R)-chains. 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (42) QDPSizeChangeProof (EQUIVALENT) 130.57/78.23 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. 130.57/78.23 130.57/78.23 From the DPs we obtained the following set of size-change graphs: 130.57/78.23 *new_deleteMax(zzz47460, zzz47461, zzz47462, zzz47463, Branch(zzz474640, zzz474641, zzz474642, zzz474643, zzz474644), h, ba) -> new_deleteMax(zzz474640, zzz474641, zzz474642, zzz474643, zzz474644, h, ba) 130.57/78.23 The graph contains the following edges 5 > 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 6 >= 6, 7 >= 7 130.57/78.23 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (43) 130.57/78.23 YES 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (44) 130.57/78.23 Obligation: 130.57/78.23 Q DP problem: 130.57/78.23 The TRS P consists of the following rules: 130.57/78.23 130.57/78.23 new_splitLT26(Pos(Succ(zzz197000)), zzz1971, zzz1972, zzz1973, zzz1974, zzz1975, ba) -> new_splitLT27(zzz197000, zzz1971, zzz1972, zzz1973, zzz1974, zzz1975, zzz1975, zzz197000, ba) 130.57/78.23 new_splitLT10(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, Succ(zzz41840), Succ(zzz41850), h) -> new_splitLT10(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, zzz41840, zzz41850, h) 130.57/78.23 new_splitLT27(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Zero, Zero, bb) -> new_splitLT28(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, bb) 130.57/78.23 new_splitLT10(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, Succ(zzz41840), Zero, h) -> new_splitLT4(zzz4182, zzz4183, h) 130.57/78.23 new_splitLT27(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Zero, Succ(zzz31400), bb) -> new_splitLT4(zzz3136, zzz3138, bb) 130.57/78.23 new_splitLT26(Neg(zzz19700), zzz1971, zzz1972, Branch(zzz19730, zzz19731, zzz19732, zzz19733, zzz19734), Branch(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744), zzz1975, ba) -> new_splitLT26(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744, zzz1975, ba) 130.57/78.23 new_splitLT26(Pos(Zero), zzz1971, zzz1972, zzz1973, Branch(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744), zzz1975, ba) -> new_splitLT30(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744, zzz1975, ba) 130.57/78.23 new_splitLT28(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, bb) -> new_splitLT10(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Succ(zzz3138), Succ(zzz3133), bb) 130.57/78.23 new_splitLT26(Neg(zzz19700), zzz1971, zzz1972, EmptyFM, zzz1974, zzz1975, ba) -> new_splitLT4(zzz1974, zzz1975, ba) 130.57/78.23 new_splitLT30(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744, zzz1975, ba) -> new_splitLT26(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744, zzz1975, ba) 130.57/78.23 new_splitLT27(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Succ(zzz31390), Succ(zzz31400), bb) -> new_splitLT27(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, zzz31390, zzz31400, bb) 130.57/78.23 new_splitLT4(Branch(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744), zzz1975, ba) -> new_splitLT30(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744, zzz1975, ba) 130.57/78.23 new_splitLT27(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Succ(zzz31390), Zero, bb) -> new_splitLT10(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Succ(zzz3138), Succ(zzz3133), bb) 130.57/78.23 130.57/78.23 R is empty. 130.57/78.23 Q is empty. 130.57/78.23 We have to consider all minimal (P,Q,R)-chains. 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (45) QDPSizeChangeProof (EQUIVALENT) 130.57/78.23 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. 130.57/78.23 130.57/78.23 From the DPs we obtained the following set of size-change graphs: 130.57/78.23 *new_splitLT27(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Succ(zzz31390), Zero, bb) -> new_splitLT10(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Succ(zzz3138), Succ(zzz3133), bb) 130.57/78.23 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 9 130.57/78.23 130.57/78.23 130.57/78.23 *new_splitLT10(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, Succ(zzz41840), Succ(zzz41850), h) -> new_splitLT10(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, zzz41840, zzz41850, h) 130.57/78.23 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9 130.57/78.23 130.57/78.23 130.57/78.23 *new_splitLT10(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, Succ(zzz41840), Zero, h) -> new_splitLT4(zzz4182, zzz4183, h) 130.57/78.23 The graph contains the following edges 5 >= 1, 6 >= 2, 9 >= 3 130.57/78.23 130.57/78.23 130.57/78.23 *new_splitLT28(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, bb) -> new_splitLT10(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Succ(zzz3138), Succ(zzz3133), bb) 130.57/78.23 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 9 130.57/78.23 130.57/78.23 130.57/78.23 *new_splitLT27(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Succ(zzz31390), Succ(zzz31400), bb) -> new_splitLT27(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, zzz31390, zzz31400, bb) 130.57/78.23 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9 130.57/78.23 130.57/78.23 130.57/78.23 *new_splitLT26(Pos(Succ(zzz197000)), zzz1971, zzz1972, zzz1973, zzz1974, zzz1975, ba) -> new_splitLT27(zzz197000, zzz1971, zzz1972, zzz1973, zzz1974, zzz1975, zzz1975, zzz197000, ba) 130.57/78.23 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 6 >= 7, 1 > 8, 7 >= 9 130.57/78.23 130.57/78.23 130.57/78.23 *new_splitLT4(Branch(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744), zzz1975, ba) -> new_splitLT30(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744, zzz1975, ba) 130.57/78.23 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 >= 6, 3 >= 7 130.57/78.23 130.57/78.23 130.57/78.23 *new_splitLT26(Neg(zzz19700), zzz1971, zzz1972, Branch(zzz19730, zzz19731, zzz19732, zzz19733, zzz19734), Branch(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744), zzz1975, ba) -> new_splitLT26(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744, zzz1975, ba) 130.57/78.23 The graph contains the following edges 5 > 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 6 >= 6, 7 >= 7 130.57/78.23 130.57/78.23 130.57/78.23 *new_splitLT30(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744, zzz1975, ba) -> new_splitLT26(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744, zzz1975, ba) 130.57/78.23 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7 130.57/78.23 130.57/78.23 130.57/78.23 *new_splitLT27(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Zero, Zero, bb) -> new_splitLT28(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, bb) 130.57/78.23 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 7 130.57/78.23 130.57/78.23 130.57/78.23 *new_splitLT27(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Zero, Succ(zzz31400), bb) -> new_splitLT4(zzz3136, zzz3138, bb) 130.57/78.23 The graph contains the following edges 4 >= 1, 6 >= 2, 9 >= 3 130.57/78.23 130.57/78.23 130.57/78.23 *new_splitLT26(Pos(Zero), zzz1971, zzz1972, zzz1973, Branch(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744), zzz1975, ba) -> new_splitLT30(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744, zzz1975, ba) 130.57/78.23 The graph contains the following edges 5 > 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 6 >= 6, 7 >= 7 130.57/78.23 130.57/78.23 130.57/78.23 *new_splitLT26(Neg(zzz19700), zzz1971, zzz1972, EmptyFM, zzz1974, zzz1975, ba) -> new_splitLT4(zzz1974, zzz1975, ba) 130.57/78.23 The graph contains the following edges 5 >= 1, 6 >= 2, 7 >= 3 130.57/78.23 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (46) 130.57/78.23 YES 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (47) 130.57/78.23 Obligation: 130.57/78.23 Q DP problem: 130.57/78.23 The TRS P consists of the following rules: 130.57/78.23 130.57/78.23 new_glueBal2Mid_elt10(zzz6427, zzz6428, zzz6429, zzz6430, zzz6431, zzz6432, zzz6433, zzz6434, zzz6435, zzz6436, zzz6437, zzz6438, zzz6439, zzz6440, Branch(zzz64410, zzz64411, zzz64412, zzz64413, zzz64414), h, ba) -> new_glueBal2Mid_elt10(zzz6427, zzz6428, zzz6429, zzz6430, zzz6431, zzz6432, zzz6433, zzz6434, zzz6435, zzz6436, zzz64410, zzz64411, zzz64412, zzz64413, zzz64414, h, ba) 130.57/78.23 130.57/78.23 R is empty. 130.57/78.23 Q is empty. 130.57/78.23 We have to consider all minimal (P,Q,R)-chains. 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (48) QDPSizeChangeProof (EQUIVALENT) 130.57/78.23 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. 130.57/78.23 130.57/78.23 From the DPs we obtained the following set of size-change graphs: 130.57/78.23 *new_glueBal2Mid_elt10(zzz6427, zzz6428, zzz6429, zzz6430, zzz6431, zzz6432, zzz6433, zzz6434, zzz6435, zzz6436, zzz6437, zzz6438, zzz6439, zzz6440, Branch(zzz64410, zzz64411, zzz64412, zzz64413, zzz64414), h, ba) -> new_glueBal2Mid_elt10(zzz6427, zzz6428, zzz6429, zzz6430, zzz6431, zzz6432, zzz6433, zzz6434, zzz6435, zzz6436, zzz64410, zzz64411, zzz64412, zzz64413, zzz64414, h, ba) 130.57/78.23 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 15 > 11, 15 > 12, 15 > 13, 15 > 14, 15 > 15, 16 >= 16, 17 >= 17 130.57/78.23 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (49) 130.57/78.23 YES 130.57/78.23 130.57/78.23 ---------------------------------------- 130.57/78.23 130.57/78.23 (50) 130.57/78.23 Obligation: 130.57/78.23 Q DP problem: 130.57/78.23 The TRS P consists of the following rules: 130.57/78.23 130.57/78.23 new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, Succ(zzz21580), Succ(zzz21590), ed, ee) -> new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, zzz21580, zzz21590, ed, ee) 130.57/78.23 new_intersectFM_C(Branch(Neg(Succ(zzz3000)), zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C113(zzz3000, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, bd, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, Neg(Zero), zzz894, zzz895, zzz896, zzz897, eh, fa) -> new_intersectFM_C2IntersectFM_C138(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz896, eh, fa) 130.57/78.23 new_intersectFM_C2IntersectFM_C138(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, EmptyFM, eh, fa) -> new_intersectFM_C(new_intersectFM_C2Lts6(zzz884, zzz885, zzz886, zzz887, zzz888, eh), zzz891, eh) 130.57/78.23 new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Pos(Succ(zzz90800)), zzz909, zzz910, EmptyFM, zzz912, ga, gb) -> new_intersectFM_C2IntersectFM_C111(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, ga, gb) 130.57/78.23 new_intersectFM_C2IntersectFM_C144(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, EmptyFM, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Lts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1601, gc) 130.57/78.23 new_intersectFM_C2IntersectFM_C118(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, ca, cb) -> new_intersectFM_C(new_intersectFM_C2Lts0(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, ca), zzz3532, ca) 130.57/78.23 new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, Branch(Neg(zzz209100), zzz20911, zzz20912, zzz20913, zzz20914), h, ba) -> new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz20914, h, ba) 130.57/78.23 new_intersectFM_C2IntersectFM_C120(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, EmptyFM, cc, cd) -> new_intersectFM_C(new_intersectFM_C2Lts1(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, cc), zzz1390, cc) 130.57/78.23 new_intersectFM_C(Branch(Pos(Succ(zzz3000)), zzz31, zzz32, EmptyFM, zzz34), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C111(zzz3000, zzz31, zzz32, EmptyFM, zzz34, zzz41, zzz42, zzz43, zzz44, bd, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C137(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, Succ(zzz15910), Succ(zzz15920), fb, fc) -> new_intersectFM_C2IntersectFM_C137(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, zzz15910, zzz15920, fb, fc) 130.57/78.23 new_intersectFM_C2IntersectFM_C132(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, eb, ec) -> new_intersectFM_C(new_intersectFM_C2Gts4(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, eb), zzz2764, eb) 130.57/78.23 new_intersectFM_C2IntersectFM_C115(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, EmptyFM, be, bf) -> new_intersectFM_C(new_intersectFM_C2Gts0(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, be), zzz2742, be) 130.57/78.23 new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Pos(Zero), zzz909, zzz910, zzz911, zzz912, ga, gb) -> new_intersectFM_C(new_intersectFM_C2Lts7(zzz899, zzz900, zzz901, zzz902, zzz903, ga), zzz906, ga) 130.57/78.23 new_intersectFM_C2IntersectFM_C137(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, Zero, Succ(zzz15920), fb, fc) -> new_intersectFM_C2IntersectFM_C138(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1589, fb, fc) 130.57/78.23 new_intersectFM_C2IntersectFM_C144(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Branch(zzz16060, zzz16061, zzz16062, zzz16063, zzz16064), gc, gd) -> new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz16060, zzz16061, zzz16062, zzz16063, zzz16064, gc, gd) 130.57/78.23 new_intersectFM_C2IntersectFM_C115(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, Branch(zzz27470, zzz27471, zzz27472, zzz27473, zzz27474), be, bf) -> new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, zzz27470, zzz27471, zzz27472, zzz27473, zzz27474, be, bf) 130.57/78.23 new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, Pos(zzz8930), zzz894, zzz895, EmptyFM, zzz897, eh, fa) -> new_intersectFM_C(new_intersectFM_C2Lts6(zzz884, zzz885, zzz886, zzz887, zzz888, eh), zzz891, eh) 130.57/78.23 new_intersectFM_C2IntersectFM_C10(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, Zero, Zero, bb, bc) -> new_intersectFM_C2IntersectFM_C13(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, bb, bc) 130.57/78.23 new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Pos(Succ(zzz160300)), zzz1604, zzz1605, EmptyFM, zzz1607, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Gts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1602, gc) 130.57/78.23 new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Pos(Zero), zzz909, zzz910, zzz911, zzz912, ga, gb) -> new_intersectFM_C(new_intersectFM_C2Gts7(zzz899, zzz900, zzz901, zzz902, zzz903, ga), zzz907, ga) 130.57/78.23 new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, Pos(Zero), zzz1393, zzz1394, zzz1395, zzz1396, cc, cd) -> new_intersectFM_C2IntersectFM_C120(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, zzz1396, cc, cd) 130.57/78.23 new_intersectFM_C(Branch(Neg(Succ(zzz3000)), zzz31, zzz32, zzz33, EmptyFM), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_mkVBalBranch6(zzz3000, zzz31, zzz33, new_splitLT5(bd), bd), zzz43, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, Neg(Zero), zzz753, zzz754, zzz755, zzz756, df, dg) -> new_intersectFM_C2IntersectFM_C129(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, zzz755, df, dg) 130.57/78.23 new_intersectFM_C(Branch(Pos(Zero), zzz31, zzz32, zzz33, EmptyFM), Branch(Pos(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitGT6(zzz4000, bd), zzz44, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, EmptyFM, zzz2092, Zero, Succ(zzz20940), h, ba) -> new_intersectFM_C(new_intersectFM_C2Gts(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, h), zzz2087, h) 130.57/78.23 new_intersectFM_C2IntersectFM_C132(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, eb, ec) -> new_intersectFM_C(new_intersectFM_C2Lts4(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, eb), zzz2763, eb) 130.57/78.23 new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Neg(Succ(zzz62700)), zzz628, zzz629, zzz630, zzz631, db, dc) -> new_intersectFM_C2IntersectFM_C124(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, zzz631, db, dc) 130.57/78.23 new_intersectFM_C2IntersectFM_C121(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, Succ(zzz31780), Zero, cg, da) -> new_intersectFM_C2IntersectFM_C120(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3177, cg, da) 130.57/78.23 new_intersectFM_C2IntersectFM_C115(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, EmptyFM, be, bf) -> new_intersectFM_C(new_intersectFM_C2Lts0(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, be), zzz2741, be) 130.57/78.23 new_intersectFM_C(Branch(Pos(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT210(zzz31, zzz32, zzz33, zzz34, bd), zzz43, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C133(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, Zero, Succ(zzz26430), ef, eg) -> new_intersectFM_C(new_intersectFM_C2Gts5(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, ef), zzz2636, ef) 130.57/78.23 new_intersectFM_C2IntersectFM_C116(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, Zero, Succ(zzz35400), ca, cb) -> new_intersectFM_C(new_intersectFM_C2Lts0(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, ca), zzz3532, ca) 130.57/78.23 new_intersectFM_C(Branch(Neg(zzz300), zzz31, zzz32, zzz33, EmptyFM), Branch(Pos(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT29(Neg(zzz300), zzz31, zzz32, zzz33, EmptyFM, zzz4000, bd), zzz43, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, Pos(zzz8930), zzz894, zzz895, EmptyFM, zzz897, eh, fa) -> new_intersectFM_C(new_intersectFM_C2Gts6(zzz884, zzz885, zzz886, zzz887, zzz888, eh), zzz892, eh) 130.57/78.23 new_intersectFM_C2IntersectFM_C114(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, Zero, Succ(zzz30830), bg, bh) -> new_intersectFM_C2IntersectFM_C115(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3080, bg, bh) 130.57/78.23 new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Neg(Zero), zzz628, zzz629, zzz630, zzz631, db, dc) -> new_intersectFM_C2IntersectFM_C125(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, zzz628, db, dc) 130.57/78.23 new_intersectFM_C2IntersectFM_C133(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, Succ(zzz26420), Succ(zzz26430), ef, eg) -> new_intersectFM_C2IntersectFM_C133(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, zzz26420, zzz26430, ef, eg) 130.57/78.23 new_intersectFM_C(Branch(Pos(Zero), zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(Pos(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C14(zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz4000, zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, bd, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C13(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, bb, bc) -> new_intersectFM_C(new_intersectFM_C2Lts(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, bb), zzz2617, bb) 130.57/78.23 new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Pos(Zero), zzz628, zzz629, zzz630, zzz631, db, dc) -> new_intersectFM_C(new_intersectFM_C2Lts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz625, db) 130.57/78.23 new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, Zero, Zero, ed, ee) -> new_intersectFM_C2IntersectFM_C135(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, ed, ee) 130.57/78.23 new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, Pos(zzz7520), zzz753, zzz754, EmptyFM, zzz756, df, dg) -> new_intersectFM_C(new_intersectFM_C2Lts4(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df), zzz750, df) 130.57/78.23 new_intersectFM_C2IntersectFM_C129(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, EmptyFM, df, dg) -> new_intersectFM_C(new_intersectFM_C2Lts4(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df), zzz750, df) 130.57/78.23 new_intersectFM_C2IntersectFM_C10(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, Zero, Succ(zzz26250), bb, bc) -> new_intersectFM_C(new_intersectFM_C2Gts(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, bb), zzz2618, bb) 130.57/78.23 new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, Neg(zzz27430), zzz2744, zzz2745, zzz2746, EmptyFM, be, bf) -> new_intersectFM_C(new_intersectFM_C2Gts0(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, be), zzz2742, be) 130.57/78.23 new_intersectFM_C(Branch(Neg(Succ(zzz3000)), zzz31, zzz32, zzz33, EmptyFM), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_mkVBalBranch6(zzz3000, zzz31, zzz33, new_splitLT9(EmptyFM, bd), bd), zzz43, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Neg(Zero), zzz1202, zzz1203, zzz1204, zzz1205, dd, de) -> new_intersectFM_C2IntersectFM_C127(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, zzz1202, dd, de) 130.57/78.23 new_intersectFM_C2IntersectFM_C141(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, fd, ff) -> new_intersectFM_C(new_intersectFM_C2Gts6(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, fd), zzz2892, fd) 130.57/78.23 new_intersectFM_C(Branch(Pos(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT8(zzz31, zzz32, zzz33, zzz34, bd), zzz43, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C116(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, Zero, Zero, ca, cb) -> new_intersectFM_C2IntersectFM_C118(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, ca, cb) 130.57/78.23 new_intersectFM_C2IntersectFM_C122(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, ce, cf) -> new_intersectFM_C2IntersectFM_C121(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, Succ(zzz1982), Succ(zzz1987), ce, cf) 130.57/78.23 new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Pos(Succ(zzz120100)), zzz1202, zzz1203, EmptyFM, zzz1205, dd, de) -> new_intersectFM_C(new_intersectFM_C2Lts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1199, dd) 130.57/78.23 new_intersectFM_C2IntersectFM_C120(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, Branch(zzz13960, zzz13961, zzz13962, zzz13963, zzz13964), cc, cd) -> new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, zzz13960, zzz13961, zzz13962, zzz13963, zzz13964, cc, cd) 130.57/78.23 new_intersectFM_C2IntersectFM_C117(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, bg, bh) -> new_intersectFM_C2IntersectFM_C116(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, Succ(zzz3072), Succ(zzz3077), bg, bh) 130.57/78.23 new_intersectFM_C2IntersectFM_C130(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, Zero, Succ(zzz27710), eb, ec) -> new_intersectFM_C(new_intersectFM_C2Lts4(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, eb), zzz2763, eb) 130.57/78.23 new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, Branch(Neg(Zero), zzz21561, zzz21562, zzz21563, zzz21564), ed, ee) -> new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz21563, ed, ee) 130.57/78.23 new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, Succ(zzz20930), Succ(zzz20940), h, ba) -> new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, zzz20930, zzz20940, h, ba) 130.57/78.23 new_intersectFM_C(Branch(Neg(zzz300), zzz31, zzz32, zzz33, EmptyFM), Branch(Pos(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitGT6(zzz4000, bd), zzz44, bd) 130.57/78.23 new_intersectFM_C(Branch(Pos(zzz300), zzz31, zzz32, EmptyFM, zzz34), Branch(Neg(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_mkVBalBranch5(zzz300, zzz31, new_splitGT8(zzz4000, bd), zzz34, bd), zzz44, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C133(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, Zero, Succ(zzz26430), ef, eg) -> new_intersectFM_C(new_intersectFM_C2Lts5(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, ef), zzz2635, ef) 130.57/78.23 new_intersectFM_C(Branch(Neg(Succ(zzz3000)), zzz31, zzz32, zzz33, zzz34), Branch(Neg(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C19(zzz3000, zzz31, zzz32, zzz33, zzz34, zzz4000, zzz41, zzz42, zzz43, zzz44, zzz3000, zzz31, zzz32, zzz33, zzz34, zzz3000, zzz4000, bd, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C123(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, cg, da) -> new_intersectFM_C(new_intersectFM_C2Lts1(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, cg), zzz3171, cg) 130.57/78.23 new_intersectFM_C2IntersectFM_C116(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, Zero, Succ(zzz35400), ca, cb) -> new_intersectFM_C(new_intersectFM_C2Gts0(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, ca), zzz3533, ca) 130.57/78.23 new_intersectFM_C2IntersectFM_C140(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, fb, fc) -> new_intersectFM_C2IntersectFM_C139(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, Succ(zzz1586), Succ(zzz1581), fb, fc) 130.57/78.23 new_intersectFM_C(Branch(Neg(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT211(zzz31, zzz32, zzz33, zzz34, bd), zzz43, bd) 130.57/78.23 new_intersectFM_C(Branch(Pos(zzz300), zzz31, zzz32, EmptyFM, zzz34), Branch(Neg(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT6(zzz300, zzz31, zzz32, zzz34, zzz4000, bd), zzz43, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, Neg(zzz27430), zzz2744, zzz2745, zzz2746, EmptyFM, be, bf) -> new_intersectFM_C(new_intersectFM_C2Lts0(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, be), zzz2741, be) 130.57/78.23 new_intersectFM_C2IntersectFM_C126(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, EmptyFM, dd, de) -> new_intersectFM_C(new_intersectFM_C2Gts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1200, dd) 130.57/78.23 new_intersectFM_C2IntersectFM_C13(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, bb, bc) -> new_intersectFM_C(new_intersectFM_C2Gts(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, bb), zzz2618, bb) 130.57/78.23 new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, Zero, Zero, h, ba) -> new_intersectFM_C2IntersectFM_C12(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, h, ba) 130.57/78.23 new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Pos(Succ(zzz120100)), zzz1202, zzz1203, Branch(zzz12040, zzz12041, zzz12042, zzz12043, zzz12044), zzz1205, dd, de) -> new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, zzz12040, zzz12041, zzz12042, zzz12043, zzz12044, dd, de) 130.57/78.23 new_intersectFM_C2IntersectFM_C116(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, Succ(zzz35390), Zero, ca, cb) -> new_intersectFM_C2IntersectFM_C115(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3538, ca, cb) 130.57/78.23 new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, Neg(Succ(zzz89300)), zzz894, zzz895, zzz896, zzz897, eh, fa) -> new_intersectFM_C2IntersectFM_C137(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz89300, zzz894, zzz895, zzz896, zzz897, zzz89300, zzz888, eh, fa) 130.57/78.23 new_intersectFM_C2IntersectFM_C119(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, Succ(zzz19920), Zero, ce, cf) -> new_intersectFM_C2IntersectFM_C121(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, Succ(zzz1982), Succ(zzz1987), ce, cf) 130.57/78.23 new_intersectFM_C2IntersectFM_C128(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, Succ(zzz14130), Zero, dh, ea) -> new_intersectFM_C2IntersectFM_C130(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, Succ(zzz1408), Succ(zzz1403), dh, ea) 130.57/78.23 new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, Branch(Neg(Succ(zzz2156000)), zzz21561, zzz21562, zzz21563, zzz21564), zzz2157, Zero, Succ(zzz21590), ed, ee) -> new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2156000, zzz21561, zzz21562, zzz21563, zzz21564, zzz2156000, zzz2148, ed, ee) 130.57/78.23 new_intersectFM_C2IntersectFM_C138(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, EmptyFM, eh, fa) -> new_intersectFM_C(new_intersectFM_C2Gts6(zzz884, zzz885, zzz886, zzz887, zzz888, eh), zzz892, eh) 130.57/78.23 new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Pos(Zero), zzz1202, zzz1203, zzz1204, zzz1205, dd, de) -> new_intersectFM_C(new_intersectFM_C2Lts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1199, dd) 130.57/78.23 new_intersectFM_C2IntersectFM_C135(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, ed, ee) -> new_intersectFM_C2IntersectFM_C133(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, Succ(zzz2153), Succ(zzz2148), ed, ee) 130.57/78.23 new_intersectFM_C2IntersectFM_C136(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, ef, eg) -> new_intersectFM_C(new_intersectFM_C2Lts5(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, ef), zzz2635, ef) 130.57/78.23 new_intersectFM_C2IntersectFM_C118(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, ca, cb) -> new_intersectFM_C(new_intersectFM_C2Gts0(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, ca), zzz3533, ca) 130.57/78.23 new_intersectFM_C2IntersectFM_C10(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, Succ(zzz26240), Zero, bb, bc) -> new_intersectFM_C2IntersectFM_C11(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2623, bb, bc) 130.57/78.23 new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, Branch(Neg(zzz209100), zzz20911, zzz20912, zzz20913, zzz20914), zzz2092, Zero, Succ(zzz20940), h, ba) -> new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz20914, h, ba) 130.57/78.23 new_intersectFM_C2IntersectFM_C119(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, Zero, Succ(zzz19930), ce, cf) -> new_intersectFM_C2IntersectFM_C120(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1990, ce, cf) 130.57/78.23 new_intersectFM_C(Branch(Pos(Succ(zzz3000)), zzz31, zzz32, EmptyFM, zzz34), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT5(bd), zzz43, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, Pos(zzz8930), zzz894, zzz895, Branch(zzz8960, zzz8961, zzz8962, zzz8963, zzz8964), zzz897, eh, fa) -> new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz8960, zzz8961, zzz8962, zzz8963, zzz8964, eh, fa) 130.57/78.23 new_intersectFM_C2IntersectFM_C121(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, Zero, Succ(zzz31790), cg, da) -> new_intersectFM_C(new_intersectFM_C2Lts1(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, cg), zzz3171, cg) 130.57/78.23 new_intersectFM_C2IntersectFM_C121(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, Succ(zzz31780), Succ(zzz31790), cg, da) -> new_intersectFM_C2IntersectFM_C121(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, zzz31780, zzz31790, cg, da) 130.57/78.23 new_intersectFM_C2IntersectFM_C130(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, Succ(zzz27700), Zero, eb, ec) -> new_intersectFM_C2IntersectFM_C129(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2769, eb, ec) 130.57/78.23 new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, EmptyFM, ed, ee) -> new_intersectFM_C(new_intersectFM_C2Gts5(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, ed), zzz2152, ed) 130.57/78.23 new_intersectFM_C(Branch(Neg(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT11(zzz31, zzz32, zzz33, zzz34, bd), zzz43, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C111(zzz830, zzz831, zzz832, zzz833, zzz834, zzz835, zzz836, zzz837, zzz838, fg, fh) -> new_intersectFM_C(new_intersectFM_C2Gts7(zzz830, zzz831, zzz832, zzz833, zzz834, fg), zzz838, fg) 130.57/78.23 new_intersectFM_C2IntersectFM_C130(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, Zero, Succ(zzz27710), eb, ec) -> new_intersectFM_C(new_intersectFM_C2Gts4(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, eb), zzz2764, eb) 130.57/78.23 new_intersectFM_C2IntersectFM_C129(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, Branch(zzz7550, zzz7551, zzz7552, zzz7553, zzz7554), df, dg) -> new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, zzz7550, zzz7551, zzz7552, zzz7553, zzz7554, df, dg) 130.57/78.23 new_intersectFM_C2IntersectFM_C142(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Branch(zzz9110, zzz9111, zzz9112, zzz9113, zzz9114), ga, gb) -> new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz9110, zzz9111, zzz9112, zzz9113, zzz9114, ga, gb) 130.57/78.23 new_intersectFM_C(Branch(Pos(Succ(zzz3000)), zzz31, zzz32, EmptyFM, zzz34), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_mkVBalBranch5(Succ(zzz3000), zzz31, new_splitGT7(bd), zzz34, bd), zzz44, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, EmptyFM, zzz2157, Zero, Succ(zzz21590), ed, ee) -> new_intersectFM_C(new_intersectFM_C2Gts5(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, ed), zzz2152, ed) 130.57/78.23 new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, Pos(Succ(zzz274300)), zzz2744, zzz2745, zzz2746, zzz2747, be, bf) -> new_intersectFM_C2IntersectFM_C114(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, zzz274300, zzz2744, zzz2745, zzz2746, zzz2747, zzz2738, zzz274300, be, bf) 130.57/78.23 new_intersectFM_C2IntersectFM_C141(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, fd, ff) -> new_intersectFM_C(new_intersectFM_C2Lts6(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, fd), zzz2891, fd) 130.57/78.23 new_intersectFM_C2IntersectFM_C139(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, Zero, Succ(zzz28990), fd, ff) -> new_intersectFM_C(new_intersectFM_C2Lts6(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, fd), zzz2891, fd) 130.57/78.23 new_intersectFM_C(Branch(Neg(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitGT214(zzz31, zzz32, zzz33, zzz34, bd), zzz44, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, Branch(Pos(zzz215600), zzz21561, zzz21562, zzz21563, zzz21564), zzz2157, Zero, Succ(zzz21590), ed, ee) -> new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz21563, ed, ee) 130.57/78.23 new_intersectFM_C2IntersectFM_C139(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, Zero, Zero, fd, ff) -> new_intersectFM_C2IntersectFM_C141(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, fd, ff) 130.57/78.23 new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Neg(Succ(zzz90800)), zzz909, zzz910, zzz911, zzz912, ga, gb) -> new_intersectFM_C2IntersectFM_C142(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz912, ga, gb) 130.57/78.23 new_intersectFM_C2IntersectFM_C143(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz909, ga, gb) -> new_intersectFM_C(new_intersectFM_C2Lts7(zzz899, zzz900, zzz901, zzz902, zzz903, ga), zzz906, ga) 130.57/78.23 new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, Succ(zzz20930), Zero, h, ba) -> new_intersectFM_C2IntersectFM_C10(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, Succ(zzz2083), Succ(zzz2088), h, ba) 130.57/78.23 new_intersectFM_C2IntersectFM_C121(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, Zero, Succ(zzz31790), cg, da) -> new_intersectFM_C(new_intersectFM_C2Gts1(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, cg), zzz3172, cg) 130.57/78.23 new_intersectFM_C2IntersectFM_C130(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, Succ(zzz27700), Succ(zzz27710), eb, ec) -> new_intersectFM_C2IntersectFM_C130(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, zzz27700, zzz27710, eb, ec) 130.57/78.23 new_intersectFM_C2IntersectFM_C126(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Branch(zzz12040, zzz12041, zzz12042, zzz12043, zzz12044), dd, de) -> new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, zzz12040, zzz12041, zzz12042, zzz12043, zzz12044, dd, de) 130.57/78.23 new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Pos(Succ(zzz62700)), zzz628, zzz629, EmptyFM, zzz631, db, dc) -> new_intersectFM_C(new_intersectFM_C2Gts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz626, db) 130.57/78.23 new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Pos(Succ(zzz62700)), zzz628, zzz629, Branch(zzz6300, zzz6301, zzz6302, zzz6303, zzz6304), zzz631, db, dc) -> new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, db, dc) 130.57/78.23 new_intersectFM_C2IntersectFM_C137(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, Succ(zzz15910), Zero, fb, fc) -> new_intersectFM_C2IntersectFM_C139(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, Succ(zzz1586), Succ(zzz1581), fb, fc) 130.57/78.23 new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Pos(Zero), zzz1604, zzz1605, zzz1606, zzz1607, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Lts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1601, gc) 130.57/78.23 new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Neg(Succ(zzz160300)), zzz1604, zzz1605, zzz1606, zzz1607, gc, gd) -> new_intersectFM_C2IntersectFM_C144(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1607, gc, gd) 130.57/78.23 new_intersectFM_C2IntersectFM_C10(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, Zero, Succ(zzz26250), bb, bc) -> new_intersectFM_C(new_intersectFM_C2Lts(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, bb), zzz2617, bb) 130.57/78.23 new_intersectFM_C2IntersectFM_C124(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, EmptyFM, db, dc) -> new_intersectFM_C(new_intersectFM_C2Lts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz625, db) 130.57/78.23 new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, Branch(Pos(Zero), zzz20911, zzz20912, zzz20913, zzz20914), h, ba) -> new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz20914, h, ba) 130.57/78.23 new_intersectFM_C(Branch(Pos(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitGT215(zzz31, zzz32, zzz33, zzz34, bd), zzz44, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Pos(Succ(zzz90800)), zzz909, zzz910, Branch(zzz9110, zzz9111, zzz9112, zzz9113, zzz9114), zzz912, ga, gb) -> new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz9110, zzz9111, zzz9112, zzz9113, zzz9114, ga, gb) 130.57/78.23 new_intersectFM_C2IntersectFM_C143(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz909, ga, gb) -> new_intersectFM_C(new_intersectFM_C2Gts7(zzz899, zzz900, zzz901, zzz902, zzz903, ga), zzz907, ga) 130.57/78.23 new_intersectFM_C2IntersectFM_C145(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1604, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Lts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1601, gc) 130.57/78.23 new_intersectFM_C(Branch(Pos(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitGT213(zzz31, zzz32, zzz33, zzz34, bd), zzz44, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C131(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, dh, ea) -> new_intersectFM_C2IntersectFM_C130(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, Succ(zzz1408), Succ(zzz1403), dh, ea) 130.57/78.23 new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, Succ(zzz21580), Zero, ed, ee) -> new_intersectFM_C2IntersectFM_C133(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, Succ(zzz2153), Succ(zzz2148), ed, ee) 130.57/78.23 new_intersectFM_C2IntersectFM_C119(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, Succ(zzz19920), Succ(zzz19930), ce, cf) -> new_intersectFM_C2IntersectFM_C119(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz19920, zzz19930, ce, cf) 130.57/78.23 new_intersectFM_C2IntersectFM_C130(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, Zero, Zero, eb, ec) -> new_intersectFM_C2IntersectFM_C132(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, eb, ec) 130.57/78.23 new_intersectFM_C2IntersectFM_C139(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, Zero, Succ(zzz28990), fd, ff) -> new_intersectFM_C(new_intersectFM_C2Gts6(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, fd), zzz2892, fd) 130.57/78.23 new_intersectFM_C2IntersectFM_C139(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, Succ(zzz28980), Succ(zzz28990), fd, ff) -> new_intersectFM_C2IntersectFM_C139(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, zzz28980, zzz28990, fd, ff) 130.57/78.23 new_intersectFM_C2IntersectFM_C123(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, cg, da) -> new_intersectFM_C(new_intersectFM_C2Gts1(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, cg), zzz3172, cg) 130.57/78.23 new_intersectFM_C(Branch(Neg(Succ(zzz3000)), zzz31, zzz32, zzz33, EmptyFM), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitGT7(bd), zzz44, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C142(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, EmptyFM, ga, gb) -> new_intersectFM_C2IntersectFM_C111(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, ga, gb) 130.57/78.23 new_intersectFM_C2IntersectFM_C133(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, Succ(zzz26420), Zero, ef, eg) -> new_intersectFM_C2IntersectFM_C134(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2641, ef, eg) 130.57/78.23 new_intersectFM_C2IntersectFM_C124(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, EmptyFM, db, dc) -> new_intersectFM_C(new_intersectFM_C2Gts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz626, db) 130.57/78.23 new_intersectFM_C2IntersectFM_C126(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, EmptyFM, dd, de) -> new_intersectFM_C(new_intersectFM_C2Lts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1199, dd) 130.57/78.23 new_intersectFM_C2IntersectFM_C127(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, zzz1202, dd, de) -> new_intersectFM_C(new_intersectFM_C2Gts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1200, dd) 130.57/78.23 new_intersectFM_C2IntersectFM_C128(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, Zero, Succ(zzz14140), dh, ea) -> new_intersectFM_C2IntersectFM_C129(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1411, dh, ea) 130.57/78.23 new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, Pos(Zero), zzz2744, zzz2745, zzz2746, zzz2747, be, bf) -> new_intersectFM_C2IntersectFM_C115(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, zzz2747, be, bf) 130.57/78.23 new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Pos(Zero), zzz1604, zzz1605, zzz1606, zzz1607, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Gts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1602, gc) 130.57/78.23 new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, EmptyFM, zzz2157, Zero, Succ(zzz21590), ed, ee) -> new_intersectFM_C(new_intersectFM_C2Lts5(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, ed), zzz2151, ed) 130.57/78.23 new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, EmptyFM, ed, ee) -> new_intersectFM_C(new_intersectFM_C2Lts5(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, ed), zzz2151, ed) 130.57/78.23 new_intersectFM_C(Branch(Neg(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitGT216(zzz31, zzz32, zzz33, zzz34, bd), zzz44, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, Pos(zzz7520), zzz753, zzz754, Branch(zzz7550, zzz7551, zzz7552, zzz7553, zzz7554), zzz756, df, dg) -> new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, zzz7550, zzz7551, zzz7552, zzz7553, zzz7554, df, dg) 130.57/78.23 new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, EmptyFM, zzz2092, Zero, Succ(zzz20940), h, ba) -> new_intersectFM_C(new_intersectFM_C2Lts(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, h), zzz2086, h) 130.57/78.23 new_intersectFM_C2IntersectFM_C111(zzz830, zzz831, zzz832, zzz833, zzz834, zzz835, zzz836, zzz837, zzz838, fg, fh) -> new_intersectFM_C(new_intersectFM_C2Lts7(zzz830, zzz831, zzz832, zzz833, zzz834, fg), zzz837, fg) 130.57/78.23 new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Neg(Zero), zzz909, zzz910, zzz911, zzz912, ga, gb) -> new_intersectFM_C2IntersectFM_C143(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz909, ga, gb) 130.57/78.23 new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, Branch(Pos(Succ(zzz2091000)), zzz20911, zzz20912, zzz20913, zzz20914), h, ba) -> new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2091000, zzz20911, zzz20912, zzz20913, zzz20914, zzz2083, zzz2091000, h, ba) 130.57/78.23 new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, Branch(Neg(Succ(zzz2156000)), zzz21561, zzz21562, zzz21563, zzz21564), ed, ee) -> new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2156000, zzz21561, zzz21562, zzz21563, zzz21564, zzz2156000, zzz2148, ed, ee) 130.57/78.23 new_intersectFM_C2IntersectFM_C136(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, ef, eg) -> new_intersectFM_C(new_intersectFM_C2Gts5(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, ef), zzz2636, ef) 130.57/78.23 new_intersectFM_C2IntersectFM_C139(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, Succ(zzz28980), Zero, fd, ff) -> new_intersectFM_C2IntersectFM_C138(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2897, fd, ff) 130.57/78.23 new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Pos(Zero), zzz1202, zzz1203, zzz1204, zzz1205, dd, de) -> new_intersectFM_C(new_intersectFM_C2Gts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1200, dd) 130.57/78.23 new_intersectFM_C2IntersectFM_C145(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1604, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Gts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1602, gc) 130.57/78.23 new_intersectFM_C(Branch(Neg(Zero), zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(Neg(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C110(zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz4000, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, bd, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, Branch(Pos(zzz215600), zzz21561, zzz21562, zzz21563, zzz21564), ed, ee) -> new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz21563, ed, ee) 130.57/78.23 new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, Neg(Succ(zzz75200)), zzz753, zzz754, zzz755, zzz756, df, dg) -> new_intersectFM_C2IntersectFM_C128(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, zzz75200, zzz753, zzz754, zzz755, zzz756, zzz75200, zzz747, df, dg) 130.57/78.23 new_intersectFM_C2IntersectFM_C128(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, Succ(zzz14130), Succ(zzz14140), dh, ea) -> new_intersectFM_C2IntersectFM_C128(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, zzz14130, zzz14140, dh, ea) 130.57/78.23 new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Pos(Succ(zzz160300)), zzz1604, zzz1605, EmptyFM, zzz1607, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Lts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1601, gc) 130.57/78.23 new_intersectFM_C(Branch(Neg(Zero), zzz31, zzz32, EmptyFM, zzz34), Branch(Neg(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_mkVBalBranch7(zzz31, new_splitGT8(zzz4000, bd), zzz34, bd), zzz44, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Pos(Zero), zzz628, zzz629, zzz630, zzz631, db, dc) -> new_intersectFM_C(new_intersectFM_C2Gts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz626, db) 130.57/78.23 new_intersectFM_C2IntersectFM_C133(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, Zero, Zero, ef, eg) -> new_intersectFM_C2IntersectFM_C136(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, ef, eg) 130.57/78.23 new_intersectFM_C(Branch(Pos(Zero), zzz31, zzz32, zzz33, EmptyFM), Branch(Pos(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT29(Pos(Zero), zzz31, zzz32, zzz33, EmptyFM, zzz4000, bd), zzz43, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C129(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, EmptyFM, df, dg) -> new_intersectFM_C(new_intersectFM_C2Gts4(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df), zzz751, df) 130.57/78.23 new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Pos(Succ(zzz62700)), zzz628, zzz629, EmptyFM, zzz631, db, dc) -> new_intersectFM_C(new_intersectFM_C2Lts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz625, db) 130.57/78.23 new_intersectFM_C2IntersectFM_C125(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, zzz628, db, dc) -> new_intersectFM_C(new_intersectFM_C2Gts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz626, db) 130.57/78.23 new_intersectFM_C2IntersectFM_C138(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, Branch(zzz8960, zzz8961, zzz8962, zzz8963, zzz8964), eh, fa) -> new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz8960, zzz8961, zzz8962, zzz8963, zzz8964, eh, fa) 130.57/78.23 new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, Neg(zzz13920), zzz1393, zzz1394, zzz1395, EmptyFM, cc, cd) -> new_intersectFM_C(new_intersectFM_C2Gts1(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, cc), zzz1391, cc) 130.57/78.23 new_intersectFM_C2IntersectFM_C116(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, Succ(zzz35390), Succ(zzz35400), ca, cb) -> new_intersectFM_C2IntersectFM_C116(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, zzz35390, zzz35400, ca, cb) 130.57/78.23 new_intersectFM_C(Branch(Pos(Succ(zzz3000)), zzz31, zzz32, zzz33, zzz34), Branch(Pos(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C1(zzz3000, zzz31, zzz32, zzz33, zzz34, zzz4000, zzz41, zzz42, zzz43, zzz44, zzz3000, zzz31, zzz32, zzz33, zzz34, zzz4000, zzz3000, bd, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, Branch(Pos(Succ(zzz2091000)), zzz20911, zzz20912, zzz20913, zzz20914), zzz2092, Zero, Succ(zzz20940), h, ba) -> new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2091000, zzz20911, zzz20912, zzz20913, zzz20914, zzz2083, zzz2091000, h, ba) 130.57/78.23 new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, Neg(zzz13920), zzz1393, zzz1394, zzz1395, EmptyFM, cc, cd) -> new_intersectFM_C(new_intersectFM_C2Lts1(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, cc), zzz1390, cc) 130.57/78.23 new_intersectFM_C2IntersectFM_C120(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, EmptyFM, cc, cd) -> new_intersectFM_C(new_intersectFM_C2Gts1(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, cc), zzz1391, cc) 130.57/78.23 new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, EmptyFM, h, ba) -> new_intersectFM_C(new_intersectFM_C2Lts(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, h), zzz2086, h) 130.57/78.23 new_intersectFM_C(Branch(Pos(Succ(zzz3000)), zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C112(zzz3000, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, bd, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C121(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, Zero, Zero, cg, da) -> new_intersectFM_C2IntersectFM_C123(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, cg, da) 130.57/78.23 new_intersectFM_C2IntersectFM_C128(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, Zero, Zero, dh, ea) -> new_intersectFM_C2IntersectFM_C131(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, dh, ea) 130.57/78.23 new_intersectFM_C2IntersectFM_C12(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, h, ba) -> new_intersectFM_C2IntersectFM_C10(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, Succ(zzz2083), Succ(zzz2088), h, ba) 130.57/78.23 new_intersectFM_C2IntersectFM_C144(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, EmptyFM, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Gts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1602, gc) 130.57/78.23 new_intersectFM_C(Branch(Neg(zzz300), zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(Pos(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C15(zzz300, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz4000, zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, bd, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Pos(Succ(zzz160300)), zzz1604, zzz1605, Branch(zzz16060, zzz16061, zzz16062, zzz16063, zzz16064), zzz1607, gc, gd) -> new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz16060, zzz16061, zzz16062, zzz16063, zzz16064, gc, gd) 130.57/78.23 new_intersectFM_C2IntersectFM_C137(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, Zero, Zero, fb, fc) -> new_intersectFM_C2IntersectFM_C140(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, fb, fc) 130.57/78.23 new_intersectFM_C(Branch(Neg(Zero), zzz31, zzz32, EmptyFM, zzz34), Branch(Neg(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT7(zzz31, zzz32, zzz34, zzz4000, bd), zzz43, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Neg(Zero), zzz1604, zzz1605, zzz1606, zzz1607, gc, gd) -> new_intersectFM_C2IntersectFM_C145(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1604, gc, gd) 130.57/78.23 new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, Neg(zzz27430), zzz2744, zzz2745, zzz2746, Branch(zzz27470, zzz27471, zzz27472, zzz27473, zzz27474), be, bf) -> new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, zzz27470, zzz27471, zzz27472, zzz27473, zzz27474, be, bf) 130.57/78.23 new_intersectFM_C2IntersectFM_C114(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, Succ(zzz30820), Succ(zzz30830), bg, bh) -> new_intersectFM_C2IntersectFM_C114(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, zzz30820, zzz30830, bg, bh) 130.57/78.23 new_intersectFM_C2IntersectFM_C124(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Branch(zzz6300, zzz6301, zzz6302, zzz6303, zzz6304), db, dc) -> new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, db, dc) 130.57/78.23 new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, Branch(Neg(Zero), zzz21561, zzz21562, zzz21563, zzz21564), zzz2157, Zero, Succ(zzz21590), ed, ee) -> new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz21563, ed, ee) 130.57/78.23 new_intersectFM_C2IntersectFM_C127(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, zzz1202, dd, de) -> new_intersectFM_C(new_intersectFM_C2Lts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1199, dd) 130.57/78.23 new_intersectFM_C(Branch(Pos(zzz300), zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(Neg(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C18(zzz300, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz4000, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, bd, bd) 130.57/78.23 new_intersectFM_C(Branch(Neg(Succ(zzz3000)), zzz31, zzz32, zzz33, EmptyFM), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitGT9(bd), zzz44, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C125(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, zzz628, db, dc) -> new_intersectFM_C(new_intersectFM_C2Lts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz625, db) 130.57/78.23 new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, Pos(zzz7520), zzz753, zzz754, EmptyFM, zzz756, df, dg) -> new_intersectFM_C(new_intersectFM_C2Gts4(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df), zzz751, df) 130.57/78.23 new_intersectFM_C2IntersectFM_C10(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, Succ(zzz26240), Succ(zzz26250), bb, bc) -> new_intersectFM_C2IntersectFM_C10(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, zzz26240, zzz26250, bb, bc) 130.57/78.23 new_intersectFM_C(Branch(Neg(Succ(zzz3000)), zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C17(zzz3000, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, bd, bd) 130.57/78.23 new_intersectFM_C(Branch(Pos(Succ(zzz3000)), zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C16(zzz3000, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, bd, bd) 130.57/78.23 new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Pos(Succ(zzz120100)), zzz1202, zzz1203, EmptyFM, zzz1205, dd, de) -> new_intersectFM_C(new_intersectFM_C2Gts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1200, dd) 130.57/78.23 new_intersectFM_C2IntersectFM_C119(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, Zero, Zero, ce, cf) -> new_intersectFM_C2IntersectFM_C122(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, ce, cf) 130.57/78.23 new_intersectFM_C2IntersectFM_C114(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, Zero, Zero, bg, bh) -> new_intersectFM_C2IntersectFM_C117(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, bg, bh) 130.57/78.23 new_intersectFM_C2IntersectFM_C114(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, Succ(zzz30820), Zero, bg, bh) -> new_intersectFM_C2IntersectFM_C116(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, Succ(zzz3072), Succ(zzz3077), bg, bh) 130.57/78.23 new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, Pos(Succ(zzz139200)), zzz1393, zzz1394, zzz1395, zzz1396, cc, cd) -> new_intersectFM_C2IntersectFM_C119(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, zzz139200, zzz1393, zzz1394, zzz1395, zzz1396, zzz1387, zzz139200, cc, cd) 130.57/78.23 new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, Branch(Pos(Zero), zzz20911, zzz20912, zzz20913, zzz20914), zzz2092, Zero, Succ(zzz20940), h, ba) -> new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz20914, h, ba) 130.57/78.23 new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, Neg(zzz13920), zzz1393, zzz1394, zzz1395, Branch(zzz13960, zzz13961, zzz13962, zzz13963, zzz13964), cc, cd) -> new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, zzz13960, zzz13961, zzz13962, zzz13963, zzz13964, cc, cd) 130.57/78.23 new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, EmptyFM, h, ba) -> new_intersectFM_C(new_intersectFM_C2Gts(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, h), zzz2087, h) 130.57/78.23 new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Neg(Succ(zzz120100)), zzz1202, zzz1203, zzz1204, zzz1205, dd, de) -> new_intersectFM_C2IntersectFM_C126(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, zzz1205, dd, de) 130.57/78.23 130.57/78.23 The TRS R consists of the following rules: 130.57/78.23 130.57/78.23 new_mkBalBranch6MkBalBranch41(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64470), gf, gg) -> new_mkBalBranch6MkBalBranch42(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.23 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234, bd) -> new_mkBalBranch(zzz5230, zzz5231, new_mkVBalBranch8(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, bd), zzz5234, ty_Int, bd) 130.57/78.23 new_mkBalBranch6MkBalBranch113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Succ(zzz6476000), Zero, gf, gg) -> new_mkBalBranch6MkBalBranch114(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.23 new_mkVBalBranch3MkVBalBranch148(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bd) 130.57/78.23 new_mkBalBranch6MkBalBranch314(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, zzz6461, gf, gg) -> new_mkBalBranch6MkBalBranch36(zzz474034, zzz474030, zzz474031, zzz6373, zzz6461, zzz645200, gf, gg) 130.57/78.23 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.23 new_mkVBalBranch3MkVBalBranch230(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bbf) -> new_mkVBalBranch3MkVBalBranch240(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bbf) 130.57/78.23 new_mkBalBranch6MkBalBranch415(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Succ(zzz644300)), Pos(zzz64420), gf, gg) -> new_mkBalBranch6MkBalBranch410(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, new_primMulNat(zzz64420), gf, gg) 130.57/78.23 new_splitGT18(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, Succ(zzz45010), Zero, bcf) -> new_splitGT19(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, bcf) 130.57/78.23 new_splitLT216(Pos(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_splitLT217(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.23 new_splitLT217(zzz830, zzz831, zzz832, zzz833, zzz834, fg) -> new_splitLT9(zzz833, fg) 130.57/78.23 new_splitLT211(zzz31, zzz32, zzz33, zzz34, bd) -> zzz33 130.57/78.23 new_mkVBalBranch3MkVBalBranch239(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, he) -> new_mkVBalBranch3MkVBalBranch232(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, he) 130.57/78.23 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.57/78.23 new_mkBalBranch6MkBalBranch43(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBalBranch6MkBalBranch40(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.23 new_mkBalBranch6MkBalBranch310(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64620), gf, gg) -> new_mkBalBranch6MkBalBranch38(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.23 new_mkBalBranch6MkBalBranch44(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64510), gf, gg) -> new_mkBalBranch6MkBalBranch45(zzz474034, zzz474030, zzz474031, zzz6373, zzz64510, Zero, gf, gg) 130.57/78.23 new_mkVBalBranch3MkVBalBranch130(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Zero, bce) -> new_mkVBalBranch3MkVBalBranch153(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, bce) 130.57/78.23 new_mkBalBranch6MkBalBranch34(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, Succ(zzz64560), gf, gg) -> new_mkBalBranch6MkBalBranch37(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, zzz64560, gf, gg) 130.57/78.23 new_mkBalBranch6MkBalBranch31(zzz474034, zzz474030, zzz474031, EmptyFM, gf, gg) -> error([]) 130.57/78.23 new_mkBalBranch6MkBalBranch30(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64590), gf, gg) -> new_mkBalBranch6MkBalBranch31(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.23 new_mkBalBranch6MkBalBranch019(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch014(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.23 new_mkVBalBranch3MkVBalBranch126(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), bcd) -> new_mkBalBranch(zzz6020, zzz6021, zzz6023, new_mkVBalBranch5(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), bcd), ty_Int, bcd) 130.57/78.23 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(zzz300), zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), ty_Int, bd) 130.57/78.23 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234, bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(zzz300), zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234), ty_Int, bd) 130.57/78.23 new_primPlusNat2(Zero) -> Zero 130.57/78.23 new_intersectFM_C2Gts6(zzz884, zzz885, zzz886, zzz887, zzz888, eh) -> new_splitGT219(zzz884, zzz885, zzz886, zzz887, zzz888, eh) 130.57/78.23 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Succ(zzz426200)), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch133(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz4260, zzz4261, zzz426200, zzz4263, zzz4264, Succ(zzz3000), zzz31, new_primPlusNat0(new_primMulNat0(zzz426200), Succ(zzz426200)), bd) 130.57/78.23 new_mkVBalBranch3MkVBalBranch239(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), he) -> new_mkVBalBranch3MkVBalBranch222(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, he) 130.57/78.23 new_splitGT229(zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, bbh) -> new_splitGT13(zzz16124, zzz1613, bbh) 130.57/78.23 new_addToFM_C11(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, Succ(zzz43100), Succ(zzz43110), bae) -> new_addToFM_C11(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, zzz43100, zzz43110, bae) 130.57/78.23 new_splitLT41(zzz4000, bd) -> new_emptyFM(bd) 130.57/78.23 new_mkVBalBranch12(zzz6130, zzz6131, EmptyFM, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, bcb) -> new_addToFM2(zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, zzz6130, zzz6131, bcb) 130.57/78.23 new_splitGT12(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, Succ(zzz44340), Zero, bbb) -> new_splitGT17(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, bbb) 130.57/78.23 new_splitGT42(zzz4000, bd) -> new_emptyFM(bd) 130.57/78.23 new_mkVBalBranch3MkVBalBranch142(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, bbf) -> new_mkVBalBranch3MkVBalBranch139(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Zero, bbf) 130.57/78.23 new_intersectFM_C2Lts7(zzz830, zzz831, zzz832, zzz833, zzz834, fg) -> new_splitLT217(zzz830, zzz831, zzz832, zzz833, zzz834, fg) 130.57/78.23 new_mkVBalBranch3MkVBalBranch136(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, he) -> new_mkVBalBranch3MkVBalBranch130(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Zero, he) 130.57/78.23 new_splitGT12(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, Zero, Zero, bbb) -> new_splitGT17(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, bbb) 130.57/78.23 new_mkBalBranch6MkBalBranch413(zzz474034, zzz474030, zzz474031, zzz6373, zzz6442, gf, gg) -> new_mkBalBranch6MkBalBranch415(zzz474034, zzz474030, zzz474031, zzz6373, new_mkBalBranch6Size_r(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg), zzz6442, gf, gg) 130.57/78.23 new_mkBalBranch6MkBalBranch015(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Neg(Zero), Pos(zzz64550), gf, gg) -> new_mkBalBranch6MkBalBranch0111(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, new_primMulNat8(zzz64550), gf, gg) 130.57/78.23 new_mkVBalBranch3MkVBalBranch137(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bd) 130.57/78.23 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch235(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bd) 130.57/78.23 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch8(Zero, zzz31, zzz3530, zzz3531, Neg(Succ(zzz353200)), zzz3533, zzz3534, zzz343, bd), zzz344, ty_Int, bd) 130.57/78.23 new_mkVBalBranch3MkVBalBranch143(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bac) -> new_mkVBalBranch3MkVBalBranch145(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bac) 130.57/78.23 new_mkVBalBranch3MkVBalBranch140(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, bbd) -> new_mkVBalBranch3MkVBalBranch126(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), bbd) 130.57/78.23 new_splitGT11(EmptyFM, dd) -> new_splitGT43(dd) 130.57/78.23 new_mkVBalBranch3MkVBalBranch133(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), bd) -> new_mkVBalBranch3MkVBalBranch154(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, bd) 130.57/78.23 new_mkBalBranch6MkBalBranch35(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Zero), Neg(zzz64530), gf, gg) -> new_mkBalBranch6MkBalBranch313(zzz474034, zzz474030, zzz474031, zzz6373, new_primMulNat(zzz64530), gf, gg) 130.57/78.23 new_splitLT15(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, Succ(zzz45100), Succ(zzz45110), ha) -> new_splitLT15(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, zzz45100, zzz45110, ha) 130.57/78.23 new_primMulNat(Succ(zzz633700)) -> new_primPlusNat0(new_primMulNat0(zzz633700), Succ(zzz633700)) 130.57/78.23 new_mkBalBranch6MkBalBranch117(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Succ(zzz64840), gf, gg) -> new_mkBalBranch6MkBalBranch118(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.23 new_splitGT217(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd) -> new_splitGT11(zzz1196, dd) 130.57/78.23 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, zzz2502, zzz2503, zzz2504), EmptyFM, bd) -> new_addToFM3(Branch(zzz2500, zzz2501, zzz2502, zzz2503, zzz2504), zzz300, zzz31, bd) 130.57/78.23 new_mkVBalBranch3MkVBalBranch149(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, bcb) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(zzz6130), zzz6131, Branch(zzz6120, zzz6121, Pos(Succ(zzz6122)), zzz6123, zzz6124), Branch(zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129), ty_Int, bcb) 130.57/78.23 new_addToFM_C3(Branch(Neg(Zero), zzz9821, zzz9822, zzz9823, zzz9824), Zero, zzz31, bd) -> Branch(Neg(Zero), new_addToFM0(zzz9821, zzz31, bd), zzz9822, zzz9823, zzz9824) 130.57/78.23 new_mkVBalBranch3MkVBalBranch232(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, he) -> new_mkVBalBranch3MkVBalBranch136(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), he) 130.57/78.23 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Zero), zzz31, Branch(zzz3530, zzz3531, Neg(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Int, bd) 130.57/78.23 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.23 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch147(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bd) 130.57/78.23 new_splitGT224(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, bbg) -> new_splitGT18(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Succ(zzz3494), Succ(zzz3499), bbg) 130.57/78.23 new_addToFM_C25(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, hh) -> new_addToFM_C11(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Succ(zzz3186), Succ(zzz3181), hh) 130.57/78.23 new_mkBalBranch6MkBalBranch49(zzz474034, zzz474030, zzz474031, zzz6373, Zero, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch43(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.23 new_mkBalBranch6MkBalBranch48(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, zzz6444, gf, gg) -> new_mkBalBranch6MkBalBranch45(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, zzz6444, gf, gg) 130.57/78.23 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(zzz300), zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Int, bd) 130.57/78.23 new_primPlusInt2(Pos(zzz63770), zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_primPlusInt0(zzz63770, new_sizeFM(zzz474034, gf, gg)) 130.57/78.23 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.57/78.23 new_mkBalBranch6MkBalBranch011(zzz4740340, zzz4740341, zzz4740342, Branch(zzz47403430, zzz47403431, zzz47403432, zzz47403433, zzz47403434), zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), zzz47403430, zzz47403431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), zzz474030, zzz474031, zzz6373, zzz47403433, gf, gg), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4740340, zzz4740341, zzz47403434, zzz4740344, gf, gg), gf, gg) 130.57/78.23 new_mkVBalBranch3MkVBalBranch224(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), hf) -> new_mkBalBranch(zzz3880, zzz3881, new_mkVBalBranch5(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, hf), zzz3884, ty_Int, hf) 130.57/78.23 new_mkVBalBranch7(zzz31, EmptyFM, zzz34, bd) -> new_addToFM(zzz34, zzz31, bd) 130.57/78.23 new_mkBalBranch6MkBalBranch017(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBranch(Succ(Succ(Zero)), zzz4740340, zzz4740341, new_mkBranch(Succ(Succ(Succ(Zero))), zzz474030, zzz474031, zzz6373, zzz4740343, gf, gg), zzz4740344, gf, gg) 130.57/78.23 new_splitGT215(zzz31, zzz32, zzz33, zzz34, bd) -> zzz34 130.57/78.23 new_mkVBalBranch3MkVBalBranch143(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bac) -> new_mkVBalBranch3MkVBalBranch145(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bac) 130.57/78.23 new_mkVBalBranch3MkVBalBranch146(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bd) 130.57/78.23 new_mkBalBranch6MkBalBranch37(zzz474034, zzz474030, zzz474031, zzz6373, Zero, Succ(zzz645600), gf, gg) -> new_mkBalBranch6MkBalBranch38(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.23 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Succ(Succ(Zero))), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch230(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz4260, zzz4261, Succ(Zero), zzz4263, zzz4264, Succ(zzz3000), zzz31, Zero, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), bd) 130.57/78.23 new_mkVBalBranch3MkVBalBranch133(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, bd) -> new_mkVBalBranch3MkVBalBranch154(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, bd) 130.57/78.23 new_mkBalBranch6MkBalBranch016(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Succ(zzz6454000), Succ(zzz647200), gf, gg) -> new_mkBalBranch6MkBalBranch016(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, zzz6454000, zzz647200, gf, gg) 130.57/78.23 new_splitLT42(zzz4000, bd) -> new_emptyFM(bd) 130.57/78.23 new_mkVBalBranch11(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, bd) -> new_mkVBalBranch30(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, bd) 130.57/78.23 new_primPlusInt2(Neg(zzz63770), zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_primPlusInt1(zzz63770, new_sizeFM(zzz474034, gf, gg)) 130.57/78.23 new_mkVBalBranch3MkVBalBranch227(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bac) -> new_mkVBalBranch3MkVBalBranch228(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bac) 130.57/78.23 new_splitLT12(EmptyFM, zzz1975, gh) -> new_splitLT42(zzz1975, gh) 130.57/78.23 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch133(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), bd) 130.57/78.23 new_mkBalBranch6MkBalBranch38(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBalBranch6MkBalBranch39(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.23 new_splitLT13(Branch(Pos(zzz74500), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, df) -> new_splitLT214(zzz74500, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, df) 130.57/78.23 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.23 new_mkBalBranch6MkBalBranch1110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Pos(Zero), Pos(zzz64770), gf, gg) -> new_mkBalBranch6MkBalBranch1112(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, new_primMulNat8(zzz64770), gf, gg) 130.57/78.23 new_mkVBalBranch3MkVBalBranch228(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bac) -> new_mkVBalBranch3MkVBalBranch143(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primMulNat3(zzz5096), bac) 130.57/78.23 new_addToFM_C23(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Succ(zzz33930), Zero, bca) -> new_addToFM_C26(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, bca) 130.57/78.23 new_primPlusInt0(zzz58960, Neg(zzz59000)) -> new_primMinusNat0(zzz58960, zzz59000) 130.57/78.23 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch137(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat6, bd) 130.57/78.23 new_intersectFM_C2Lts5(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, ed) -> new_splitLT13(Branch(Neg(Succ(zzz2143)), zzz2144, zzz2145, zzz2146, zzz2147), zzz2148, ed) 130.57/78.23 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Succ(Succ(zzz3532000))), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch230(zzz3530, zzz3531, zzz3532000, zzz3533, zzz3534, zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, Zero, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz3532000), Succ(zzz3532000))), Succ(zzz3532000))), Succ(zzz3532000)), zzz3532000))), bd) 130.57/78.23 new_splitLT214(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df) -> new_splitLT13(zzz745, zzz747, df) 130.57/78.23 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.23 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, bd) -> new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch10(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, bd), ty_Int, bd) 130.57/78.23 new_mkVBalBranch3MkVBalBranch150(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), bcc) -> new_mkVBalBranch3MkVBalBranch130(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), bcc) 130.57/78.23 new_intersectFM_C2Lts6(zzz884, zzz885, zzz886, zzz887, zzz888, eh) -> new_splitLT13(Branch(Neg(Zero), zzz884, zzz885, zzz886, zzz887), zzz888, eh) 130.57/78.23 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.23 new_primMinusNat0(Succ(zzz482800), Zero) -> Pos(Succ(zzz482800)) 130.57/78.23 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Zero), zzz31, Branch(zzz3530, zzz3531, Pos(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Int, bd) 130.57/78.23 new_splitLT29(Neg(zzz19700), zzz1971, zzz1972, Branch(zzz19730, zzz19731, zzz19732, zzz19733, zzz19734), Branch(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744), zzz1975, gh) -> new_mkVBalBranch8(zzz19700, zzz1971, zzz19730, zzz19731, zzz19732, zzz19733, zzz19734, new_splitLT31(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744, zzz1975, gh), gh) 130.57/78.23 new_mkBalBranch6MkBalBranch37(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz6452000), Zero, gf, gg) -> new_mkBalBranch6MkBalBranch31(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.23 new_primMulNat8(Zero) -> Zero 130.57/78.23 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch148(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat7, bd) 130.57/78.23 new_splitGT8(zzz4000, bd) -> new_splitGT41(zzz4000, bd) 130.57/78.23 new_mkBalBranch6MkBalBranch311(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64580), gf, gg) -> new_mkBalBranch6MkBalBranch36(zzz474034, zzz474030, zzz474031, zzz6373, Zero, zzz64580, gf, gg) 130.57/78.23 new_splitGT222(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Succ(zzz35000), Zero, bbg) -> new_splitGT16(zzz3498, zzz3499, bbg) 130.57/78.23 new_mkVBalBranch3MkVBalBranch225(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, hf) -> new_mkVBalBranch3MkVBalBranch236(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, hf) 130.57/78.23 new_mkBalBranch6MkBalBranch49(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz6443000), Succ(zzz644400), gf, gg) -> new_mkBalBranch6MkBalBranch49(zzz474034, zzz474030, zzz474031, zzz6373, zzz6443000, zzz644400, gf, gg) 130.57/78.23 new_mkVBalBranch3MkVBalBranch230(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bbf) -> new_mkVBalBranch3MkVBalBranch230(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bbf) 130.57/78.23 new_mkBalBranch6MkBalBranch1115(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Succ(zzz64850), gf, gg) -> new_mkBalBranch6MkBalBranch112(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz64850, Zero, gf, gg) 130.57/78.23 new_mkBalBranch6MkBalBranch1111(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, zzz6478, gf, gg) -> new_mkBalBranch6MkBalBranch112(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, zzz6478, gf, gg) 130.57/78.23 new_splitLT9(Branch(zzz8330, zzz8331, zzz8332, zzz8333, zzz8334), fg) -> new_splitLT216(zzz8330, zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.23 new_splitLT216(Neg(Zero), zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_splitLT222(zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.23 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(zzz300), zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Int, bd) 130.57/78.23 new_splitGT30(Neg(Zero), zzz7451, zzz7452, zzz7453, zzz7454, zzz747, df) -> new_splitGT219(zzz7451, zzz7452, zzz7453, zzz7454, zzz747, df) 130.57/78.23 new_splitGT17(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, bbb) -> zzz4432 130.57/78.23 new_addToFM_C11(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, Succ(zzz43100), Zero, bae) -> new_mkBalBranch(Pos(Succ(zzz4303)), zzz4304, zzz4306, new_addToFM_C4(zzz4307, Succ(zzz4308), zzz4309, bae), ty_Int, bae) 130.57/78.23 new_mkVBalBranch6(zzz3000, zzz31, EmptyFM, zzz426, bd) -> new_addToFM1(zzz426, zzz3000, zzz31, bd) 130.57/78.23 new_mkBalBranch6MkBalBranch313(zzz474034, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch32(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.23 new_mkBranch(zzz6231, zzz6232, zzz6233, zzz6234, zzz6235, hb, hc) -> Branch(zzz6232, zzz6233, new_primPlusInt(new_primPlusInt0(Succ(Zero), new_sizeFM(zzz6234, hb, hc)), zzz6234, zzz6235, zzz6232, hb, hc), zzz6234, zzz6235) 130.57/78.23 new_mkBalBranch6MkBalBranch1110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Neg(Zero), Neg(zzz64770), gf, gg) -> new_mkBalBranch6MkBalBranch1115(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, new_primMulNat8(zzz64770), gf, gg) 130.57/78.23 new_mkVBalBranch3MkVBalBranch152(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, bcd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(zzz6030), zzz6031, Branch(zzz6020, zzz6021, Pos(Succ(zzz6022)), zzz6023, zzz6024), Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ty_Int, bcd) 130.57/78.23 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.57/78.23 new_splitGT216(zzz31, zzz32, zzz33, zzz34, bd) -> zzz34 130.57/78.23 new_mkVBalBranch3MkVBalBranch146(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bd) 130.57/78.23 new_splitGT13(EmptyFM, zzz1613, bbh) -> new_splitGT42(zzz1613, bbh) 130.57/78.23 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.57/78.23 new_mkVBalBranch3MkVBalBranch231(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bbc) -> new_mkVBalBranch3MkVBalBranch242(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bbc) 130.57/78.23 new_mkVBalBranch3MkVBalBranch144(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bd) 130.57/78.23 new_mkVBalBranch3MkVBalBranch135(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(zzz300), zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234), ty_Int, bd) 130.57/78.23 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.57/78.23 new_addToFM2(zzz330, zzz331, zzz332, zzz333, zzz334, zzz300, zzz31, bd) -> new_addToFM_C3(Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz300, zzz31, bd) 130.57/78.23 new_splitGT225(Neg(zzz161200), zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, bbh) -> new_splitGT13(zzz16124, zzz1613, bbh) 130.57/78.23 new_mkVBalBranch3MkVBalBranch226(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, bab) -> new_mkVBalBranch3MkVBalBranch131(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primMulNat3(zzz5000), bab) 130.57/78.23 new_mkVBalBranch3MkVBalBranch130(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Zero, bce) -> new_mkVBalBranch3MkVBalBranch153(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, bce) 130.57/78.23 new_intersectFM_C2Lts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc) -> new_splitLT9(Branch(Neg(Succ(zzz1594)), zzz1595, zzz1596, zzz1597, zzz1598), gc) 130.57/78.23 new_mkBalBranch6MkBalBranch40(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBalBranch6MkBalBranch35(zzz474034, zzz474030, zzz474031, zzz6373, new_mkBalBranch6Size_l(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg), new_mkBalBranch6Size_r(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg), gf, gg) 130.57/78.23 new_mkBalBranch6MkBalBranch5(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Zero), gf, gg) -> new_mkBalBranch6MkBalBranch51(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.23 new_splitLT216(Neg(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_splitLT221(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.23 new_splitGT18(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, Succ(zzz45010), Succ(zzz45020), bcf) -> new_splitGT18(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, zzz45010, zzz45020, bcf) 130.57/78.23 new_sizeFM(EmptyFM, bah, bba) -> Pos(Zero) 130.57/78.23 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_splitLT5(bd) -> new_splitLT40(bd) 130.57/78.24 new_mkVBalBranch8(zzz300, zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, Branch(zzz5230, zzz5231, zzz5232, zzz5233, zzz5234), bd) -> new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, zzz5230, zzz5231, zzz5232, zzz5233, zzz5234, bd) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Succ(Succ(Succ(zzz42620000)))), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch230(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz4260, zzz4261, Succ(Succ(zzz42620000)), zzz4263, zzz4264, Succ(zzz3000), zzz31, Succ(zzz42620000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), bd) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch135(zzz3530, zzz3531, zzz3533, zzz3534, zzz340, zzz341, zzz34200, zzz343, zzz344, Zero, zzz31, new_primMulNat3(zzz34200), bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch237(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, bcc) -> new_mkVBalBranch3MkVBalBranch241(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, bcc) 130.57/78.24 new_splitLT7(zzz31, zzz32, zzz34, zzz4000, bd) -> new_splitLT16(zzz4000, bd) 130.57/78.24 new_addToFM_C13(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, Succ(zzz45450), Succ(zzz45460), bag) -> new_addToFM_C13(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, zzz45450, zzz45460, bag) 130.57/78.24 new_primPlusInt1(zzz58960, Neg(zzz59010)) -> Neg(new_primPlusNat0(zzz58960, zzz59010)) 130.57/78.24 new_mkVBalBranch3MkVBalBranch242(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bbc) -> new_mkVBalBranch3MkVBalBranch138(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primMulNat3(zzz5253), bbc) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkBalBranch(zzz2500, zzz2501, zzz2503, new_mkVBalBranch5(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd), ty_Int, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch49(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz6443000), Zero, gf, gg) -> new_mkBalBranch6MkBalBranch42(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch018(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Succ(zzz64640), gf, gg) -> new_mkBalBranch6MkBalBranch0110(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Zero, zzz64640, gf, gg) 130.57/78.24 new_splitLT17(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, Zero, Succ(zzz41850), baf) -> new_splitLT18(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, baf) 130.57/78.24 new_mkBalBranch6MkBalBranch015(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Neg(Succ(zzz645400)), Neg(zzz64550), gf, gg) -> new_mkBalBranch6MkBalBranch0110(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, new_primMulNat8(zzz64550), zzz645400, gf, gg) 130.57/78.24 new_splitGT218(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, bad) -> new_splitGT12(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Succ(zzz3401), Succ(zzz3396), bad) 130.57/78.24 new_splitGT230(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_splitGT15(zzz8334, fg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch139(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), bbe) -> new_mkVBalBranch3MkVBalBranch139(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, bbe) 130.57/78.24 new_mkBalBranch6MkBalBranch412(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64500), gf, gg) -> new_mkBalBranch6MkBalBranch411(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch311(zzz474034, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch32(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch32(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBalBranch6MkBalBranch39(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Succ(Succ(Zero))), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch231(zzz330, zzz331, zzz333, zzz334, zzz4260, zzz4261, Succ(Zero), zzz4263, zzz4264, Succ(zzz3000), zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch151(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), hf) -> new_mkVBalBranch3MkVBalBranch126(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), hf) 130.57/78.24 new_splitGT220(zzz830, zzz831, zzz832, zzz833, zzz834, fg) -> new_mkVBalBranch5(Succ(zzz830), zzz831, new_splitGT15(zzz833, fg), zzz834, fg) 130.57/78.24 new_splitGT30(Neg(Succ(zzz745000)), zzz7451, zzz7452, zzz7453, zzz7454, zzz747, df) -> new_splitGT222(zzz745000, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, zzz745000, zzz747, df) 130.57/78.24 new_addToFM_C3(Branch(Neg(Succ(zzz982000)), zzz9821, zzz9822, zzz9823, zzz9824), Succ(zzz3000), zzz31, bd) -> new_addToFM_C23(zzz982000, zzz9821, zzz9822, zzz9823, zzz9824, zzz3000, zzz31, zzz982000, zzz3000, bd) 130.57/78.24 new_primMinusNat0(Succ(zzz482800), Succ(zzz47700)) -> new_primMinusNat0(zzz482800, zzz47700) 130.57/78.24 new_intersectFM_C2Lts4(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df) -> new_splitLT214(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df) 130.57/78.24 new_mkVBalBranch3MkVBalBranch139(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), bbe) -> new_mkBalBranch(zzz6294, zzz6295, zzz6297, new_mkVBalBranch11(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, bbe), ty_Int, bbe) 130.57/78.24 new_mkVBalBranch3MkVBalBranch154(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, bd) -> new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch11(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, bd), ty_Int, bd) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) -> new_mkBalBranch(zzz2500, zzz2501, zzz2503, new_mkVBalBranch5(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd), ty_Int, bd) 130.57/78.24 new_addToFM_C4(Branch(Pos(Zero), zzz341, zzz342, zzz343, zzz344), Succ(zzz3000), zzz31, bd) -> new_mkBalBranch(Pos(Zero), zzz341, zzz343, new_addToFM_C4(zzz344, Succ(zzz3000), zzz31, bd), ty_Int, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch37(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz6452000), Succ(zzz645600), gf, gg) -> new_mkBalBranch6MkBalBranch37(zzz474034, zzz474030, zzz474031, zzz6373, zzz6452000, zzz645600, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch147(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch125(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bd) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Succ(Zero)), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch231(zzz3530, zzz3531, zzz3533, zzz3534, zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, Zero, zzz31, Succ(zzz3420000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), bd) 130.57/78.24 new_addToFM_C23(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Zero, Succ(zzz33940), bca) -> new_mkBalBranch(Neg(Succ(zzz3386)), zzz3387, new_addToFM_C3(zzz3389, Succ(zzz3391), zzz3392, bca), zzz3390, ty_Int, bca) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch238(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), bd) 130.57/78.24 new_mkBalBranch6MkBalBranch35(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Zero), Pos(zzz64530), gf, gg) -> new_mkBalBranch6MkBalBranch311(zzz474034, zzz474030, zzz474031, zzz6373, new_primMulNat(zzz64530), gf, gg) 130.57/78.24 new_addToFM0(zzz341, zzz31, bd) -> zzz31 130.57/78.24 new_splitLT220(zzz618, zzz619, zzz620, zzz621, zzz622, db) -> new_splitLT19(zzz621, db) 130.57/78.24 new_mkBalBranch6MkBalBranch015(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Neg(Succ(zzz645400)), Pos(zzz64550), gf, gg) -> new_mkBalBranch6MkBalBranch017(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.57/78.24 new_mkVBalBranch3MkVBalBranch150(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, bcc) -> new_mkVBalBranch3MkVBalBranch130(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Zero, bcc) 130.57/78.24 new_mkVBalBranch12(zzz6130, zzz6131, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, bcb) -> new_mkVBalBranch30(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bcb) 130.57/78.24 new_splitLT218(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Succ(zzz35090), Succ(zzz35100), hg) -> new_splitLT218(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, zzz35090, zzz35100, hg) 130.57/78.24 new_mkBalBranch6MkBalBranch45(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch42(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_splitLT13(Branch(Neg(Succ(zzz745000)), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, df) -> new_splitLT218(zzz745000, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, zzz745000, zzz747, df) 130.57/78.24 new_mkVBalBranch3MkVBalBranch132(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, bd) -> new_mkVBalBranch3MkVBalBranch145(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), bd) 130.57/78.24 new_addToFM_C13(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, Succ(zzz45450), Zero, bag) -> new_mkBalBranch(Neg(Succ(zzz4538)), zzz4539, zzz4541, new_addToFM_C3(zzz4542, Succ(zzz4543), zzz4544, bag), ty_Int, bag) 130.57/78.24 new_splitLT216(Pos(Zero), zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_splitLT219(zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.24 new_splitGT16(Branch(zzz7450, zzz7451, zzz7452, zzz7453, zzz7454), zzz747, df) -> new_splitGT30(zzz7450, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, df) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) -> new_mkBalBranch(zzz3530, zzz3531, zzz3533, new_mkVBalBranch7(zzz31, zzz3534, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd), ty_Int, bd) 130.57/78.24 new_splitGT14(zzz618, zzz619, zzz620, zzz621, zzz622, db) -> new_splitGT228(zzz618, zzz619, zzz620, zzz621, zzz622, db) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Succ(Succ(zzz3532000))), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch229(zzz3530, zzz3531, zzz3532000, zzz3533, zzz3534, zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, Zero, zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz3532000), Succ(zzz3532000))), Succ(zzz3532000))), Succ(zzz3532000)), zzz3532000))), zzz342000, bd) 130.57/78.24 new_splitLT212(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Succ(zzz31390), Succ(zzz31400), ge) -> new_splitLT212(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, zzz31390, zzz31400, ge) 130.57/78.24 new_splitGT222(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Zero, Succ(zzz35010), bbg) -> new_splitGT224(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, bbg) 130.57/78.24 new_mkBalBranch6MkBalBranch39(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBranch(Succ(Zero), zzz474030, zzz474031, zzz6373, zzz474034, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch139(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Zero, bbe) -> new_mkVBalBranch3MkVBalBranch141(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, bbe) 130.57/78.24 new_mkVBalBranch3MkVBalBranch230(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bbf) -> new_mkVBalBranch3MkVBalBranch240(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bbf) 130.57/78.24 new_splitGT11(Branch(Pos(Zero), zzz11961, zzz11962, zzz11963, zzz11964), dd) -> new_splitGT213(zzz11961, zzz11962, zzz11963, zzz11964, dd) 130.57/78.24 new_addToFM_C3(Branch(Pos(zzz98200), zzz9821, zzz9822, zzz9823, zzz9824), Succ(zzz3000), zzz31, bd) -> new_mkBalBranch(Pos(zzz98200), zzz9821, new_addToFM_C3(zzz9823, Succ(zzz3000), zzz31, bd), zzz9824, ty_Int, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch416(zzz474034, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch43(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_splitGT7(bd) -> new_splitGT43(bd) 130.57/78.24 new_intersectFM_C2Lts2(zzz618, zzz619, zzz620, zzz621, zzz622, db) -> new_splitLT220(zzz618, zzz619, zzz620, zzz621, zzz622, db) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), bd) -> new_mkBalBranch(zzz4260, zzz4261, new_mkVBalBranch8(Succ(zzz3000), zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz4263, bd), zzz4264, ty_Int, bd) 130.57/78.24 new_splitLT29(Pos(Zero), zzz1971, zzz1972, zzz1973, zzz1974, zzz1975, gh) -> new_mkVBalBranch5(Zero, zzz1971, zzz1973, new_splitLT12(zzz1974, zzz1975, gh), gh) 130.57/78.24 new_primMulNat(Zero) -> Zero 130.57/78.24 new_splitLT219(zzz31, zzz32, zzz33, zzz34, bd) -> zzz33 130.57/78.24 new_mkBalBranch6MkBalBranch015(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Pos(Succ(zzz645400)), Pos(zzz64550), gf, gg) -> new_mkBalBranch6MkBalBranch013(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, zzz645400, new_primMulNat8(zzz64550), gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch019(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Succ(zzz64660), gf, gg) -> new_mkBalBranch6MkBalBranch010(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_splitGT223(Pos(Zero), zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_splitGT215(zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.24 new_primPlusInt(Neg(zzz62420), zzz6234, zzz6235, zzz6232, hb, hc) -> new_primPlusInt1(zzz62420, new_sizeFM(zzz6235, hb, hc)) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Succ(zzz426200)), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch135(zzz330, zzz331, zzz333, zzz334, zzz4260, zzz4261, zzz426200, zzz4263, zzz4264, Succ(zzz3000), zzz31, new_primMulNat3(zzz426200), bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch239(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, he) -> new_mkVBalBranch3MkVBalBranch232(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, he) 130.57/78.24 new_mkVBalBranch3MkVBalBranch141(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, bbe) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(zzz6304), zzz6305, Branch(zzz6294, zzz6295, Neg(Succ(zzz6296)), zzz6297, zzz6298), Branch(zzz6299, zzz6300, Neg(Succ(zzz6301)), zzz6302, zzz6303), ty_Int, bbe) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Succ(zzz426200)), zzz4263, zzz4264), bd) -> new_mkBalBranch(zzz4260, zzz4261, new_mkVBalBranch8(Succ(zzz3000), zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz4263, bd), zzz4264, ty_Int, bd) 130.57/78.24 new_addToFM_C4(Branch(Pos(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), Succ(zzz3000), zzz31, bd) -> new_addToFM_C24(zzz34000, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, zzz3000, zzz34000, bd) 130.57/78.24 new_splitLT29(Pos(Succ(zzz197000)), zzz1971, zzz1972, zzz1973, zzz1974, zzz1975, gh) -> new_splitLT212(zzz197000, zzz1971, zzz1972, zzz1973, zzz1974, zzz1975, zzz1975, zzz197000, gh) 130.57/78.24 new_addToFM_C4(Branch(Neg(Zero), zzz341, zzz342, zzz343, zzz344), Zero, zzz31, bd) -> Branch(Pos(Zero), new_addToFM0(zzz341, zzz31, bd), zzz342, zzz343, zzz344) 130.57/78.24 new_splitLT218(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Zero, Succ(zzz35100), hg) -> new_splitLT13(zzz3506, zzz3508, hg) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_intersectFM_C2Lts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd) -> new_splitLT19(Branch(Neg(Succ(zzz1192)), zzz1193, zzz1194, zzz1195, zzz1196), dd) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch8(Zero, zzz31, zzz3530, zzz3531, Neg(Zero), zzz3533, zzz3534, zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_splitGT11(Branch(Neg(Zero), zzz11961, zzz11962, zzz11963, zzz11964), dd) -> new_splitGT214(zzz11961, zzz11962, zzz11963, zzz11964, dd) 130.57/78.24 new_mkBalBranch6MkBalBranch1113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch111(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch129(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), baa) -> new_mkVBalBranch3MkVBalBranch130(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), baa) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Succ(zzz3000)), zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), ty_Int, bd) 130.57/78.24 new_splitGT227(zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, bbh) -> new_splitGT229(zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, bbh) 130.57/78.24 new_splitGT15(Branch(zzz8330, zzz8331, zzz8332, zzz8333, zzz8334), fg) -> new_splitGT223(zzz8330, zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.24 new_mkBalBranch6MkBalBranch110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, EmptyFM, gf, gg) -> error([]) 130.57/78.24 new_primPlusInt(Pos(zzz62420), zzz6234, zzz6235, zzz6232, hb, hc) -> new_primPlusInt0(zzz62420, new_sizeFM(zzz6235, hb, hc)) 130.57/78.24 new_mkVBalBranch3MkVBalBranch126(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Zero, bcd) -> new_mkVBalBranch3MkVBalBranch152(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, bcd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch227(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bac) -> new_mkVBalBranch3MkVBalBranch227(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bac) 130.57/78.24 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.24 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.24 new_splitLT18(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, baf) -> zzz4181 130.57/78.24 new_mkVBalBranch3MkVBalBranch132(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), bd) -> new_mkVBalBranch3MkVBalBranch145(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), bd) 130.57/78.24 new_mkBalBranch6MkBalBranch42(Branch(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344), zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBalBranch6MkBalBranch015(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, new_sizeFM(zzz4740343, gf, gg), new_sizeFM(zzz4740344, gf, gg), gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch235(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, bbd) -> new_mkVBalBranch3MkVBalBranch234(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, bbd) 130.57/78.24 new_mkBalBranch6MkBalBranch35(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Zero), Pos(zzz64530), gf, gg) -> new_mkBalBranch6MkBalBranch310(zzz474034, zzz474030, zzz474031, zzz6373, new_primMulNat(zzz64530), gf, gg) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch221(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bd) 130.57/78.24 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.57/78.24 new_splitLT212(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Zero, Zero, ge) -> new_splitLT213(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, ge) 130.57/78.24 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.24 new_mkBalBranch6MkBalBranch315(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, zzz6457, gf, gg) -> new_mkBalBranch6MkBalBranch31(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch010(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBalBranch6MkBalBranch011(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch223(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, hf) -> new_mkVBalBranch3MkVBalBranch225(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, hf) 130.57/78.24 new_addToFM_C3(Branch(Pos(Succ(zzz982000)), zzz9821, zzz9822, zzz9823, zzz9824), Zero, zzz31, bd) -> new_mkBalBranch(Pos(Succ(zzz982000)), zzz9821, new_addToFM_C3(zzz9823, Zero, zzz31, bd), zzz9824, ty_Int, bd) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch135(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), bd) 130.57/78.24 new_mkBalBranch6MkBalBranch35(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Succ(zzz645200)), Pos(zzz64530), gf, gg) -> new_mkBalBranch6MkBalBranch33(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, new_primMulNat(zzz64530), gf, gg) 130.57/78.24 new_addToFM_C11(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, Zero, Zero, bae) -> new_addToFM_C12(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, bae) 130.57/78.24 new_mkVBalBranch3MkVBalBranch229(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), bab) -> new_mkVBalBranch3MkVBalBranch229(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, bab) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Succ(Zero)), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch132(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz4260, zzz4261, zzz4263, zzz4264, Succ(zzz3000), zzz31, new_primMulNat3(Zero), bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch130(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bce) -> new_mkVBalBranch3MkVBalBranch130(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bce) 130.57/78.24 new_mkBalBranch6MkBalBranch46(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, zzz6449, gf, gg) -> new_mkBalBranch6MkBalBranch47(zzz474034, zzz474030, zzz474031, zzz6373, zzz6449, zzz644300, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch313(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64630), gf, gg) -> new_mkBalBranch6MkBalBranch34(zzz474034, zzz474030, zzz474031, zzz6373, zzz64630, Zero, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch153(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, bce) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(zzz6333), zzz6334, Branch(zzz6323, zzz6324, Neg(Succ(zzz6325)), zzz6326, zzz6327), Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), ty_Int, bce) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Succ(Zero)), zzz4263, zzz4264), bd) -> new_mkBalBranch(zzz4260, zzz4261, new_mkVBalBranch8(Succ(zzz3000), zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz4263, bd), zzz4264, ty_Int, bd) 130.57/78.24 new_splitGT40(bd) -> new_emptyFM(bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch238(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz41140), zzz4455, he) -> new_mkVBalBranch3MkVBalBranch239(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz41140, zzz4455, he) 130.57/78.24 new_mkVBalBranch3MkVBalBranch151(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, hf) -> new_mkVBalBranch3MkVBalBranch126(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), hf) 130.57/78.24 new_mkBalBranch6MkBalBranch5(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Succ(Zero)), gf, gg) -> new_mkBalBranch6MkBalBranch51(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch132(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(Zero), bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch231(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bbc) -> new_mkBalBranch(zzz5251, zzz5252, new_mkVBalBranch8(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bbc), zzz5255, ty_Int, bbc) 130.57/78.24 new_primPlusInt0(zzz58960, Pos(zzz59000)) -> Pos(new_primPlusNat0(zzz58960, zzz59000)) 130.57/78.24 new_splitLT215(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, hg) -> new_splitLT15(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Succ(zzz3503), Succ(zzz3508), hg) 130.57/78.24 new_splitGT18(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, Zero, Zero, bcf) -> new_splitGT19(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, bcf) 130.57/78.24 new_mkVBalBranch3MkVBalBranch237(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, bcc) -> new_mkVBalBranch3MkVBalBranch241(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, bcc) 130.57/78.24 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.57/78.24 new_addToFM_C24(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Zero, Succ(zzz31890), hh) -> new_mkBalBranch(Pos(Succ(zzz3181)), zzz3182, new_addToFM_C4(zzz3184, Succ(zzz3186), zzz3187, hh), zzz3185, ty_Int, hh) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch8(Zero, zzz31, zzz3530, zzz3531, Neg(Succ(zzz353200)), zzz3533, zzz3534, zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch1115(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch111(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch36(zzz474034, zzz474030, zzz474031, zzz6373, Zero, zzz645200, gf, gg) -> new_mkBalBranch6MkBalBranch38(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch221(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, hd) -> new_mkBalBranch(zzz3893, zzz3894, new_mkVBalBranch5(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, hd), zzz3897, ty_Int, hd) 130.57/78.24 new_mkVBalBranch8(zzz300, zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, EmptyFM, bd) -> new_addToFM2(zzz330, zzz331, zzz332, zzz333, zzz334, zzz300, zzz31, bd) 130.57/78.24 new_splitLT218(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Succ(zzz35090), Zero, hg) -> new_splitLT215(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, hg) 130.57/78.24 new_intersectFM_C2Lts(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, h) -> new_splitLT12(Branch(Pos(Succ(zzz2078)), zzz2079, zzz2080, zzz2081, zzz2082), zzz2083, h) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch227(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz5232000, bd) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, EmptyFM, zzz34, bd) -> new_addToFM3(zzz34, zzz300, zzz31, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch50(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBalBranch6MkBalBranch413(zzz474034, zzz474030, zzz474031, zzz6373, new_mkBalBranch6Size_l(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg), gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch131(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), bab) -> new_mkVBalBranch3MkVBalBranch145(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), bab) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch231(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), bd) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkBalBranch(zzz2500, zzz2501, zzz2503, new_mkVBalBranch5(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd), ty_Int, bd) 130.57/78.24 new_splitLT40(bd) -> new_emptyFM(bd) 130.57/78.24 new_mkBalBranch6MkBalBranch5(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Succ(Succ(Zero))), gf, gg) -> new_mkBalBranch6MkBalBranch50(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch015(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Neg(Zero), Neg(zzz64550), gf, gg) -> new_mkBalBranch6MkBalBranch012(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, new_primMulNat8(zzz64550), gf, gg) 130.57/78.24 new_splitLT29(Neg(zzz19700), zzz1971, zzz1972, EmptyFM, zzz1974, zzz1975, gh) -> new_addToFM_C3(new_splitLT12(zzz1974, zzz1975, gh), zzz19700, zzz1971, gh) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Zero), zzz4263, zzz4264), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Succ(zzz3000)), zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Zero), zzz4263, zzz4264), ty_Int, bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch148(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bd) 130.57/78.24 new_splitLT15(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, Zero, Succ(zzz45110), ha) -> new_splitLT14(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, ha) 130.57/78.24 new_emptyFM(bd) -> EmptyFM 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch134(zzz3530, zzz3531, zzz3533, zzz3534, zzz340, zzz341, zzz34200, zzz343, zzz344, Zero, zzz31, new_primMulNat3(zzz34200), bd) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch8(Zero, zzz31, zzz3530, zzz3531, Neg(Succ(zzz353200)), zzz3533, zzz3534, zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Neg(Succ(zzz647600)), Pos(zzz64770), gf, gg) -> new_mkBalBranch6MkBalBranch1114(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, new_primMulNat8(zzz64770), gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch142(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bbf) -> new_mkVBalBranch3MkVBalBranch139(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bbf) 130.57/78.24 new_splitLT19(Branch(Neg(Succ(zzz621000)), zzz6211, zzz6212, zzz6213, zzz6214), db) -> new_mkVBalBranch6(zzz621000, zzz6211, zzz6213, new_splitLT19(zzz6214, db), db) 130.57/78.24 new_mkVBalBranch3MkVBalBranch224(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), hf) -> new_mkVBalBranch3MkVBalBranch224(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, hf) 130.57/78.24 new_mkVBalBranch3MkVBalBranch227(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bac) -> new_mkVBalBranch3MkVBalBranch228(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bac) 130.57/78.24 new_mkBalBranch6MkBalBranch42(EmptyFM, zzz474030, zzz474031, zzz6373, gf, gg) -> error([]) 130.57/78.24 new_mkBalBranch6MkBalBranch113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Zero, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch111(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_addToFM_C4(Branch(Pos(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), Zero, zzz31, bd) -> new_mkBalBranch(Pos(Succ(zzz34000)), zzz341, new_addToFM_C4(zzz343, Zero, zzz31, bd), zzz344, ty_Int, bd) 130.57/78.24 new_addToFM1(zzz426, zzz3000, zzz31, bd) -> new_addToFM_C3(zzz426, Succ(zzz3000), zzz31, bd) 130.57/78.24 new_splitGT41(zzz4000, bd) -> new_emptyFM(bd) 130.57/78.24 new_splitGT30(Pos(zzz74500), zzz7451, zzz7452, zzz7453, zzz7454, zzz747, df) -> new_splitGT221(zzz74500, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, df) 130.57/78.24 new_mkBalBranch6MkBalBranch415(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Zero), Neg(zzz64420), gf, gg) -> new_mkBalBranch6MkBalBranch41(zzz474034, zzz474030, zzz474031, zzz6373, new_primMulNat(zzz64420), gf, gg) 130.57/78.24 new_splitLT8(zzz31, zzz32, zzz33, zzz34, bd) -> new_splitLT219(zzz31, zzz32, zzz33, zzz34, bd) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch233(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch016(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Succ(zzz6454000), Zero, gf, gg) -> new_mkBalBranch6MkBalBranch010(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_addToFM_C13(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, Zero, Zero, bag) -> new_addToFM_C14(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, bag) 130.57/78.24 new_splitGT15(EmptyFM, fg) -> new_splitGT40(fg) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Pos(Zero), Neg(zzz64770), gf, gg) -> new_mkBalBranch6MkBalBranch1113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, new_primMulNat8(zzz64770), gf, gg) 130.57/78.24 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.24 new_mkBalBranch6MkBalBranch116(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Succ(zzz64830), zzz647600, gf, gg) -> new_mkBalBranch6MkBalBranch113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz64830, zzz647600, gf, gg) 130.57/78.24 new_splitGT223(Neg(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_splitGT230(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.24 new_splitGT43(bd) -> new_emptyFM(bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch231(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bbc) -> new_mkVBalBranch3MkVBalBranch242(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bbc) 130.57/78.24 new_mkBalBranch6MkBalBranch0110(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Succ(zzz64740), zzz645400, gf, gg) -> new_mkBalBranch6MkBalBranch016(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, zzz64740, zzz645400, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Neg(Succ(zzz647600)), Neg(zzz64770), gf, gg) -> new_mkBalBranch6MkBalBranch115(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, new_primMulNat8(zzz64770), gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch415(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Succ(zzz644300)), Neg(zzz64420), gf, gg) -> new_mkBalBranch6MkBalBranch414(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, new_primMulNat(zzz64420), gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Zero, Succ(zzz647800), gf, gg) -> new_mkBalBranch6MkBalBranch118(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234, bd) -> new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch9(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, bd), ty_Int, bd) 130.57/78.24 new_splitLT9(EmptyFM, fg) -> new_emptyFM(fg) 130.57/78.24 new_mkBalBranch6MkBalBranch1112(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch111(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), bd) -> new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch6(zzz3000, zzz31, zzz334, Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), bd), ty_Int, bd) 130.57/78.24 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.24 new_splitLT15(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, Zero, Zero, ha) -> new_splitLT14(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, ha) 130.57/78.24 new_mkVBalBranch3MkVBalBranch130(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bce) -> new_mkBalBranch(zzz6323, zzz6324, zzz6326, new_mkVBalBranch5(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bce), ty_Int, bce) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch238(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), bd) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(zzz42620), zzz4263, zzz4264), bd) -> new_mkBalBranch(zzz4260, zzz4261, new_mkVBalBranch8(Succ(zzz3000), zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz4263, bd), zzz4264, ty_Int, bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch237(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), bcc) -> new_mkBalBranch(zzz5117, zzz5118, new_mkVBalBranch5(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, bcc), zzz5121, ty_Int, bcc) 130.57/78.24 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.57/78.24 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch144(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch147(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bd) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Pos(Succ(zzz647600)), Pos(zzz64770), gf, gg) -> new_mkBalBranch6MkBalBranch1111(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, new_primMulNat8(zzz64770), gf, gg) 130.57/78.24 new_addToFM_C13(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, Zero, Succ(zzz45460), bag) -> new_addToFM_C14(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, bag) 130.57/78.24 new_mkBalBranch6MkBalBranch013(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, zzz645400, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch010(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch310(zzz474034, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch32(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234, bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(zzz300), zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234), ty_Int, bd) 130.57/78.24 new_splitLT19(Branch(Pos(Zero), zzz6211, zzz6212, zzz6213, zzz6214), db) -> new_splitLT210(zzz6211, zzz6212, zzz6213, zzz6214, db) 130.57/78.24 new_mkBalBranch6MkBalBranch0111(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch014(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(zzz300), zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), ty_Int, bd) 130.57/78.24 new_splitLT218(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Zero, Zero, hg) -> new_splitLT215(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, hg) 130.57/78.24 new_mkBalBranch6MkBalBranch415(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Succ(zzz644300)), Neg(zzz64420), gf, gg) -> new_mkBalBranch6MkBalBranch46(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, new_primMulNat(zzz64420), gf, gg) 130.57/78.24 new_intersectFM_C2Gts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd) -> new_splitGT217(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Succ(zzz3000)), zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), ty_Int, bd) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Zero), zzz4263, zzz4264), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Succ(zzz3000)), zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Zero), zzz4263, zzz4264), ty_Int, bd) 130.57/78.24 new_splitGT18(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, Zero, Succ(zzz45020), bcf) -> new_mkVBalBranch6(zzz4495, zzz4496, new_splitGT16(zzz4498, zzz4500, bcf), zzz4499, bcf) 130.57/78.24 new_mkVBalBranch3MkVBalBranch227(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bac) -> new_mkBalBranch(zzz5094, zzz5095, new_mkVBalBranch8(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bac), zzz5098, ty_Int, bac) 130.57/78.24 new_mkVBalBranch10(zzz300, zzz31, EmptyFM, zzz5230, zzz5231, zzz5233, zzz5234, bd) -> new_addToFM2(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, zzz300, zzz31, bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch236(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, hf) -> new_mkVBalBranch3MkVBalBranch151(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), hf) 130.57/78.24 new_mkVBalBranch3MkVBalBranch127(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bd) -> new_mkVBalBranch3MkVBalBranch128(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bd) 130.57/78.24 new_addToFM_C24(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Succ(zzz31880), Zero, hh) -> new_addToFM_C25(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, hh) 130.57/78.24 new_intersectFM_C2Gts5(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, ed) -> new_splitGT16(Branch(Neg(Succ(zzz2143)), zzz2144, zzz2145, zzz2146, zzz2147), zzz2148, ed) 130.57/78.24 new_mkBalBranch6MkBalBranch0111(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Succ(zzz64680), gf, gg) -> new_mkBalBranch6MkBalBranch017(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch126(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Zero, bcd) -> new_mkVBalBranch3MkVBalBranch152(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, bcd) 130.57/78.24 new_intersectFM_C2Gts(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, h) -> new_splitGT13(Branch(Pos(Succ(zzz2078)), zzz2079, zzz2080, zzz2081, zzz2082), zzz2083, h) 130.57/78.24 new_mkBalBranch6MkBalBranch114(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) -> new_mkBalBranch6MkBalBranch110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch235(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, bbd) -> new_mkVBalBranch3MkVBalBranch234(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, bbd) 130.57/78.24 new_mkBalBranch6MkBalBranch410(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, zzz6448, gf, gg) -> new_mkBalBranch6MkBalBranch411(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Succ(Succ(zzz4262000))), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch227(zzz330, zzz331, zzz333, zzz334, zzz4260, zzz4261, Succ(zzz4262000), zzz4263, zzz4264, Succ(zzz3000), zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz4262000, bd) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, bd) -> new_mkBalBranch(zzz5230, zzz5231, new_mkVBalBranch8(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, bd), zzz5234, ty_Int, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Neg(Zero), Pos(zzz64770), gf, gg) -> new_mkBalBranch6MkBalBranch117(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, new_primMulNat8(zzz64770), gf, gg) 130.57/78.24 new_primMulNat6 -> new_primPlusNat5(new_primMulNat4) 130.57/78.24 new_splitGT228(zzz618, zzz619, zzz620, zzz621, zzz622, db) -> new_mkVBalBranch5(Succ(zzz618), zzz619, new_splitGT11(zzz621, db), zzz622, db) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch132(zzz3530, zzz3531, zzz353200, zzz3533, zzz3534, zzz340, zzz341, zzz343, zzz344, Zero, zzz31, new_primMulNat3(Zero), bd) 130.57/78.24 new_primMinusNat0(Zero, Zero) -> Pos(Zero) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), EmptyFM, bd) -> new_addToFM1(Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz3000, zzz31, bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch131(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, bab) -> new_mkVBalBranch3MkVBalBranch145(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), bab) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Succ(Succ(zzz3532000))), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch230(zzz3530, zzz3531, zzz3532000, zzz3533, zzz3534, zzz340, zzz341, Succ(Zero), zzz343, zzz344, Zero, zzz31, Zero, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz3532000), Succ(zzz3532000))), Succ(zzz3532000))), Succ(zzz3532000)), zzz3532000))), bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch235(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), bbd) -> new_mkVBalBranch3MkVBalBranch235(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, bbd) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch234(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, bbd) -> new_mkVBalBranch3MkVBalBranch140(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), bbd) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch223(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bd) 130.57/78.24 new_intersectFM_C2Lts0(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, be) -> new_splitLT12(Branch(Pos(Zero), zzz2734, zzz2735, zzz2736, zzz2737), zzz2738, be) 130.57/78.24 new_mkVBalBranch3MkVBalBranch229(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), bab) -> new_mkBalBranch(zzz4998, zzz4999, new_mkVBalBranch8(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, bab), zzz5002, ty_Int, bab) 130.57/78.24 new_mkVBalBranch3MkVBalBranch229(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, bab) -> new_mkVBalBranch3MkVBalBranch226(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, bab) 130.57/78.24 new_mkBalBranch6MkBalBranch1112(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Succ(zzz64800), gf, gg) -> new_mkBalBranch6MkBalBranch116(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Zero, zzz64800, gf, gg) 130.57/78.24 new_addToFM_C12(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, bae) -> Branch(Pos(Succ(zzz4308)), new_addToFM0(zzz4304, zzz4309, bae), zzz4305, zzz4306, zzz4307) 130.57/78.24 new_mkBalBranch6MkBalBranch012(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch014(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_splitGT225(Pos(Zero), zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, bbh) -> new_splitGT227(zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, bbh) 130.57/78.24 new_splitLT17(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, Zero, Zero, baf) -> new_splitLT18(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, baf) 130.57/78.24 new_mkBalBranch6MkBalBranch015(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Pos(Zero), Pos(zzz64550), gf, gg) -> new_mkBalBranch6MkBalBranch018(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, new_primMulNat8(zzz64550), gf, gg) 130.57/78.24 new_splitLT12(Branch(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744), zzz1975, gh) -> new_splitLT31(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744, zzz1975, gh) 130.57/78.24 new_splitGT12(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, Succ(zzz44340), Succ(zzz44350), bbb) -> new_splitGT12(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, zzz44340, zzz44350, bbb) 130.57/78.24 new_mkBalBranch6MkBalBranch5(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Succ(zzz637500)), gf, gg) -> new_mkBalBranch6MkBalBranch51(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.57/78.24 new_splitLT213(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, ge) -> new_splitLT17(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Succ(zzz3138), Succ(zzz3133), ge) 130.57/78.24 new_mkVBalBranch3MkVBalBranch138(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bbc) -> new_mkVBalBranch3MkVBalBranch139(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bbc) 130.57/78.24 new_mkBalBranch6MkBalBranch47(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64490), zzz644300, gf, gg) -> new_mkBalBranch6MkBalBranch49(zzz474034, zzz474030, zzz474031, zzz6373, zzz64490, zzz644300, gf, gg) 130.57/78.24 new_splitGT223(Pos(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_splitGT220(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.24 new_splitGT226(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Zero, Succ(zzz34030), bad) -> new_splitGT218(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, bad) 130.57/78.24 new_splitGT11(Branch(Neg(Succ(zzz1196000)), zzz11961, zzz11962, zzz11963, zzz11964), dd) -> new_splitGT217(zzz1196000, zzz11961, zzz11962, zzz11963, zzz11964, dd) 130.57/78.24 new_splitGT226(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Succ(zzz34020), Zero, bad) -> new_splitGT13(zzz3400, zzz3401, bad) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) -> new_mkBalBranch(zzz2500, zzz2501, zzz2503, new_mkVBalBranch5(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd), ty_Int, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch115(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, zzz6483, gf, gg) -> new_mkBalBranch6MkBalBranch116(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz6483, zzz647600, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch127(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bd) -> new_mkVBalBranch3MkVBalBranch128(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bd) 130.57/78.24 new_addToFM(zzz34, zzz31, bd) -> new_addToFM_C3(zzz34, Zero, zzz31, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch119(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, zzz6479, gf, gg) -> new_mkBalBranch6MkBalBranch114(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch35(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Succ(zzz645200)), Pos(zzz64530), gf, gg) -> new_mkBalBranch6MkBalBranch312(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, new_primMulNat(zzz64530), gf, gg) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch230(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), bd) 130.57/78.24 new_intersectFM_C2Gts4(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df) -> new_splitGT221(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(zzz300), zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Int, bd) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(zzz300), zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Int, bd) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch146(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Zero)))), bd) 130.57/78.24 new_addToFM3(zzz34, zzz300, zzz31, bd) -> new_addToFM_C4(zzz34, zzz300, zzz31, bd) 130.57/78.24 new_splitGT222(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Zero, Zero, bbg) -> new_splitGT224(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, bbg) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Zero), zzz31, Branch(zzz3530, zzz3531, Pos(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Int, bd) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Zero), zzz31, Branch(zzz3530, zzz3531, Neg(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Int, bd) 130.57/78.24 new_splitGT9(bd) -> new_splitGT40(bd) 130.57/78.24 new_mkBalBranch6MkBalBranch415(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Zero), Neg(zzz64420), gf, gg) -> new_mkBalBranch6MkBalBranch44(zzz474034, zzz474030, zzz474031, zzz6373, new_primMulNat(zzz64420), gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch415(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Zero), Pos(zzz64420), gf, gg) -> new_mkBalBranch6MkBalBranch416(zzz474034, zzz474030, zzz474031, zzz6373, new_primMulNat(zzz64420), gf, gg) 130.57/78.24 new_splitLT17(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, Succ(zzz41840), Zero, baf) -> new_mkVBalBranch5(Succ(zzz4178), zzz4179, zzz4181, new_splitLT12(zzz4182, zzz4183, baf), baf) 130.57/78.24 new_mkVBalBranch3MkVBalBranch145(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Zero, bcb) -> new_mkVBalBranch3MkVBalBranch149(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, bcb) 130.57/78.24 new_splitLT19(Branch(Neg(Zero), zzz6211, zzz6212, zzz6213, zzz6214), db) -> new_splitLT211(zzz6211, zzz6212, zzz6213, zzz6214, db) 130.57/78.24 new_mkBalBranch6MkBalBranch117(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch111(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch112(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, Succ(zzz64780), gf, gg) -> new_mkBalBranch6MkBalBranch113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, zzz64780, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch140(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), bbd) -> new_mkVBalBranch3MkVBalBranch126(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), bbd) 130.57/78.24 new_mkVBalBranch9(zzz300, zzz31, EmptyFM, zzz5230, zzz5231, zzz5233, zzz5234, bd) -> new_addToFM2(zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234, zzz300, zzz31, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch36(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64610), zzz645200, gf, gg) -> new_mkBalBranch6MkBalBranch37(zzz474034, zzz474030, zzz474031, zzz6373, zzz64610, zzz645200, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch41(zzz474034, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch43(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch312(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, zzz6460, gf, gg) -> new_mkBalBranch6MkBalBranch38(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Zero), zzz4263, zzz4264), bd) -> new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch6(zzz3000, zzz31, zzz334, Branch(zzz4260, zzz4261, Pos(Zero), zzz4263, zzz4264), bd), ty_Int, bd) 130.57/78.24 new_splitLT16(zzz4000, bd) -> new_splitLT41(zzz4000, bd) 130.57/78.24 new_intersectFM_C2Gts1(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, cc) -> new_splitGT13(Branch(Neg(zzz1382), zzz1383, zzz1384, zzz1385, zzz1386), zzz1387, cc) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Succ(Succ(zzz4262000))), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch229(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz4260, zzz4261, Succ(zzz4262000), zzz4263, zzz4264, Succ(zzz3000), zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz4262000, bd) 130.57/78.24 new_mkBalBranch6Size_r(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_sizeFM(zzz474034, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, Branch(zzz637340, zzz637341, zzz637342, zzz637343, zzz637344), gf, gg) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), zzz637340, zzz637341, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), zzz63730, zzz63731, zzz63733, zzz637343, gf, gg), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), zzz474030, zzz474031, zzz637344, zzz474034, gf, gg), gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch233(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, baa) -> new_mkVBalBranch3MkVBalBranch129(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primMulNat3(zzz3745), baa) 130.57/78.24 new_mkBalBranch6MkBalBranch018(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch014(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch34(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch31(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch229(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz5232000, bd) 130.57/78.24 new_primMulNat2(zzz4739) -> Zero 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch134(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch137(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bd) 130.57/78.24 new_intersectFM_C2Gts7(zzz830, zzz831, zzz832, zzz833, zzz834, fg) -> new_splitGT220(zzz830, zzz831, zzz832, zzz833, zzz834, fg) 130.57/78.24 new_splitGT223(Neg(Zero), zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_splitGT216(zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch133(zzz3530, zzz3531, zzz353200, zzz3533, zzz3534, zzz340, zzz341, zzz34200, zzz343, zzz344, Zero, zzz31, new_primPlusNat0(new_primMulNat0(zzz34200), Succ(zzz34200)), bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch144(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bd) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Succ(Zero)), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch231(zzz3530, zzz3531, zzz3533, zzz3534, zzz340, zzz341, Succ(Zero), zzz343, zzz344, Zero, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), bd) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, zzz3532, zzz3533, zzz3534), EmptyFM, bd) -> new_addToFM(Branch(zzz3530, zzz3531, zzz3532, zzz3533, zzz3534), zzz31, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch49(zzz474034, zzz474030, zzz474031, zzz6373, Zero, Succ(zzz644400), gf, gg) -> new_mkBalBranch6MkBalBranch411(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Succ(zzz426200)), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch134(zzz330, zzz331, zzz333, zzz334, zzz4260, zzz4261, zzz426200, zzz4263, zzz4264, Succ(zzz3000), zzz31, new_primMulNat3(zzz426200), bd) 130.57/78.24 new_mkBalBranch6MkBalBranch35(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Succ(zzz645200)), Neg(zzz64530), gf, gg) -> new_mkBalBranch6MkBalBranch314(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, new_primMulNat(zzz64530), gf, gg) 130.57/78.24 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.57/78.24 new_addToFM_C11(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, Zero, Succ(zzz43110), bae) -> new_addToFM_C12(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, bae) 130.57/78.24 new_splitLT212(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Succ(zzz31390), Zero, ge) -> new_splitLT213(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, ge) 130.57/78.24 new_mkBalBranch6MkBalBranch016(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Zero, Succ(zzz647200), gf, gg) -> new_mkBalBranch6MkBalBranch017(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_sizeFM(Branch(zzz34900, zzz34901, zzz34902, zzz34903, zzz34904), bah, bba) -> zzz34902 130.57/78.24 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.57/78.24 new_splitLT13(Branch(Neg(Zero), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, df) -> new_splitLT13(zzz7453, zzz747, df) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch230(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), bd) 130.57/78.24 new_splitGT226(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Zero, Zero, bad) -> new_splitGT218(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, bad) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, bd) -> new_mkBalBranch(zzz5230, zzz5231, new_mkVBalBranch8(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, bd), zzz5234, ty_Int, bd) 130.57/78.24 new_mkVBalBranch11(zzz300, zzz31, EmptyFM, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, bd) -> new_addToFM2(zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, zzz300, zzz31, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch416(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64460), gf, gg) -> new_mkBalBranch6MkBalBranch47(zzz474034, zzz474030, zzz474031, zzz6373, Zero, zzz64460, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch224(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, hf) -> new_mkVBalBranch3MkVBalBranch236(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, hf) 130.57/78.24 new_mkBalBranch6MkBalBranch011(zzz4740340, zzz4740341, zzz4740342, EmptyFM, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) -> error([]) 130.57/78.24 new_mkBalBranch6MkBalBranch014(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBalBranch6MkBalBranch011(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch016(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Zero, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch014(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch013(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, zzz645400, Succ(zzz64720), gf, gg) -> new_mkBalBranch6MkBalBranch016(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, zzz645400, zzz64720, gf, gg) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch129(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bd) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Succ(Succ(Succ(zzz42620000)))), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch231(zzz330, zzz331, zzz333, zzz334, zzz4260, zzz4261, Succ(Succ(zzz42620000)), zzz4263, zzz4264, Succ(zzz3000), zzz31, Succ(zzz42620000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), bd) 130.57/78.24 new_addToFM_C3(Branch(Neg(Zero), zzz9821, zzz9822, zzz9823, zzz9824), Succ(zzz3000), zzz31, bd) -> new_mkBalBranch(Neg(Zero), zzz9821, new_addToFM_C3(zzz9823, Succ(zzz3000), zzz31, bd), zzz9824, ty_Int, bd) 130.57/78.24 new_intersectFM_C2Lts1(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, cc) -> new_splitLT29(Neg(zzz1382), zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, cc) 130.57/78.24 new_splitLT14(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, ha) -> zzz4507 130.57/78.24 new_splitLT6(zzz300, zzz31, zzz32, zzz34, zzz4000, bd) -> new_splitLT16(zzz4000, bd) 130.57/78.24 new_primMulNat8(Succ(zzz645500)) -> new_primPlusNat0(new_primMulNat1(zzz645500), Succ(zzz645500)) 130.57/78.24 new_mkVBalBranch3MkVBalBranch145(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bcb) -> new_mkBalBranch(zzz6120, zzz6121, zzz6123, new_mkVBalBranch12(zzz6130, zzz6131, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, bcb), ty_Int, bcb) 130.57/78.24 new_mkBalBranch6MkBalBranch111(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) -> new_mkBalBranch6MkBalBranch110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_splitGT222(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Succ(zzz35000), Succ(zzz35010), bbg) -> new_splitGT222(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, zzz35000, zzz35010, bbg) 130.57/78.24 new_mkBalBranch6MkBalBranch35(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Zero), Neg(zzz64530), gf, gg) -> new_mkBalBranch6MkBalBranch30(zzz474034, zzz474030, zzz474031, zzz6373, new_primMulNat(zzz64530), gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch145(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bcb) -> new_mkVBalBranch3MkVBalBranch145(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bcb) 130.57/78.24 new_mkVBalBranch3MkVBalBranch136(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), he) -> new_mkVBalBranch3MkVBalBranch130(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), he) 130.57/78.24 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.24 new_mkBalBranch(zzz474030, zzz474031, zzz6373, zzz474034, gf, gg) -> new_mkBalBranch6MkBalBranch5(zzz474034, zzz474030, zzz474031, zzz6373, new_primPlusInt2(new_mkBalBranch6Size_l(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg), zzz474034, zzz474030, zzz474031, zzz6373, gf, gg), gf, gg) 130.57/78.24 new_splitLT210(zzz31, zzz32, zzz33, zzz34, bd) -> zzz33 130.57/78.24 new_intersectFM_C2Gts2(zzz618, zzz619, zzz620, zzz621, zzz622, db) -> new_splitGT14(zzz618, zzz619, zzz620, zzz621, zzz622, db) 130.57/78.24 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.57/78.24 new_mkVBalBranch3MkVBalBranch239(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), he) -> new_mkVBalBranch3MkVBalBranch239(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, he) 130.57/78.24 new_mkBalBranch6MkBalBranch45(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, Succ(zzz64440), gf, gg) -> new_mkBalBranch6MkBalBranch49(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, zzz64440, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch128(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch238(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, zzz4455, he) -> new_mkVBalBranch3MkVBalBranch222(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, he) 130.57/78.24 new_mkBalBranch6MkBalBranch30(zzz474034, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch32(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch222(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, he) -> new_mkBalBranch(zzz4107, zzz4108, new_mkVBalBranch5(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, he), zzz4111, ty_Int, he) 130.57/78.24 new_mkBalBranch6MkBalBranch015(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Pos(Succ(zzz645400)), Neg(zzz64550), gf, gg) -> new_mkBalBranch6MkBalBranch010(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch231(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), bd) 130.57/78.24 new_splitLT17(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, Succ(zzz41840), Succ(zzz41850), baf) -> new_splitLT17(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, zzz41840, zzz41850, baf) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch8(Zero, zzz31, zzz3530, zzz3531, Pos(Zero), zzz3533, zzz3534, zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch31(zzz474034, zzz474030, zzz474031, Branch(zzz63730, zzz63731, zzz63732, zzz63733, zzz63734), gf, gg) -> new_mkBalBranch6MkBalBranch1110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, new_sizeFM(zzz63734, gf, gg), new_sizeFM(zzz63733, gf, gg), gf, gg) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch237(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000)))), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000))), bd) 130.57/78.24 new_mkBalBranch6MkBalBranch51(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBranch(Zero, zzz474030, zzz474031, zzz6373, zzz474034, gf, gg) 130.57/78.24 new_splitLT221(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_mkVBalBranch6(zzz833000, zzz8331, zzz8333, new_splitLT9(zzz8334, fg), fg) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(zzz523200)), zzz5233, zzz5234, bd) -> new_mkBalBranch(zzz5230, zzz5231, new_mkVBalBranch8(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5233, bd), zzz5234, ty_Int, bd) 130.57/78.24 new_splitLT222(zzz31, zzz32, zzz33, zzz34, bd) -> zzz33 130.57/78.24 new_splitGT225(Pos(Succ(zzz1612000)), zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, bbh) -> new_splitGT226(zzz1612000, zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, zzz1613, zzz1612000, bbh) 130.57/78.24 new_splitLT31(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744, zzz1975, gh) -> new_splitLT29(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744, zzz1975, gh) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch415(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Zero), Pos(zzz64420), gf, gg) -> new_mkBalBranch6MkBalBranch412(zzz474034, zzz474030, zzz474031, zzz6373, new_primMulNat(zzz64420), gf, gg) 130.57/78.24 new_splitGT16(EmptyFM, zzz747, df) -> new_splitGT41(zzz747, df) 130.57/78.24 new_splitLT212(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Zero, Succ(zzz31400), ge) -> new_splitLT12(zzz3136, zzz3138, ge) 130.57/78.24 new_mkBalBranch6MkBalBranch5(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Zero), gf, gg) -> new_mkBalBranch6MkBalBranch51(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch1113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Succ(zzz64810), gf, gg) -> new_mkBalBranch6MkBalBranch114(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch129(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Zero, baa) -> new_mkVBalBranch3MkVBalBranch130(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Zero, baa) 130.57/78.24 new_mkBalBranch6MkBalBranch112(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch114(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(zzz523200)), zzz5233, zzz5234, bd) -> new_mkBalBranch(zzz5230, zzz5231, new_mkVBalBranch8(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5233, bd), zzz5234, ty_Int, bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch229(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, bab) -> new_mkVBalBranch3MkVBalBranch226(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, bab) 130.57/78.24 new_mkVBalBranch3MkVBalBranch224(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, hf) -> new_mkVBalBranch3MkVBalBranch225(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, hf) 130.57/78.24 new_mkVBalBranch9(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz5233, zzz5234, bd) -> new_mkVBalBranch30(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234, bd) 130.57/78.24 new_addToFM_C23(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Zero, Zero, bca) -> new_addToFM_C26(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, bca) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch237(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000)))), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000))), bd) 130.57/78.24 new_splitLT11(zzz31, zzz32, zzz33, zzz34, bd) -> new_splitLT222(zzz31, zzz32, zzz33, zzz34, bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch230(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bbf) -> new_mkBalBranch(zzz5135, zzz5136, new_mkVBalBranch8(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bbf), zzz5139, ty_Int, bbf) 130.57/78.24 new_splitLT29(Neg(zzz19700), zzz1971, zzz1972, Branch(zzz19730, zzz19731, zzz19732, zzz19733, zzz19734), EmptyFM, zzz1975, gh) -> new_mkVBalBranch8(zzz19700, zzz1971, zzz19730, zzz19731, zzz19732, zzz19733, zzz19734, new_splitLT42(zzz1975, gh), gh) 130.57/78.24 new_addToFM_C4(EmptyFM, zzz300, zzz31, bd) -> Branch(Pos(zzz300), zzz31, Pos(Succ(Zero)), new_emptyFM(bd), new_emptyFM(bd)) 130.57/78.24 new_primPlusNat3(Zero) -> Succ(Zero) 130.57/78.24 new_mkVBalBranch3MkVBalBranch145(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Zero, bcb) -> new_mkVBalBranch3MkVBalBranch149(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, bcb) 130.57/78.24 new_mkBalBranch6MkBalBranch411(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBalBranch6MkBalBranch40(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch139(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Zero, bbe) -> new_mkVBalBranch3MkVBalBranch141(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, bbe) 130.57/78.24 new_mkBalBranch6MkBalBranch5(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Succ(Succ(Succ(zzz63750000)))), gf, gg) -> new_mkBalBranch6MkBalBranch50(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_addToFM_C4(Branch(Neg(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), Zero, zzz31, bd) -> new_mkBalBranch(Neg(Succ(zzz34000)), zzz341, zzz343, new_addToFM_C4(zzz344, Zero, zzz31, bd), ty_Int, bd) 130.57/78.24 new_addToFM_C23(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Succ(zzz33930), Succ(zzz33940), bca) -> new_addToFM_C23(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, zzz33930, zzz33940, bca) 130.57/78.24 new_mkVBalBranch3MkVBalBranch240(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bbf) -> new_mkVBalBranch3MkVBalBranch142(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bbf) 130.57/78.24 new_mkVBalBranch3MkVBalBranch237(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), bcc) -> new_mkVBalBranch3MkVBalBranch237(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, bcc) 130.57/78.24 new_intersectFM_C2Gts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc) -> new_splitGT15(Branch(Neg(Succ(zzz1594)), zzz1595, zzz1596, zzz1597, zzz1598), gc) 130.57/78.24 new_splitGT19(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, bcf) -> zzz4499 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) -> new_mkBalBranch(zzz3530, zzz3531, zzz3533, new_mkVBalBranch7(zzz31, zzz3534, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd), ty_Int, bd) 130.57/78.24 new_mkVBalBranch10(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz5233, zzz5234, bd) -> new_mkVBalBranch30(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, bd) 130.57/78.24 new_splitGT214(zzz31, zzz32, zzz33, zzz34, bd) -> zzz34 130.57/78.24 new_mkVBalBranch3MkVBalBranch241(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, bcc) -> new_mkVBalBranch3MkVBalBranch150(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), bcc) 130.57/78.24 new_mkVBalBranch3MkVBalBranch134(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), bd) -> new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch11(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, bd), ty_Int, bd) 130.57/78.24 new_splitGT11(Branch(Pos(Succ(zzz1196000)), zzz11961, zzz11962, zzz11963, zzz11964), dd) -> new_splitGT228(zzz1196000, zzz11961, zzz11962, zzz11963, zzz11964, dd) 130.57/78.24 new_mkBalBranch6MkBalBranch116(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Zero, zzz647600, gf, gg) -> new_mkBalBranch6MkBalBranch118(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_splitLT15(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, Succ(zzz45100), Zero, ha) -> new_mkVBalBranch6(zzz4504, zzz4505, zzz4507, new_splitLT13(zzz4508, zzz4509, ha), ha) 130.57/78.24 new_mkBalBranch6MkBalBranch1114(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, zzz6482, gf, gg) -> new_mkBalBranch6MkBalBranch118(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_primMinusNat0(Zero, Succ(zzz47700)) -> Neg(Succ(zzz47700)) 130.57/78.24 new_mkBalBranch6MkBalBranch113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Succ(zzz6476000), Succ(zzz647800), gf, gg) -> new_mkBalBranch6MkBalBranch113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz6476000, zzz647800, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch414(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, zzz6445, gf, gg) -> new_mkBalBranch6MkBalBranch42(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch012(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Succ(zzz64700), gf, gg) -> new_mkBalBranch6MkBalBranch013(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, zzz64700, Zero, gf, gg) 130.57/78.24 new_addToFM_C26(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, bca) -> new_addToFM_C13(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Succ(zzz3386), Succ(zzz3391), bca) 130.57/78.24 new_mkBalBranch6MkBalBranch412(zzz474034, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch43(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Succ(zzz426200)), zzz4263, zzz4264), bd) -> new_mkBalBranch(zzz4260, zzz4261, new_mkVBalBranch8(Succ(zzz3000), zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz4263, bd), zzz4264, ty_Int, bd) 130.57/78.24 new_addToFM_C3(Branch(Neg(Succ(zzz982000)), zzz9821, zzz9822, zzz9823, zzz9824), Zero, zzz31, bd) -> new_mkBalBranch(Neg(Succ(zzz982000)), zzz9821, zzz9823, new_addToFM_C3(zzz9824, Zero, zzz31, bd), ty_Int, bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch134(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(zzz300), zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234), ty_Int, bd) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkBalBranch(zzz2500, zzz2501, zzz2503, new_mkVBalBranch5(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd), ty_Int, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch35(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Succ(zzz645200)), Neg(zzz64530), gf, gg) -> new_mkBalBranch6MkBalBranch315(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, new_primMulNat(zzz64530), gf, gg) 130.57/78.24 new_addToFM_C24(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Zero, Zero, hh) -> new_addToFM_C25(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, hh) 130.57/78.24 new_splitLT19(EmptyFM, db) -> new_splitLT40(db) 130.57/78.24 new_mkBalBranch6MkBalBranch33(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, zzz6456, gf, gg) -> new_mkBalBranch6MkBalBranch34(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, zzz6456, gf, gg) 130.57/78.24 new_addToFM_C4(Branch(Neg(zzz3400), zzz341, zzz342, zzz343, zzz344), Succ(zzz3000), zzz31, bd) -> new_mkBalBranch(Neg(zzz3400), zzz341, zzz343, new_addToFM_C4(zzz344, Succ(zzz3000), zzz31, bd), ty_Int, bd) 130.57/78.24 new_splitGT12(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, Zero, Succ(zzz44350), bbb) -> new_mkVBalBranch5(Succ(zzz4428), zzz4429, new_splitGT13(zzz4431, zzz4433, bbb), zzz4432, bbb) 130.57/78.24 new_mkVBalBranch3MkVBalBranch126(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), bcd) -> new_mkVBalBranch3MkVBalBranch126(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, bcd) 130.57/78.24 new_mkBalBranch6MkBalBranch118(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), zzz63730, zzz63731, zzz63733, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), zzz474030, zzz474031, zzz63734, zzz474034, gf, gg), gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch125(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bd) 130.57/78.24 new_addToFM_C4(Branch(Pos(Zero), zzz341, zzz342, zzz343, zzz344), Zero, zzz31, bd) -> Branch(Pos(Zero), new_addToFM0(zzz341, zzz31, bd), zzz342, zzz343, zzz344) 130.57/78.24 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.57/78.24 new_addToFM_C3(EmptyFM, zzz300, zzz31, bd) -> Branch(Neg(zzz300), zzz31, Pos(Succ(Zero)), new_emptyFM(bd), new_emptyFM(bd)) 130.57/78.24 new_mkBalBranch6MkBalBranch015(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Pos(Zero), Neg(zzz64550), gf, gg) -> new_mkBalBranch6MkBalBranch019(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, new_primMulNat8(zzz64550), gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch138(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, bbc) -> new_mkVBalBranch3MkVBalBranch139(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Zero, bbc) 130.57/78.24 new_splitGT219(zzz884, zzz885, zzz886, zzz887, zzz888, eh) -> new_mkVBalBranch7(zzz884, new_splitGT16(zzz886, zzz888, eh), zzz887, eh) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch127(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat4, bd) 130.57/78.24 new_splitGT221(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df) -> new_mkVBalBranch5(zzz742, zzz743, new_splitGT16(zzz745, zzz747, df), zzz746, df) 130.57/78.24 new_mkBalBranch6MkBalBranch47(zzz474034, zzz474030, zzz474031, zzz6373, Zero, zzz644300, gf, gg) -> new_mkBalBranch6MkBalBranch411(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_addToFM_C3(Branch(Pos(Zero), zzz9821, zzz9822, zzz9823, zzz9824), Zero, zzz31, bd) -> Branch(Neg(Zero), new_addToFM0(zzz9821, zzz31, bd), zzz9822, zzz9823, zzz9824) 130.57/78.24 new_mkVBalBranch3MkVBalBranch223(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Succ(zzz388700), hf) -> new_mkVBalBranch3MkVBalBranch224(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, zzz388700, hf) 130.57/78.24 new_mkBalBranch6MkBalBranch37(zzz474034, zzz474030, zzz474031, zzz6373, Zero, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch32(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Pos(Succ(zzz647600)), Neg(zzz64770), gf, gg) -> new_mkBalBranch6MkBalBranch119(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, new_primMulNat8(zzz64770), gf, gg) 130.57/78.24 new_splitGT6(zzz4000, bd) -> new_splitGT42(zzz4000, bd) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Succ(Zero)), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch227(zzz3530, zzz3531, zzz3533, zzz3534, zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, Zero, zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz342000, bd) 130.57/78.24 new_mkBalBranch6Size_l(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_sizeFM(zzz6373, gf, gg) 130.57/78.24 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.24 new_mkBalBranch6MkBalBranch0110(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Zero, zzz645400, gf, gg) -> new_mkBalBranch6MkBalBranch017(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_intersectFM_C2Gts0(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, be) -> new_splitGT13(Branch(Pos(Zero), zzz2734, zzz2735, zzz2736, zzz2737), zzz2738, be) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch125(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bd) 130.57/78.24 new_splitGT226(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Succ(zzz34020), Succ(zzz34030), bad) -> new_splitGT226(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, zzz34020, zzz34030, bad) 130.57/78.24 new_splitGT13(Branch(zzz16120, zzz16121, zzz16122, zzz16123, zzz16124), zzz1613, bbh) -> new_splitGT225(zzz16120, zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, bbh) 130.57/78.24 new_mkVBalBranch3MkVBalBranch235(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), bbd) -> new_mkBalBranch(zzz4706, zzz4707, new_mkVBalBranch5(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, bbd), zzz4710, ty_Int, bbd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch135(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), bd) -> new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch11(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, bd), ty_Int, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch44(zzz474034, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch43(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_addToFM_C24(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Succ(zzz31880), Succ(zzz31890), hh) -> new_addToFM_C24(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, zzz31880, zzz31890, hh) 130.57/78.24 new_primPlusInt1(zzz58960, Pos(zzz59010)) -> new_primMinusNat0(zzz59010, zzz58960) 130.57/78.24 new_splitGT213(zzz31, zzz32, zzz33, zzz34, bd) -> zzz34 130.57/78.24 new_mkBalBranch6MkBalBranch415(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Succ(zzz644300)), Pos(zzz64420), gf, gg) -> new_mkBalBranch6MkBalBranch48(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, new_primMulNat(zzz64420), gf, gg) 130.57/78.24 new_splitLT19(Branch(Pos(Succ(zzz621000)), zzz6211, zzz6212, zzz6213, zzz6214), db) -> new_splitLT220(zzz621000, zzz6211, zzz6212, zzz6213, zzz6214, db) 130.57/78.24 new_mkVBalBranch3MkVBalBranch231(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bbc) -> new_mkVBalBranch3MkVBalBranch231(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bbc) 130.57/78.24 new_splitLT13(EmptyFM, zzz747, df) -> new_splitLT41(zzz747, df) 130.57/78.24 new_addToFM_C14(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, bag) -> Branch(Neg(Succ(zzz4543)), new_addToFM0(zzz4539, zzz4544, bag), zzz4540, zzz4541, zzz4542) 130.57/78.24 130.57/78.24 The set Q consists of the following terms: 130.57/78.24 130.57/78.24 new_intersectFM_C2Lts8(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_splitGT15(Branch(x0, x1, x2, x3, x4), x5) 130.57/78.24 new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Zero, x4, x5) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Zero), x4, x5, x6, x7, Neg(Zero), x8, x9, x10) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Zero), x4, x5, x6, x7, Pos(Zero), x8, x9, x10) 130.57/78.24 new_splitGT14(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_splitLT213(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_mkVBalBranch3MkVBalBranch238(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11, x12) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Zero), x4, x5, x6, x7, Neg(Zero), x8, x9, x10) 130.57/78.24 new_splitLT41(x0, x1) 130.57/78.24 new_mkVBalBranch5(x0, x1, EmptyFM, x2, x3) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Succ(Zero)), x3, x4), Branch(x5, x6, Neg(Succ(Succ(Zero))), x7, x8), x9) 130.57/78.24 new_splitLT18(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_mkVBalBranch3MkVBalBranch130(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13) 130.57/78.24 new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13) 130.57/78.24 new_splitLT216(Neg(Succ(x0)), x1, x2, x3, x4, x5) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Succ(Zero))), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Succ(Succ(Succ(x8)))))), x9, x10), x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.24 new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, Succ(x5), x6, x7) 130.57/78.24 new_splitLT218(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) 130.57/78.24 new_intersectFM_C2Lts6(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.24 new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Zero, x4, x5) 130.57/78.24 new_primPlusNat8(Zero, x0) 130.57/78.24 new_primPlusInt1(x0, Neg(x1)) 130.57/78.24 new_addToFM_C24(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8) 130.57/78.24 new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12) 130.57/78.24 new_primMulNat1(x0) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Zero), x4, x5, x6, x7, Pos(Zero), x8, x9, x10) 130.57/78.24 new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10) 130.57/78.24 new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Succ(x4), x5, x6) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(Succ(Succ(x4)))), x5, x6), Branch(x7, x8, Pos(Succ(Succ(Succ(Succ(x9))))), x10, x11), x12) 130.57/78.24 new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13) 130.57/78.24 new_splitGT12(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch231(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13) 130.57/78.24 new_intersectFM_C2Lts2(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkBalBranch6MkBalBranch31(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9) 130.57/78.24 new_primMinusNat0(Zero, Zero) 130.57/78.24 new_addToFM3(x0, x1, x2, x3) 130.57/78.24 new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14) 130.57/78.24 new_primMulNat8(Succ(x0)) 130.57/78.24 new_mkVBalBranch3MkVBalBranch136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.24 new_primMulNat7 130.57/78.24 new_splitGT30(Pos(x0), x1, x2, x3, x4, x5, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch41(x0, x1, x2, x3, Zero, x4, x5) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10) 130.57/78.24 new_primMulNat3(x0) 130.57/78.24 new_splitGT18(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) 130.57/78.24 new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, Zero, x5, x6) 130.57/78.24 new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.24 new_mkVBalBranch12(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9, x10, x11, x12) 130.57/78.24 new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14) 130.57/78.24 new_primPlusInt1(x0, Pos(x1)) 130.57/78.24 new_splitGT18(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) 130.57/78.24 new_addToFM_C24(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8) 130.57/78.24 new_addToFM_C3(Branch(Neg(Succ(x0)), x1, x2, x3, x4), Zero, x5, x6) 130.57/78.24 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.24 new_primPlusInt2(Pos(x0), x1, x2, x3, x4, x5, x6) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Succ(Zero))), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Succ(Succ(Zero))))), x8, x9), x10) 130.57/78.24 new_splitLT19(Branch(Neg(Zero), x0, x1, x2, x3), x4) 130.57/78.24 new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Succ(x4), x5, x6) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, Pos(x9), x10, x11), x12) 130.57/78.24 new_mkVBalBranch3MkVBalBranch222(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, Pos(Zero), x9, x10), x11) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13) 130.57/78.24 new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.24 new_splitGT18(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) 130.57/78.24 new_splitLT216(Neg(Zero), x0, x1, x2, x3, x4) 130.57/78.24 new_splitGT6(x0, x1) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Succ(Zero)), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Zero))), x8, x9), x10) 130.57/78.24 new_addToFM_C4(Branch(Pos(Succ(x0)), x1, x2, x3, x4), Zero, x5, x6) 130.57/78.24 new_addToFM_C4(Branch(Neg(Succ(x0)), x1, x2, x3, x4), Zero, x5, x6) 130.57/78.24 new_primPlusNat2(Zero) 130.57/78.24 new_mkVBalBranch3MkVBalBranch221(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.24 new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Succ(x4), x5, x6) 130.57/78.24 new_mkVBalBranch3MkVBalBranch240(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Succ(Succ(x4))), x5, x6, x7, x8, Pos(Succ(Succ(x9))), x10, x11, x12) 130.57/78.24 new_addToFM_C3(Branch(Pos(Succ(x0)), x1, x2, x3, x4), Zero, x5, x6) 130.57/78.24 new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.24 new_primPlusNat6(x0, Succ(x1)) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Succ(Zero)), x3, x4), Branch(x5, x6, Pos(Succ(Succ(x7))), x8, x9), x10) 130.57/78.24 new_intersectFM_C2Lts0(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_splitLT11(x0, x1, x2, x3, x4) 130.57/78.24 new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, Succ(x4), x5, x6) 130.57/78.24 new_splitGT30(Neg(Zero), x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11) 130.57/78.24 new_mkBalBranch6MkBalBranch011(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9, x10, x11, x12, x13) 130.57/78.24 new_splitLT218(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) 130.57/78.24 new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9) 130.57/78.24 new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10) 130.57/78.24 new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10) 130.57/78.24 new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) 130.57/78.24 new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.24 new_intersectFM_C2Lts3(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10) 130.57/78.24 new_splitGT226(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) 130.57/78.24 new_splitLT15(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) 130.57/78.24 new_primPlusNat4(Zero) 130.57/78.24 new_primPlusNat2(Succ(x0)) 130.57/78.24 new_addToFM_C4(Branch(Pos(Zero), x0, x1, x2, x3), Zero, x4, x5) 130.57/78.24 new_mkVBalBranch3MkVBalBranch223(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13) 130.57/78.24 new_mkBalBranch6MkBalBranch41(x0, x1, x2, x3, Succ(x4), x5, x6) 130.57/78.24 new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.24 new_primPlusNat1(Succ(x0)) 130.57/78.24 new_splitGT16(Branch(x0, x1, x2, x3, x4), x5, x6) 130.57/78.24 new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10) 130.57/78.24 new_splitLT212(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11) 130.57/78.24 new_splitLT29(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12) 130.57/78.24 new_splitGT219(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_primMulNat8(Zero) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10) 130.57/78.24 new_mkBalBranch(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_splitLT218(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Succ(Succ(x4))), x5, x6, x7, x8, Neg(Succ(Succ(Succ(x9)))), x10, x11, x12) 130.57/78.24 new_addToFM_C25(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.24 new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.24 new_primPlusInt2(Neg(x0), x1, x2, x3, x4, x5, x6) 130.57/78.24 new_splitLT19(Branch(Pos(Zero), x0, x1, x2, x3), x4) 130.57/78.24 new_intersectFM_C2Lts5(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, Succ(x4), x5, x6, x7) 130.57/78.24 new_splitGT226(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10) 130.57/78.24 new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Zero), x4, x5, x6, x7, Neg(Succ(x8)), x9, x10, x11) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Zero), x4, x5, x6, x7, Pos(Succ(x8)), x9, x10, x11) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Succ(Succ(x3))), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Succ(x8)))), x9, x10), x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10) 130.57/78.24 new_addToFM2(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.24 new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9) 130.57/78.24 new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10) 130.57/78.24 new_addToFM_C13(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Succ(Succ(x4))), x5, x6, x7, x8, Neg(Succ(Succ(Zero))), x9, x10, x11) 130.57/78.24 new_addToFM_C13(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8) 130.57/78.24 new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8) 130.57/78.24 new_intersectFM_C2Gts2(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13) 130.57/78.24 new_mkBalBranch6MkBalBranch42(EmptyFM, x0, x1, x2, x3, x4) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10) 130.57/78.24 new_mkVBalBranch3MkVBalBranch227(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, Neg(Zero), x9, x10), x11) 130.57/78.24 new_primPlusNat8(Succ(x0), x1) 130.57/78.24 new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7) 130.57/78.24 new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.24 new_splitGT220(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Succ(x4), x5, x6, x7) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10) 130.57/78.24 new_splitLT15(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) 130.57/78.24 new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13) 130.57/78.24 new_mkVBalBranch3MkVBalBranch227(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12) 130.57/78.24 new_splitGT9(x0) 130.57/78.24 new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7) 130.57/78.24 new_primPlusNat4(Succ(x0)) 130.57/78.24 new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, Zero, x4, x5, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, Pos(x8), x9, x10), x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch241(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.24 new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7) 130.57/78.24 new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7) 130.57/78.24 new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Zero, Succ(x4), x5, x6) 130.57/78.24 new_primPlusNat7(x0, Succ(x1)) 130.57/78.24 new_addToFM_C13(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8) 130.57/78.24 new_mkVBalBranch9(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9, x10, x11) 130.57/78.24 new_addToFM_C11(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7) 130.57/78.24 new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14) 130.57/78.24 new_splitGT213(x0, x1, x2, x3, x4) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10) 130.57/78.24 new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch227(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11) 130.57/78.24 new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Succ(x4), Zero, x5, x6) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Succ(Zero)), x4, x5, x6, x7, Neg(Succ(Succ(Zero))), x8, x9, x10) 130.57/78.24 new_mkBalBranch6MkBalBranch1112(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10) 130.57/78.24 new_addToFM_C13(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9) 130.57/78.24 new_splitGT225(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(Succ(Zero))), x4, x5), Branch(x6, x7, Pos(Succ(Succ(Succ(Succ(x8))))), x9, x10), x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch129(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.24 new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, Zero, x4, x5) 130.57/78.24 new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13) 130.57/78.24 new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9) 130.57/78.24 new_splitGT18(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.24 new_splitLT13(Branch(Neg(Zero), x0, x1, x2, x3), x4, x5) 130.57/78.24 new_splitGT12(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Zero, Zero, x4, x5) 130.57/78.24 new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.24 new_addToFM_C3(Branch(Neg(Zero), x0, x1, x2, x3), Zero, x4, x5) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6) 130.57/78.24 new_primPlusNat5(Succ(x0)) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11) 130.57/78.24 new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Zero, Zero, x4, x5) 130.57/78.24 new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13) 130.57/78.24 new_mkVBalBranch8(x0, x1, x2, x3, x4, x5, x6, EmptyFM, x7) 130.57/78.24 new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.24 new_splitLT5(x0) 130.57/78.24 new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.24 new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.24 new_splitGT222(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) 130.57/78.24 new_mkBalBranch6MkBalBranch1112(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Succ(Succ(x4)))), x5, x6), Branch(x7, x8, Neg(Succ(Succ(Succ(Succ(Zero))))), x9, x10), x11) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Zero)), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Succ(Succ(Succ(Succ(x8))))))), x9, x10), x11) 130.57/78.24 new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.24 new_addToFM_C4(Branch(Pos(Zero), x0, x1, x2, x3), Succ(x4), x5, x6) 130.57/78.24 new_splitGT222(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Zero), x4, x5, x6, x7, Neg(Succ(x8)), x9, x10, x11) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11) 130.57/78.24 new_mkVBalBranch10(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9, x10, x11) 130.57/78.24 new_intersectFM_C2Gts(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Succ(Zero)), x4, x5) 130.57/78.24 new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), x12, x13) 130.57/78.24 new_addToFM_C3(EmptyFM, x0, x1, x2) 130.57/78.24 new_emptyFM(x0) 130.57/78.24 new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10) 130.57/78.24 new_sizeFM(EmptyFM, x0, x1) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(Zero)), x4, x5), Branch(x6, x7, Pos(Succ(Succ(Succ(Succ(Zero))))), x8, x9), x10) 130.57/78.24 new_splitLT17(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Zero)), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Succ(Succ(Zero))))), x8, x9), x10) 130.57/78.24 new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14) 130.57/78.24 new_splitLT217(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_splitLT218(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) 130.57/78.24 new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.24 new_addToFM_C14(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6, x7, x8, Pos(x9), x10, x11, x12) 130.57/78.24 new_splitLT214(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_splitGT43(x0) 130.57/78.24 new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_splitGT230(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, Neg(Zero), x9, x10), x11) 130.57/78.24 new_splitLT211(x0, x1, x2, x3, x4) 130.57/78.24 new_splitLT6(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14) 130.57/78.24 new_splitLT212(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) 130.57/78.24 new_mkVBalBranch8(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), x12) 130.57/78.24 new_splitLT216(Pos(Zero), x0, x1, x2, x3, x4) 130.57/78.24 new_primMulNat5 130.57/78.24 new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Zero, Succ(x4), x5, x6) 130.57/78.24 new_splitGT214(x0, x1, x2, x3, x4) 130.57/78.24 new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9) 130.57/78.24 new_addToFM_C26(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.24 new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8) 130.57/78.24 new_splitGT222(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) 130.57/78.24 new_intersectFM_C2Lts(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Zero, x4, x5, x6) 130.57/78.24 new_addToFM_C12(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.24 new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) 130.57/78.24 new_splitGT222(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) 130.57/78.24 new_primPlusNat3(Succ(x0)) 130.57/78.24 new_splitGT11(EmptyFM, x0) 130.57/78.24 new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11) 130.57/78.24 new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6) 130.57/78.24 new_splitGT16(EmptyFM, x0, x1) 130.57/78.24 new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7) 130.57/78.24 new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.24 new_addToFM(x0, x1, x2) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10) 130.57/78.24 new_addToFM_C11(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9) 130.57/78.24 new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13) 130.57/78.24 new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Succ(x4), Zero, x5, x6) 130.57/78.24 new_addToFM_C4(Branch(Neg(x0), x1, x2, x3, x4), Succ(x5), x6, x7) 130.57/78.24 new_primPlusNat3(Zero) 130.57/78.24 new_intersectFM_C2Gts0(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, Neg(Succ(x9)), x10, x11), x12) 130.57/78.24 new_splitGT11(Branch(Neg(Succ(x0)), x1, x2, x3, x4), x5) 130.57/78.24 new_splitGT224(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_splitLT16(x0, x1) 130.57/78.24 new_mkVBalBranch3MkVBalBranch133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13) 130.57/78.24 new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10) 130.57/78.24 new_splitGT223(Neg(Succ(x0)), x1, x2, x3, x4, x5) 130.57/78.24 new_mkVBalBranch3MkVBalBranch239(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11) 130.57/78.24 new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7) 130.57/78.24 new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, Neg(Succ(Zero)), x8, x9), x10) 130.57/78.24 new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Neg(Zero), x4, x5) 130.57/78.24 new_primMulNat0(x0) 130.57/78.24 new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_splitGT19(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, Neg(Succ(x9)), x10, x11), x12) 130.57/78.24 new_splitGT225(Neg(x0), x1, x2, x3, x4, x5, x6) 130.57/78.24 new_mkVBalBranch3MkVBalBranch131(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13) 130.57/78.24 new_splitGT223(Pos(Succ(x0)), x1, x2, x3, x4, x5) 130.57/78.24 new_splitLT13(EmptyFM, x0, x1) 130.57/78.24 new_mkVBalBranch3MkVBalBranch127(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.24 new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Zero), x4, x5) 130.57/78.24 new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6) 130.57/78.24 new_primMinusNat0(Succ(x0), Zero) 130.57/78.24 new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7) 130.57/78.24 new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7) 130.57/78.24 new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch125(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Succ(x4)), x5, x6, x7, x8, Neg(Zero), x9, x10, x11) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(Succ(x4))), x5, x6), Branch(x7, x8, Pos(Succ(Succ(Succ(Zero)))), x9, x10), x11) 130.57/78.24 new_splitLT42(x0, x1) 130.57/78.24 new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10) 130.57/78.24 new_intersectFM_C2Gts4(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7) 130.57/78.24 new_addToFM_C3(Branch(Pos(x0), x1, x2, x3, x4), Succ(x5), x6, x7) 130.57/78.24 new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12) 130.57/78.24 new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Succ(x4)), x5, x6, x7, x8, Pos(Zero), x9, x10, x11) 130.57/78.24 new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Succ(Succ(x3))), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Zero))), x8, x9), x10) 130.57/78.24 new_splitGT227(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.24 new_mkVBalBranch3MkVBalBranch126(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13) 130.57/78.24 new_splitGT15(EmptyFM, x0) 130.57/78.24 new_splitLT15(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) 130.57/78.24 new_mkVBalBranch3MkVBalBranch130(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6, x7, x8, Neg(Succ(Zero)), x9, x10, x11) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11) 130.57/78.24 new_splitLT221(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_splitGT228(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch239(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12) 130.57/78.24 new_splitLT14(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_splitGT217(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9) 130.57/78.24 new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10) 130.57/78.24 new_primMulNat4 130.57/78.24 new_mkVBalBranch7(x0, EmptyFM, x1, x2) 130.57/78.24 new_splitGT11(Branch(Pos(Zero), x0, x1, x2, x3), x4) 130.57/78.24 new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Zero, x4, x5) 130.57/78.24 new_splitLT19(EmptyFM, x0) 130.57/78.24 new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10) 130.57/78.24 new_primPlusNat5(Zero) 130.57/78.24 new_primMinusNat0(Zero, Succ(x0)) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Succ(x4)), x5, x6, x7, x8, Pos(Succ(Zero)), x9, x10, x11) 130.57/78.24 new_primPlusInt0(x0, Pos(x1)) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Zero)), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), x8, x9), x10) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Succ(x4))), x5, x6), Branch(x7, x8, Neg(Succ(Succ(Succ(Zero)))), x9, x10), x11) 130.57/78.24 new_splitLT29(Neg(x0), x1, x2, EmptyFM, x3, x4, x5) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, Pos(Succ(Zero)), x8, x9), x10) 130.57/78.24 new_mkVBalBranch3MkVBalBranch223(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12) 130.57/78.24 new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7) 130.57/78.24 new_primPlusNat0(Zero, Zero) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Succ(x4)), x5, x6, x7, x8, Neg(Succ(x9)), x10, x11, x12) 130.57/78.24 new_mkVBalBranch10(x0, x1, EmptyFM, x2, x3, x4, x5, x6) 130.57/78.24 new_splitGT221(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.24 new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12) 130.57/78.24 new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14) 130.57/78.24 new_mkBalBranch6MkBalBranch011(x0, x1, x2, EmptyFM, x3, x4, x5, x6, x7, x8) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10) 130.57/78.24 new_primPlusNat1(Zero) 130.57/78.24 new_primPlusInt(Neg(x0), x1, x2, x3, x4, x5) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Succ(x4))), x5, x6), Branch(x7, x8, Neg(Succ(Succ(Zero))), x9, x10), x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch131(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12) 130.57/78.24 new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13) 130.57/78.24 new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6) 130.57/78.24 new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13) 130.57/78.24 new_splitLT210(x0, x1, x2, x3, x4) 130.57/78.24 new_addToFM_C4(EmptyFM, x0, x1, x2) 130.57/78.24 new_mkVBalBranch3MkVBalBranch126(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13) 130.57/78.24 new_mkVBalBranch3MkVBalBranch130(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9) 130.57/78.24 new_splitGT30(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6) 130.57/78.24 new_splitLT19(Branch(Neg(Succ(x0)), x1, x2, x3, x4), x5) 130.57/78.24 new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, x4, Succ(x5), x6, x7) 130.57/78.24 new_splitLT19(Branch(Pos(Succ(x0)), x1, x2, x3, x4), x5) 130.57/78.24 new_primPlusInt(Pos(x0), x1, x2, x3, x4, x5) 130.57/78.24 new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10) 130.57/78.24 new_splitGT223(Neg(Zero), x0, x1, x2, x3, x4) 130.57/78.24 new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6) 130.57/78.24 new_addToFM_C3(Branch(Neg(Succ(x0)), x1, x2, x3, x4), Succ(x5), x6, x7) 130.57/78.24 new_splitLT212(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, Succ(x4), x5, x6) 130.57/78.24 new_splitGT12(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) 130.57/78.24 new_splitGT13(Branch(x0, x1, x2, x3, x4), x5, x6) 130.57/78.24 new_mkVBalBranch3MkVBalBranch225(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, Pos(Succ(Zero)), x9, x10), x11) 130.57/78.24 new_splitGT13(EmptyFM, x0, x1) 130.57/78.24 new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13) 130.57/78.24 new_primPlusInt0(x0, Neg(x1)) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Succ(Zero)), x3, x4), Branch(x5, x6, Neg(Succ(Succ(Succ(x7)))), x8, x9), x10) 130.57/78.24 new_splitLT17(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) 130.57/78.24 new_primMulNat6 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(Zero)), x4, x5), Branch(x6, x7, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x8, x9), x10) 130.57/78.24 new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.24 new_mkVBalBranch3MkVBalBranch154(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.24 new_mkVBalBranch3MkVBalBranch239(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13) 130.57/78.24 new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_mkVBalBranch3MkVBalBranch231(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7) 130.57/78.24 new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Zero)), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Succ(Zero)))), x8, x9), x10) 130.57/78.24 new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, Zero, x4, x5) 130.57/78.24 new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.24 new_intersectFM_C2Gts6(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkVBalBranch3MkVBalBranch231(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12) 130.57/78.24 new_mkVBalBranch3MkVBalBranch233(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.24 new_splitLT17(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) 130.57/78.24 new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, EmptyFM, x7, x8) 130.57/78.24 new_mkVBalBranch3MkVBalBranch227(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13) 130.57/78.24 new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9) 130.57/78.24 new_primMulNat2(x0) 130.57/78.24 new_primPlusNat0(Succ(x0), Zero) 130.57/78.24 new_mkBalBranch6MkBalBranch31(x0, x1, x2, EmptyFM, x3, x4) 130.57/78.24 new_splitGT215(x0, x1, x2, x3, x4) 130.57/78.24 new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Succ(Succ(Succ(x4)))), x5, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch119(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.24 new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, Succ(x4), x5, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10) 130.57/78.24 new_splitLT29(Pos(Zero), x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7) 130.57/78.24 new_mkVBalBranch3MkVBalBranch126(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12) 130.57/78.24 new_mkVBalBranch11(x0, x1, EmptyFM, x2, x3, x4, x5, x6, x7) 130.57/78.24 new_splitGT229(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11) 130.57/78.24 new_addToFM_C3(Branch(Neg(Zero), x0, x1, x2, x3), Succ(x4), x5, x6) 130.57/78.24 new_splitGT225(Pos(Zero), x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkBranch(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, Pos(Zero), x9, x10), x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch232(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.24 new_addToFM_C24(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10) 130.57/78.24 new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, x4, Zero, x5, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10) 130.57/78.24 new_splitLT215(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_splitGT7(x0) 130.57/78.24 new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.24 new_intersectFM_C2Gts7(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Succ(Zero)), x4, x5), Branch(x6, x7, Pos(Succ(Succ(x8))), x9, x10), x11) 130.57/78.24 new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) 130.57/78.24 new_addToFM_C24(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7) 130.57/78.24 new_splitLT219(x0, x1, x2, x3, x4) 130.57/78.24 new_splitLT212(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) 130.57/78.24 new_splitGT12(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) 130.57/78.24 new_splitLT8(x0, x1, x2, x3, x4) 130.57/78.24 new_intersectFM_C2Lts1(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.24 new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Zero, x4, x5) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, Pos(Succ(Zero)), x9, x10), x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12) 130.57/78.24 new_addToFM_C11(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Succ(Succ(x4))), x5, x6), Branch(x7, x8, Pos(Succ(Succ(x9))), x10, x11), x12) 130.57/78.24 new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13) 130.57/78.24 new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch129(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(Zero)), x4, x5), Branch(x6, x7, Pos(Succ(Succ(Succ(Succ(Succ(Succ(x8))))))), x9, x10), x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.24 new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, Neg(Zero), x9, x10), x11) 130.57/78.24 new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) 130.57/78.24 new_splitLT7(x0, x1, x2, x3, x4) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Succ(Succ(x4)))), x5, x6), Branch(x7, x8, Neg(Succ(Succ(Succ(Succ(Succ(x9)))))), x10, x11), x12) 130.57/78.24 new_splitLT220(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkVBalBranch9(x0, x1, EmptyFM, x2, x3, x4, x5, x6) 130.57/78.24 new_splitGT11(Branch(Pos(Succ(x0)), x1, x2, x3, x4), x5) 130.57/78.24 new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_splitLT17(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch33(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.24 new_mkVBalBranch12(x0, x1, EmptyFM, x2, x3, x4, x5, x6, x7) 130.57/78.24 new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.24 new_intersectFM_C2Gts8(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Zero)), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Zero))), x8, x9), x10) 130.57/78.24 new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12) 130.57/78.24 new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(Succ(x4))), x5, x6), Branch(x7, x8, Pos(Succ(Succ(Zero))), x9, x10), x11) 130.57/78.24 new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9) 130.57/78.24 new_mkVBalBranch3MkVBalBranch126(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14) 130.57/78.24 new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Succ(Succ(Zero))), x4, x5) 130.57/78.24 new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10) 130.57/78.24 new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9) 130.57/78.24 new_splitGT42(x0, x1) 130.57/78.24 new_addToFM_C11(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8) 130.57/78.24 new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13) 130.57/78.24 new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10) 130.57/78.24 new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.24 new_primPlusNat7(x0, Zero) 130.57/78.24 new_intersectFM_C2Lts4(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_splitLT12(Branch(x0, x1, x2, x3, x4), x5, x6) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Succ(Succ(x3))), x4, x5), Branch(x6, x7, Pos(Succ(Succ(x8))), x9, x10), x11) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, Neg(Succ(Zero)), x9, x10), x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch231(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10) 130.57/78.24 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10) 130.57/78.24 new_mkVBalBranch3MkVBalBranch239(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12) 130.57/78.24 new_splitLT40(x0) 130.57/78.24 new_splitLT9(EmptyFM, x0) 130.57/78.24 new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10) 130.57/78.24 new_splitLT15(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) 130.57/78.24 new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9) 130.57/78.24 new_splitGT226(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) 130.57/78.24 new_splitGT11(Branch(Neg(Zero), x0, x1, x2, x3), x4) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, Pos(x9), x10, x11), x12) 130.57/78.24 new_splitGT223(Pos(Zero), x0, x1, x2, x3, x4) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, Neg(Zero), x9, x10), x11) 130.57/78.24 new_addToFM0(x0, x1, x2) 130.57/78.24 new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch242(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.24 new_mkBalBranch6MkBalBranch42(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8, x9) 130.57/78.24 new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch127(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.24 new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10) 130.57/78.24 new_addToFM_C4(Branch(Neg(Zero), x0, x1, x2, x3), Zero, x4, x5) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Succ(Succ(x4))), x5, x6), Branch(x7, x8, Neg(Succ(Succ(Zero))), x9, x10), x11) 130.57/78.24 new_splitGT216(x0, x1, x2, x3, x4) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Succ(Zero)), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Succ(x8)))), x9, x10), x11) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Zero), x4, x5, x6, x7, Pos(Succ(x8)), x9, x10, x11) 130.57/78.24 new_addToFM_C4(Branch(Pos(Succ(x0)), x1, x2, x3, x4), Succ(x5), x6, x7) 130.57/78.24 new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.24 new_primPlusNat6(x0, Zero) 130.57/78.24 new_primMulNat(Succ(x0)) 130.57/78.24 new_intersectFM_C2Gts5(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10) 130.57/78.24 new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.24 new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10) 130.57/78.24 new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12) 130.57/78.24 new_splitLT29(Neg(x0), x1, x2, Branch(x3, x4, x5, x6, x7), EmptyFM, x8, x9) 130.57/78.24 new_splitLT13(Branch(Pos(x0), x1, x2, x3, x4), x5, x6) 130.57/78.24 new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12) 130.57/78.24 new_splitLT29(Neg(x0), x1, x2, Branch(x3, x4, x5, x6, x7), Branch(x8, x9, x10, x11, x12), x13, x14) 130.57/78.24 new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch238(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12, x13) 130.57/78.24 new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(Zero)), x4, x5), Branch(x6, x7, Pos(Succ(Succ(Succ(Zero)))), x8, x9), x10) 130.57/78.24 new_splitGT40(x0) 130.57/78.24 new_intersectFM_C2Gts1(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Succ(Zero)), x4, x5, x6, x7, Pos(Succ(Succ(x8))), x9, x10, x11) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10) 130.57/78.24 new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11) 130.57/78.24 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(Zero)), x4, x5), Branch(x6, x7, Pos(Succ(Succ(Zero))), x8, x9), x10) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Succ(Succ(x4))), x5, x6), Branch(x7, x8, Neg(Succ(Succ(Succ(x9)))), x10, x11), x12) 130.57/78.24 new_splitLT31(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_splitLT9(Branch(x0, x1, x2, x3, x4), x5) 130.57/78.24 new_splitLT13(Branch(Neg(Succ(x0)), x1, x2, x3, x4), x5, x6) 130.57/78.24 new_splitGT17(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10) 130.57/78.24 new_primMinusNat0(Succ(x0), Succ(x1)) 130.57/78.24 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, Neg(Succ(Zero)), x9, x10), x11) 130.57/78.24 new_primMulNat(Zero) 130.57/78.24 new_splitGT226(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) 130.57/78.24 new_splitGT41(x0, x1) 130.57/78.24 new_splitGT218(x0, x1, x2, x3, x4, x5, x6) 130.57/78.24 new_addToFM1(x0, x1, x2, x3) 130.57/78.24 new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Succ(Zero)), x4, x5, x6, x7, Neg(Succ(Succ(Succ(x8)))), x9, x10, x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10) 130.57/78.24 new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13) 130.57/78.24 new_intersectFM_C2Lts7(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.24 new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13) 130.57/78.24 new_mkVBalBranch3MkVBalBranch125(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10) 130.57/78.24 new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Succ(x4), x5, x6) 130.57/78.24 new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11) 130.57/78.24 new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.24 new_mkVBalBranch3MkVBalBranch130(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13) 130.57/78.24 new_splitGT8(x0, x1) 130.57/78.24 new_splitLT222(x0, x1, x2, x3, x4) 130.57/78.24 new_mkVBalBranch3MkVBalBranch128(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.24 new_addToFM_C3(Branch(Pos(Zero), x0, x1, x2, x3), Zero, x4, x5) 130.57/78.24 new_splitLT216(Pos(Succ(x0)), x1, x2, x3, x4, x5) 130.57/78.24 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6, x7, x8, Neg(Zero), x9, x10, x11) 130.57/78.24 new_splitLT12(EmptyFM, x0, x1) 130.57/78.24 new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, Zero, x4, x5) 130.57/78.24 new_intersectFM_C2Gts3(x0, x1, x2, x3, x4, x5) 130.57/78.24 new_mkVBalBranch11(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9, x10, x11, x12) 130.57/78.24 new_mkVBalBranch6(x0, x1, EmptyFM, x2, x3) 130.57/78.24 130.57/78.24 We have to consider all minimal (P,Q,R)-chains. 130.57/78.24 ---------------------------------------- 130.57/78.24 130.57/78.24 (51) DependencyGraphProof (EQUIVALENT) 130.57/78.24 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 7 less nodes. 130.57/78.24 ---------------------------------------- 130.57/78.24 130.57/78.24 (52) 130.57/78.24 Obligation: 130.57/78.24 Q DP problem: 130.57/78.24 The TRS P consists of the following rules: 130.57/78.24 130.57/78.24 new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, Zero, Zero, ed, ee) -> new_intersectFM_C2IntersectFM_C135(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, ed, ee) 130.57/78.24 new_intersectFM_C2IntersectFM_C135(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, ed, ee) -> new_intersectFM_C2IntersectFM_C133(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, Succ(zzz2153), Succ(zzz2148), ed, ee) 130.57/78.24 new_intersectFM_C2IntersectFM_C133(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, Succ(zzz26420), Succ(zzz26430), ef, eg) -> new_intersectFM_C2IntersectFM_C133(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, zzz26420, zzz26430, ef, eg) 130.57/78.24 new_intersectFM_C2IntersectFM_C133(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, Zero, Succ(zzz26430), ef, eg) -> new_intersectFM_C(new_intersectFM_C2Gts5(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, ef), zzz2636, ef) 130.57/78.24 new_intersectFM_C(Branch(Neg(Succ(zzz3000)), zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C113(zzz3000, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, bd, bd) 130.57/78.24 new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Pos(Succ(zzz160300)), zzz1604, zzz1605, EmptyFM, zzz1607, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Gts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1602, gc) 130.57/78.24 new_intersectFM_C(Branch(Pos(Succ(zzz3000)), zzz31, zzz32, EmptyFM, zzz34), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C111(zzz3000, zzz31, zzz32, EmptyFM, zzz34, zzz41, zzz42, zzz43, zzz44, bd, bd) 130.57/78.24 new_intersectFM_C2IntersectFM_C111(zzz830, zzz831, zzz832, zzz833, zzz834, zzz835, zzz836, zzz837, zzz838, fg, fh) -> new_intersectFM_C(new_intersectFM_C2Gts7(zzz830, zzz831, zzz832, zzz833, zzz834, fg), zzz838, fg) 130.57/78.24 new_intersectFM_C(Branch(Neg(Succ(zzz3000)), zzz31, zzz32, zzz33, EmptyFM), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_mkVBalBranch6(zzz3000, zzz31, zzz33, new_splitLT5(bd), bd), zzz43, bd) 130.57/78.24 new_intersectFM_C(Branch(Pos(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT210(zzz31, zzz32, zzz33, zzz34, bd), zzz43, bd) 130.57/78.24 new_intersectFM_C(Branch(Neg(zzz300), zzz31, zzz32, zzz33, EmptyFM), Branch(Pos(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT29(Neg(zzz300), zzz31, zzz32, zzz33, EmptyFM, zzz4000, bd), zzz43, bd) 130.57/78.24 new_intersectFM_C(Branch(Pos(Zero), zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(Pos(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C14(zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz4000, zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, bd, bd) 130.57/78.24 new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, Neg(zzz27430), zzz2744, zzz2745, zzz2746, EmptyFM, be, bf) -> new_intersectFM_C(new_intersectFM_C2Gts0(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, be), zzz2742, be) 130.57/78.24 new_intersectFM_C(Branch(Neg(Succ(zzz3000)), zzz31, zzz32, zzz33, EmptyFM), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_mkVBalBranch6(zzz3000, zzz31, zzz33, new_splitLT9(EmptyFM, bd), bd), zzz43, bd) 130.57/78.24 new_intersectFM_C(Branch(Pos(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT8(zzz31, zzz32, zzz33, zzz34, bd), zzz43, bd) 130.57/78.24 new_intersectFM_C(Branch(Pos(zzz300), zzz31, zzz32, EmptyFM, zzz34), Branch(Neg(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_mkVBalBranch5(zzz300, zzz31, new_splitGT8(zzz4000, bd), zzz34, bd), zzz44, bd) 130.57/78.24 new_intersectFM_C(Branch(Neg(Succ(zzz3000)), zzz31, zzz32, zzz33, zzz34), Branch(Neg(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C19(zzz3000, zzz31, zzz32, zzz33, zzz34, zzz4000, zzz41, zzz42, zzz43, zzz44, zzz3000, zzz31, zzz32, zzz33, zzz34, zzz3000, zzz4000, bd, bd) 130.57/78.24 new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, Succ(zzz21580), Succ(zzz21590), ed, ee) -> new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, zzz21580, zzz21590, ed, ee) 130.57/78.24 new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, Branch(Neg(Succ(zzz2156000)), zzz21561, zzz21562, zzz21563, zzz21564), zzz2157, Zero, Succ(zzz21590), ed, ee) -> new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2156000, zzz21561, zzz21562, zzz21563, zzz21564, zzz2156000, zzz2148, ed, ee) 130.57/78.24 new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, EmptyFM, zzz2157, Zero, Succ(zzz21590), ed, ee) -> new_intersectFM_C(new_intersectFM_C2Gts5(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, ed), zzz2152, ed) 130.57/78.24 new_intersectFM_C(Branch(Neg(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT211(zzz31, zzz32, zzz33, zzz34, bd), zzz43, bd) 130.57/78.24 new_intersectFM_C(Branch(Neg(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT11(zzz31, zzz32, zzz33, zzz34, bd), zzz43, bd) 130.57/78.24 new_intersectFM_C(Branch(Pos(Succ(zzz3000)), zzz31, zzz32, EmptyFM, zzz34), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_mkVBalBranch5(Succ(zzz3000), zzz31, new_splitGT7(bd), zzz34, bd), zzz44, bd) 130.57/78.24 new_intersectFM_C(Branch(Neg(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitGT214(zzz31, zzz32, zzz33, zzz34, bd), zzz44, bd) 130.57/78.24 new_intersectFM_C(Branch(Pos(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitGT215(zzz31, zzz32, zzz33, zzz34, bd), zzz44, bd) 130.57/78.24 new_intersectFM_C(Branch(Pos(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitGT213(zzz31, zzz32, zzz33, zzz34, bd), zzz44, bd) 130.57/78.24 new_intersectFM_C(Branch(Neg(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitGT216(zzz31, zzz32, zzz33, zzz34, bd), zzz44, bd) 130.57/78.24 new_intersectFM_C(Branch(Neg(Zero), zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(Neg(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C110(zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz4000, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, bd, bd) 130.57/78.24 new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, Neg(Zero), zzz894, zzz895, zzz896, zzz897, eh, fa) -> new_intersectFM_C2IntersectFM_C138(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz896, eh, fa) 130.57/78.24 new_intersectFM_C2IntersectFM_C138(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, EmptyFM, eh, fa) -> new_intersectFM_C(new_intersectFM_C2Lts6(zzz884, zzz885, zzz886, zzz887, zzz888, eh), zzz891, eh) 130.57/78.24 new_intersectFM_C(Branch(Neg(Zero), zzz31, zzz32, EmptyFM, zzz34), Branch(Neg(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_mkVBalBranch7(zzz31, new_splitGT8(zzz4000, bd), zzz34, bd), zzz44, bd) 130.57/78.24 new_intersectFM_C(Branch(Pos(Zero), zzz31, zzz32, zzz33, EmptyFM), Branch(Pos(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT29(Pos(Zero), zzz31, zzz32, zzz33, EmptyFM, zzz4000, bd), zzz43, bd) 130.57/78.24 new_intersectFM_C(Branch(Pos(Succ(zzz3000)), zzz31, zzz32, zzz33, zzz34), Branch(Pos(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C1(zzz3000, zzz31, zzz32, zzz33, zzz34, zzz4000, zzz41, zzz42, zzz43, zzz44, zzz3000, zzz31, zzz32, zzz33, zzz34, zzz4000, zzz3000, bd, bd) 130.57/78.24 new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, EmptyFM, zzz2092, Zero, Succ(zzz20940), h, ba) -> new_intersectFM_C(new_intersectFM_C2Gts(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, h), zzz2087, h) 130.57/78.24 new_intersectFM_C(Branch(Pos(Succ(zzz3000)), zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C112(zzz3000, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, bd, bd) 130.57/78.24 new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Pos(Succ(zzz90800)), zzz909, zzz910, EmptyFM, zzz912, ga, gb) -> new_intersectFM_C2IntersectFM_C111(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, ga, gb) 130.57/78.24 new_intersectFM_C2IntersectFM_C111(zzz830, zzz831, zzz832, zzz833, zzz834, zzz835, zzz836, zzz837, zzz838, fg, fh) -> new_intersectFM_C(new_intersectFM_C2Lts7(zzz830, zzz831, zzz832, zzz833, zzz834, fg), zzz837, fg) 130.57/78.24 new_intersectFM_C(Branch(Neg(zzz300), zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(Pos(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C15(zzz300, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz4000, zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, bd, bd) 130.57/78.24 new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, Pos(Zero), zzz1393, zzz1394, zzz1395, zzz1396, cc, cd) -> new_intersectFM_C2IntersectFM_C120(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, zzz1396, cc, cd) 130.57/78.24 new_intersectFM_C2IntersectFM_C120(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, EmptyFM, cc, cd) -> new_intersectFM_C(new_intersectFM_C2Lts1(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, cc), zzz1390, cc) 130.57/78.24 new_intersectFM_C(Branch(Pos(zzz300), zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(Neg(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C18(zzz300, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz4000, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, bd, bd) 130.57/78.24 new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, Neg(Zero), zzz753, zzz754, zzz755, zzz756, df, dg) -> new_intersectFM_C2IntersectFM_C129(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, zzz755, df, dg) 130.57/78.24 new_intersectFM_C2IntersectFM_C129(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, EmptyFM, df, dg) -> new_intersectFM_C(new_intersectFM_C2Lts4(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df), zzz750, df) 130.57/78.24 new_intersectFM_C(Branch(Neg(Succ(zzz3000)), zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C17(zzz3000, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, bd, bd) 130.57/78.24 new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Neg(Zero), zzz1202, zzz1203, zzz1204, zzz1205, dd, de) -> new_intersectFM_C2IntersectFM_C127(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, zzz1202, dd, de) 130.57/78.24 new_intersectFM_C2IntersectFM_C127(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, zzz1202, dd, de) -> new_intersectFM_C(new_intersectFM_C2Gts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1200, dd) 130.57/78.24 new_intersectFM_C(Branch(Pos(Succ(zzz3000)), zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C16(zzz3000, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, bd, bd) 130.57/78.24 new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Neg(Succ(zzz62700)), zzz628, zzz629, zzz630, zzz631, db, dc) -> new_intersectFM_C2IntersectFM_C124(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, zzz631, db, dc) 130.57/78.24 new_intersectFM_C2IntersectFM_C124(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, EmptyFM, db, dc) -> new_intersectFM_C(new_intersectFM_C2Lts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz625, db) 130.57/78.24 new_intersectFM_C2IntersectFM_C124(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, EmptyFM, db, dc) -> new_intersectFM_C(new_intersectFM_C2Gts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz626, db) 130.57/78.24 new_intersectFM_C2IntersectFM_C124(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Branch(zzz6300, zzz6301, zzz6302, zzz6303, zzz6304), db, dc) -> new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, db, dc) 130.57/78.24 new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Neg(Zero), zzz628, zzz629, zzz630, zzz631, db, dc) -> new_intersectFM_C2IntersectFM_C125(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, zzz628, db, dc) 130.57/78.24 new_intersectFM_C2IntersectFM_C125(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, zzz628, db, dc) -> new_intersectFM_C(new_intersectFM_C2Gts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz626, db) 130.57/78.24 new_intersectFM_C2IntersectFM_C125(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, zzz628, db, dc) -> new_intersectFM_C(new_intersectFM_C2Lts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz625, db) 130.57/78.24 new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Pos(Zero), zzz628, zzz629, zzz630, zzz631, db, dc) -> new_intersectFM_C(new_intersectFM_C2Lts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz625, db) 130.57/78.24 new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Pos(Succ(zzz62700)), zzz628, zzz629, EmptyFM, zzz631, db, dc) -> new_intersectFM_C(new_intersectFM_C2Gts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz626, db) 130.57/78.24 new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Pos(Succ(zzz62700)), zzz628, zzz629, Branch(zzz6300, zzz6301, zzz6302, zzz6303, zzz6304), zzz631, db, dc) -> new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, db, dc) 130.57/78.24 new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Pos(Zero), zzz628, zzz629, zzz630, zzz631, db, dc) -> new_intersectFM_C(new_intersectFM_C2Gts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz626, db) 130.57/78.24 new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Pos(Succ(zzz62700)), zzz628, zzz629, EmptyFM, zzz631, db, dc) -> new_intersectFM_C(new_intersectFM_C2Lts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz625, db) 130.57/78.24 new_intersectFM_C2IntersectFM_C127(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, zzz1202, dd, de) -> new_intersectFM_C(new_intersectFM_C2Lts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1199, dd) 130.57/78.24 new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Pos(Succ(zzz120100)), zzz1202, zzz1203, EmptyFM, zzz1205, dd, de) -> new_intersectFM_C(new_intersectFM_C2Lts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1199, dd) 130.57/78.24 new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Pos(Succ(zzz120100)), zzz1202, zzz1203, Branch(zzz12040, zzz12041, zzz12042, zzz12043, zzz12044), zzz1205, dd, de) -> new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, zzz12040, zzz12041, zzz12042, zzz12043, zzz12044, dd, de) 130.57/78.24 new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Pos(Zero), zzz1202, zzz1203, zzz1204, zzz1205, dd, de) -> new_intersectFM_C(new_intersectFM_C2Lts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1199, dd) 130.57/78.24 new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Pos(Zero), zzz1202, zzz1203, zzz1204, zzz1205, dd, de) -> new_intersectFM_C(new_intersectFM_C2Gts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1200, dd) 130.57/78.24 new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Pos(Succ(zzz120100)), zzz1202, zzz1203, EmptyFM, zzz1205, dd, de) -> new_intersectFM_C(new_intersectFM_C2Gts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1200, dd) 130.57/78.24 new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Neg(Succ(zzz120100)), zzz1202, zzz1203, zzz1204, zzz1205, dd, de) -> new_intersectFM_C2IntersectFM_C126(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, zzz1205, dd, de) 130.57/78.24 new_intersectFM_C2IntersectFM_C126(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, EmptyFM, dd, de) -> new_intersectFM_C(new_intersectFM_C2Gts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1200, dd) 130.57/78.24 new_intersectFM_C2IntersectFM_C126(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Branch(zzz12040, zzz12041, zzz12042, zzz12043, zzz12044), dd, de) -> new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, zzz12040, zzz12041, zzz12042, zzz12043, zzz12044, dd, de) 130.57/78.24 new_intersectFM_C2IntersectFM_C126(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, EmptyFM, dd, de) -> new_intersectFM_C(new_intersectFM_C2Lts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1199, dd) 130.57/78.24 new_intersectFM_C2IntersectFM_C129(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, Branch(zzz7550, zzz7551, zzz7552, zzz7553, zzz7554), df, dg) -> new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, zzz7550, zzz7551, zzz7552, zzz7553, zzz7554, df, dg) 130.57/78.24 new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, Pos(zzz7520), zzz753, zzz754, EmptyFM, zzz756, df, dg) -> new_intersectFM_C(new_intersectFM_C2Lts4(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df), zzz750, df) 130.57/78.24 new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, Pos(zzz7520), zzz753, zzz754, Branch(zzz7550, zzz7551, zzz7552, zzz7553, zzz7554), zzz756, df, dg) -> new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, zzz7550, zzz7551, zzz7552, zzz7553, zzz7554, df, dg) 130.57/78.24 new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, Neg(Succ(zzz75200)), zzz753, zzz754, zzz755, zzz756, df, dg) -> new_intersectFM_C2IntersectFM_C128(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, zzz75200, zzz753, zzz754, zzz755, zzz756, zzz75200, zzz747, df, dg) 130.57/78.24 new_intersectFM_C2IntersectFM_C128(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, Succ(zzz14130), Zero, dh, ea) -> new_intersectFM_C2IntersectFM_C130(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, Succ(zzz1408), Succ(zzz1403), dh, ea) 130.57/78.24 new_intersectFM_C2IntersectFM_C130(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, Succ(zzz27700), Succ(zzz27710), eb, ec) -> new_intersectFM_C2IntersectFM_C130(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, zzz27700, zzz27710, eb, ec) 130.57/78.24 new_intersectFM_C2IntersectFM_C130(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, Zero, Succ(zzz27710), eb, ec) -> new_intersectFM_C(new_intersectFM_C2Lts4(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, eb), zzz2763, eb) 130.57/78.24 new_intersectFM_C2IntersectFM_C130(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, Succ(zzz27700), Zero, eb, ec) -> new_intersectFM_C2IntersectFM_C129(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2769, eb, ec) 130.57/78.24 new_intersectFM_C2IntersectFM_C129(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, EmptyFM, df, dg) -> new_intersectFM_C(new_intersectFM_C2Gts4(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df), zzz751, df) 130.57/78.24 new_intersectFM_C2IntersectFM_C130(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, Zero, Succ(zzz27710), eb, ec) -> new_intersectFM_C(new_intersectFM_C2Gts4(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, eb), zzz2764, eb) 130.57/78.24 new_intersectFM_C2IntersectFM_C130(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, Zero, Zero, eb, ec) -> new_intersectFM_C2IntersectFM_C132(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, eb, ec) 130.57/78.24 new_intersectFM_C2IntersectFM_C132(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, eb, ec) -> new_intersectFM_C(new_intersectFM_C2Gts4(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, eb), zzz2764, eb) 130.57/78.24 new_intersectFM_C2IntersectFM_C132(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, eb, ec) -> new_intersectFM_C(new_intersectFM_C2Lts4(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, eb), zzz2763, eb) 130.57/78.24 new_intersectFM_C2IntersectFM_C128(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, Zero, Succ(zzz14140), dh, ea) -> new_intersectFM_C2IntersectFM_C129(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1411, dh, ea) 130.57/78.24 new_intersectFM_C2IntersectFM_C128(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, Succ(zzz14130), Succ(zzz14140), dh, ea) -> new_intersectFM_C2IntersectFM_C128(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, zzz14130, zzz14140, dh, ea) 130.57/78.24 new_intersectFM_C2IntersectFM_C128(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, Zero, Zero, dh, ea) -> new_intersectFM_C2IntersectFM_C131(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, dh, ea) 130.57/78.24 new_intersectFM_C2IntersectFM_C131(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, dh, ea) -> new_intersectFM_C2IntersectFM_C130(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, Succ(zzz1408), Succ(zzz1403), dh, ea) 130.57/78.24 new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, Pos(zzz7520), zzz753, zzz754, EmptyFM, zzz756, df, dg) -> new_intersectFM_C(new_intersectFM_C2Gts4(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df), zzz751, df) 130.57/78.24 new_intersectFM_C2IntersectFM_C120(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, Branch(zzz13960, zzz13961, zzz13962, zzz13963, zzz13964), cc, cd) -> new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, zzz13960, zzz13961, zzz13962, zzz13963, zzz13964, cc, cd) 130.57/78.24 new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, Neg(zzz13920), zzz1393, zzz1394, zzz1395, EmptyFM, cc, cd) -> new_intersectFM_C(new_intersectFM_C2Gts1(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, cc), zzz1391, cc) 130.57/78.24 new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, Neg(zzz13920), zzz1393, zzz1394, zzz1395, EmptyFM, cc, cd) -> new_intersectFM_C(new_intersectFM_C2Lts1(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, cc), zzz1390, cc) 130.57/78.24 new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, Pos(Succ(zzz139200)), zzz1393, zzz1394, zzz1395, zzz1396, cc, cd) -> new_intersectFM_C2IntersectFM_C119(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, zzz139200, zzz1393, zzz1394, zzz1395, zzz1396, zzz1387, zzz139200, cc, cd) 130.57/78.24 new_intersectFM_C2IntersectFM_C119(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, Succ(zzz19920), Zero, ce, cf) -> new_intersectFM_C2IntersectFM_C121(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, Succ(zzz1982), Succ(zzz1987), ce, cf) 130.57/78.24 new_intersectFM_C2IntersectFM_C121(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, Succ(zzz31780), Succ(zzz31790), cg, da) -> new_intersectFM_C2IntersectFM_C121(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, zzz31780, zzz31790, cg, da) 130.57/78.24 new_intersectFM_C2IntersectFM_C121(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, Succ(zzz31780), Zero, cg, da) -> new_intersectFM_C2IntersectFM_C120(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3177, cg, da) 130.57/78.24 new_intersectFM_C2IntersectFM_C120(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, EmptyFM, cc, cd) -> new_intersectFM_C(new_intersectFM_C2Gts1(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, cc), zzz1391, cc) 130.57/78.24 new_intersectFM_C2IntersectFM_C121(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, Zero, Succ(zzz31790), cg, da) -> new_intersectFM_C(new_intersectFM_C2Lts1(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, cg), zzz3171, cg) 130.57/78.24 new_intersectFM_C2IntersectFM_C121(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, Zero, Succ(zzz31790), cg, da) -> new_intersectFM_C(new_intersectFM_C2Gts1(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, cg), zzz3172, cg) 130.57/78.24 new_intersectFM_C2IntersectFM_C121(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, Zero, Zero, cg, da) -> new_intersectFM_C2IntersectFM_C123(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, cg, da) 130.57/78.24 new_intersectFM_C2IntersectFM_C123(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, cg, da) -> new_intersectFM_C(new_intersectFM_C2Lts1(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, cg), zzz3171, cg) 130.57/78.24 new_intersectFM_C2IntersectFM_C123(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, cg, da) -> new_intersectFM_C(new_intersectFM_C2Gts1(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, cg), zzz3172, cg) 130.57/78.24 new_intersectFM_C2IntersectFM_C119(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, Zero, Succ(zzz19930), ce, cf) -> new_intersectFM_C2IntersectFM_C120(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1990, ce, cf) 130.57/78.24 new_intersectFM_C2IntersectFM_C119(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, Succ(zzz19920), Succ(zzz19930), ce, cf) -> new_intersectFM_C2IntersectFM_C119(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz19920, zzz19930, ce, cf) 130.57/78.24 new_intersectFM_C2IntersectFM_C119(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, Zero, Zero, ce, cf) -> new_intersectFM_C2IntersectFM_C122(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, ce, cf) 130.57/78.24 new_intersectFM_C2IntersectFM_C122(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, ce, cf) -> new_intersectFM_C2IntersectFM_C121(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, Succ(zzz1982), Succ(zzz1987), ce, cf) 130.57/78.24 new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, Neg(zzz13920), zzz1393, zzz1394, zzz1395, Branch(zzz13960, zzz13961, zzz13962, zzz13963, zzz13964), cc, cd) -> new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, zzz13960, zzz13961, zzz13962, zzz13963, zzz13964, cc, cd) 130.57/78.24 new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Pos(Zero), zzz909, zzz910, zzz911, zzz912, ga, gb) -> new_intersectFM_C(new_intersectFM_C2Lts7(zzz899, zzz900, zzz901, zzz902, zzz903, ga), zzz906, ga) 130.57/78.24 new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Pos(Zero), zzz909, zzz910, zzz911, zzz912, ga, gb) -> new_intersectFM_C(new_intersectFM_C2Gts7(zzz899, zzz900, zzz901, zzz902, zzz903, ga), zzz907, ga) 130.57/78.24 new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Neg(Succ(zzz90800)), zzz909, zzz910, zzz911, zzz912, ga, gb) -> new_intersectFM_C2IntersectFM_C142(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz912, ga, gb) 130.57/78.24 new_intersectFM_C2IntersectFM_C142(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Branch(zzz9110, zzz9111, zzz9112, zzz9113, zzz9114), ga, gb) -> new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz9110, zzz9111, zzz9112, zzz9113, zzz9114, ga, gb) 130.57/78.24 new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Pos(Succ(zzz90800)), zzz909, zzz910, Branch(zzz9110, zzz9111, zzz9112, zzz9113, zzz9114), zzz912, ga, gb) -> new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz9110, zzz9111, zzz9112, zzz9113, zzz9114, ga, gb) 130.57/78.24 new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Neg(Zero), zzz909, zzz910, zzz911, zzz912, ga, gb) -> new_intersectFM_C2IntersectFM_C143(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz909, ga, gb) 130.57/78.24 new_intersectFM_C2IntersectFM_C143(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz909, ga, gb) -> new_intersectFM_C(new_intersectFM_C2Lts7(zzz899, zzz900, zzz901, zzz902, zzz903, ga), zzz906, ga) 130.57/78.24 new_intersectFM_C2IntersectFM_C143(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz909, ga, gb) -> new_intersectFM_C(new_intersectFM_C2Gts7(zzz899, zzz900, zzz901, zzz902, zzz903, ga), zzz907, ga) 130.57/78.24 new_intersectFM_C2IntersectFM_C142(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, EmptyFM, ga, gb) -> new_intersectFM_C2IntersectFM_C111(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, ga, gb) 130.57/78.24 new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, Succ(zzz20930), Succ(zzz20940), h, ba) -> new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, zzz20930, zzz20940, h, ba) 130.57/78.24 new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, Zero, Zero, h, ba) -> new_intersectFM_C2IntersectFM_C12(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, h, ba) 130.57/78.24 new_intersectFM_C2IntersectFM_C12(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, h, ba) -> new_intersectFM_C2IntersectFM_C10(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, Succ(zzz2083), Succ(zzz2088), h, ba) 130.57/78.24 new_intersectFM_C2IntersectFM_C10(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, Succ(zzz26240), Succ(zzz26250), bb, bc) -> new_intersectFM_C2IntersectFM_C10(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, zzz26240, zzz26250, bb, bc) 130.57/78.24 new_intersectFM_C2IntersectFM_C10(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, Zero, Zero, bb, bc) -> new_intersectFM_C2IntersectFM_C13(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, bb, bc) 130.57/78.24 new_intersectFM_C2IntersectFM_C13(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, bb, bc) -> new_intersectFM_C(new_intersectFM_C2Lts(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, bb), zzz2617, bb) 130.57/78.24 new_intersectFM_C2IntersectFM_C13(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, bb, bc) -> new_intersectFM_C(new_intersectFM_C2Gts(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, bb), zzz2618, bb) 130.57/78.24 new_intersectFM_C2IntersectFM_C10(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, Zero, Succ(zzz26250), bb, bc) -> new_intersectFM_C(new_intersectFM_C2Gts(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, bb), zzz2618, bb) 130.57/78.24 new_intersectFM_C2IntersectFM_C10(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, Succ(zzz26240), Zero, bb, bc) -> new_intersectFM_C2IntersectFM_C11(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2623, bb, bc) 130.57/78.24 new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, Branch(Neg(zzz209100), zzz20911, zzz20912, zzz20913, zzz20914), h, ba) -> new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz20914, h, ba) 130.57/78.24 new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, Branch(Pos(Zero), zzz20911, zzz20912, zzz20913, zzz20914), h, ba) -> new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz20914, h, ba) 130.57/78.24 new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, Branch(Pos(Succ(zzz2091000)), zzz20911, zzz20912, zzz20913, zzz20914), h, ba) -> new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2091000, zzz20911, zzz20912, zzz20913, zzz20914, zzz2083, zzz2091000, h, ba) 130.57/78.24 new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, Branch(Neg(zzz209100), zzz20911, zzz20912, zzz20913, zzz20914), zzz2092, Zero, Succ(zzz20940), h, ba) -> new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz20914, h, ba) 130.57/78.24 new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, EmptyFM, h, ba) -> new_intersectFM_C(new_intersectFM_C2Lts(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, h), zzz2086, h) 130.57/78.24 new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, EmptyFM, h, ba) -> new_intersectFM_C(new_intersectFM_C2Gts(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, h), zzz2087, h) 130.57/78.24 new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, Succ(zzz20930), Zero, h, ba) -> new_intersectFM_C2IntersectFM_C10(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, Succ(zzz2083), Succ(zzz2088), h, ba) 130.57/78.24 new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, EmptyFM, zzz2092, Zero, Succ(zzz20940), h, ba) -> new_intersectFM_C(new_intersectFM_C2Lts(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, h), zzz2086, h) 130.57/78.24 new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, Branch(Pos(Succ(zzz2091000)), zzz20911, zzz20912, zzz20913, zzz20914), zzz2092, Zero, Succ(zzz20940), h, ba) -> new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2091000, zzz20911, zzz20912, zzz20913, zzz20914, zzz2083, zzz2091000, h, ba) 130.57/78.24 new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, Branch(Pos(Zero), zzz20911, zzz20912, zzz20913, zzz20914), zzz2092, Zero, Succ(zzz20940), h, ba) -> new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz20914, h, ba) 130.57/78.24 new_intersectFM_C2IntersectFM_C10(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, Zero, Succ(zzz26250), bb, bc) -> new_intersectFM_C(new_intersectFM_C2Lts(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, bb), zzz2617, bb) 130.57/78.24 new_intersectFM_C2IntersectFM_C138(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, EmptyFM, eh, fa) -> new_intersectFM_C(new_intersectFM_C2Gts6(zzz884, zzz885, zzz886, zzz887, zzz888, eh), zzz892, eh) 130.57/78.24 new_intersectFM_C2IntersectFM_C138(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, Branch(zzz8960, zzz8961, zzz8962, zzz8963, zzz8964), eh, fa) -> new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz8960, zzz8961, zzz8962, zzz8963, zzz8964, eh, fa) 130.57/78.24 new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, Pos(zzz8930), zzz894, zzz895, EmptyFM, zzz897, eh, fa) -> new_intersectFM_C(new_intersectFM_C2Lts6(zzz884, zzz885, zzz886, zzz887, zzz888, eh), zzz891, eh) 130.57/78.24 new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, Pos(zzz8930), zzz894, zzz895, EmptyFM, zzz897, eh, fa) -> new_intersectFM_C(new_intersectFM_C2Gts6(zzz884, zzz885, zzz886, zzz887, zzz888, eh), zzz892, eh) 130.57/78.24 new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, Neg(Succ(zzz89300)), zzz894, zzz895, zzz896, zzz897, eh, fa) -> new_intersectFM_C2IntersectFM_C137(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz89300, zzz894, zzz895, zzz896, zzz897, zzz89300, zzz888, eh, fa) 130.57/78.24 new_intersectFM_C2IntersectFM_C137(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, Succ(zzz15910), Succ(zzz15920), fb, fc) -> new_intersectFM_C2IntersectFM_C137(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, zzz15910, zzz15920, fb, fc) 130.57/78.24 new_intersectFM_C2IntersectFM_C137(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, Zero, Succ(zzz15920), fb, fc) -> new_intersectFM_C2IntersectFM_C138(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1589, fb, fc) 130.57/78.24 new_intersectFM_C2IntersectFM_C137(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, Succ(zzz15910), Zero, fb, fc) -> new_intersectFM_C2IntersectFM_C139(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, Succ(zzz1586), Succ(zzz1581), fb, fc) 130.57/78.24 new_intersectFM_C2IntersectFM_C139(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, Succ(zzz28980), Succ(zzz28990), fd, ff) -> new_intersectFM_C2IntersectFM_C139(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, zzz28980, zzz28990, fd, ff) 130.57/78.24 new_intersectFM_C2IntersectFM_C139(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, Zero, Succ(zzz28990), fd, ff) -> new_intersectFM_C(new_intersectFM_C2Lts6(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, fd), zzz2891, fd) 130.57/78.24 new_intersectFM_C2IntersectFM_C139(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, Zero, Zero, fd, ff) -> new_intersectFM_C2IntersectFM_C141(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, fd, ff) 130.57/78.24 new_intersectFM_C2IntersectFM_C141(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, fd, ff) -> new_intersectFM_C(new_intersectFM_C2Gts6(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, fd), zzz2892, fd) 130.57/78.24 new_intersectFM_C2IntersectFM_C141(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, fd, ff) -> new_intersectFM_C(new_intersectFM_C2Lts6(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, fd), zzz2891, fd) 130.57/78.24 new_intersectFM_C2IntersectFM_C139(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, Zero, Succ(zzz28990), fd, ff) -> new_intersectFM_C(new_intersectFM_C2Gts6(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, fd), zzz2892, fd) 130.57/78.24 new_intersectFM_C2IntersectFM_C139(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, Succ(zzz28980), Zero, fd, ff) -> new_intersectFM_C2IntersectFM_C138(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2897, fd, ff) 130.57/78.24 new_intersectFM_C2IntersectFM_C137(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, Zero, Zero, fb, fc) -> new_intersectFM_C2IntersectFM_C140(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, fb, fc) 130.57/78.24 new_intersectFM_C2IntersectFM_C140(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, fb, fc) -> new_intersectFM_C2IntersectFM_C139(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, Succ(zzz1586), Succ(zzz1581), fb, fc) 130.57/78.24 new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, Pos(zzz8930), zzz894, zzz895, Branch(zzz8960, zzz8961, zzz8962, zzz8963, zzz8964), zzz897, eh, fa) -> new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz8960, zzz8961, zzz8962, zzz8963, zzz8964, eh, fa) 130.57/78.24 new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, Branch(Pos(zzz215600), zzz21561, zzz21562, zzz21563, zzz21564), zzz2157, Zero, Succ(zzz21590), ed, ee) -> new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz21563, ed, ee) 130.57/78.24 new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, Branch(Neg(Zero), zzz21561, zzz21562, zzz21563, zzz21564), ed, ee) -> new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz21563, ed, ee) 130.57/78.24 new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, EmptyFM, ed, ee) -> new_intersectFM_C(new_intersectFM_C2Gts5(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, ed), zzz2152, ed) 130.57/78.24 new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, EmptyFM, ed, ee) -> new_intersectFM_C(new_intersectFM_C2Lts5(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, ed), zzz2151, ed) 130.57/78.24 new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, Branch(Neg(Succ(zzz2156000)), zzz21561, zzz21562, zzz21563, zzz21564), ed, ee) -> new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2156000, zzz21561, zzz21562, zzz21563, zzz21564, zzz2156000, zzz2148, ed, ee) 130.57/78.24 new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, Succ(zzz21580), Zero, ed, ee) -> new_intersectFM_C2IntersectFM_C133(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, Succ(zzz2153), Succ(zzz2148), ed, ee) 130.57/78.24 new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, EmptyFM, zzz2157, Zero, Succ(zzz21590), ed, ee) -> new_intersectFM_C(new_intersectFM_C2Lts5(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, ed), zzz2151, ed) 130.57/78.24 new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, Branch(Neg(Zero), zzz21561, zzz21562, zzz21563, zzz21564), zzz2157, Zero, Succ(zzz21590), ed, ee) -> new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz21563, ed, ee) 130.57/78.24 new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, Branch(Pos(zzz215600), zzz21561, zzz21562, zzz21563, zzz21564), ed, ee) -> new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz21563, ed, ee) 130.57/78.24 new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, Neg(zzz27430), zzz2744, zzz2745, zzz2746, EmptyFM, be, bf) -> new_intersectFM_C(new_intersectFM_C2Lts0(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, be), zzz2741, be) 130.57/78.24 new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, Pos(Succ(zzz274300)), zzz2744, zzz2745, zzz2746, zzz2747, be, bf) -> new_intersectFM_C2IntersectFM_C114(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, zzz274300, zzz2744, zzz2745, zzz2746, zzz2747, zzz2738, zzz274300, be, bf) 130.57/78.24 new_intersectFM_C2IntersectFM_C114(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, Zero, Succ(zzz30830), bg, bh) -> new_intersectFM_C2IntersectFM_C115(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3080, bg, bh) 130.57/78.24 new_intersectFM_C2IntersectFM_C115(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, EmptyFM, be, bf) -> new_intersectFM_C(new_intersectFM_C2Gts0(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, be), zzz2742, be) 130.57/78.24 new_intersectFM_C2IntersectFM_C115(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, Branch(zzz27470, zzz27471, zzz27472, zzz27473, zzz27474), be, bf) -> new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, zzz27470, zzz27471, zzz27472, zzz27473, zzz27474, be, bf) 130.57/78.24 new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, Pos(Zero), zzz2744, zzz2745, zzz2746, zzz2747, be, bf) -> new_intersectFM_C2IntersectFM_C115(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, zzz2747, be, bf) 130.57/78.24 new_intersectFM_C2IntersectFM_C115(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, EmptyFM, be, bf) -> new_intersectFM_C(new_intersectFM_C2Lts0(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, be), zzz2741, be) 130.57/78.24 new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, Neg(zzz27430), zzz2744, zzz2745, zzz2746, Branch(zzz27470, zzz27471, zzz27472, zzz27473, zzz27474), be, bf) -> new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, zzz27470, zzz27471, zzz27472, zzz27473, zzz27474, be, bf) 130.57/78.24 new_intersectFM_C2IntersectFM_C114(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, Succ(zzz30820), Succ(zzz30830), bg, bh) -> new_intersectFM_C2IntersectFM_C114(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, zzz30820, zzz30830, bg, bh) 130.57/78.24 new_intersectFM_C2IntersectFM_C114(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, Zero, Zero, bg, bh) -> new_intersectFM_C2IntersectFM_C117(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, bg, bh) 130.57/78.24 new_intersectFM_C2IntersectFM_C117(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, bg, bh) -> new_intersectFM_C2IntersectFM_C116(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, Succ(zzz3072), Succ(zzz3077), bg, bh) 130.57/78.24 new_intersectFM_C2IntersectFM_C116(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, Succ(zzz35390), Succ(zzz35400), ca, cb) -> new_intersectFM_C2IntersectFM_C116(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, zzz35390, zzz35400, ca, cb) 130.57/78.24 new_intersectFM_C2IntersectFM_C116(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, Zero, Succ(zzz35400), ca, cb) -> new_intersectFM_C(new_intersectFM_C2Lts0(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, ca), zzz3532, ca) 130.57/78.24 new_intersectFM_C2IntersectFM_C116(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, Zero, Zero, ca, cb) -> new_intersectFM_C2IntersectFM_C118(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, ca, cb) 130.57/78.24 new_intersectFM_C2IntersectFM_C118(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, ca, cb) -> new_intersectFM_C(new_intersectFM_C2Lts0(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, ca), zzz3532, ca) 130.57/78.24 new_intersectFM_C2IntersectFM_C118(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, ca, cb) -> new_intersectFM_C(new_intersectFM_C2Gts0(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, ca), zzz3533, ca) 130.57/78.24 new_intersectFM_C2IntersectFM_C116(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, Zero, Succ(zzz35400), ca, cb) -> new_intersectFM_C(new_intersectFM_C2Gts0(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, ca), zzz3533, ca) 130.57/78.24 new_intersectFM_C2IntersectFM_C116(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, Succ(zzz35390), Zero, ca, cb) -> new_intersectFM_C2IntersectFM_C115(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3538, ca, cb) 130.57/78.24 new_intersectFM_C2IntersectFM_C114(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, Succ(zzz30820), Zero, bg, bh) -> new_intersectFM_C2IntersectFM_C116(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, Succ(zzz3072), Succ(zzz3077), bg, bh) 130.57/78.24 new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Pos(Zero), zzz1604, zzz1605, zzz1606, zzz1607, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Lts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1601, gc) 130.57/78.24 new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Neg(Succ(zzz160300)), zzz1604, zzz1605, zzz1606, zzz1607, gc, gd) -> new_intersectFM_C2IntersectFM_C144(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1607, gc, gd) 130.57/78.24 new_intersectFM_C2IntersectFM_C144(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, EmptyFM, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Lts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1601, gc) 130.57/78.24 new_intersectFM_C2IntersectFM_C144(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Branch(zzz16060, zzz16061, zzz16062, zzz16063, zzz16064), gc, gd) -> new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz16060, zzz16061, zzz16062, zzz16063, zzz16064, gc, gd) 130.57/78.24 new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Pos(Zero), zzz1604, zzz1605, zzz1606, zzz1607, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Gts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1602, gc) 130.57/78.24 new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Pos(Succ(zzz160300)), zzz1604, zzz1605, EmptyFM, zzz1607, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Lts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1601, gc) 130.57/78.24 new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Pos(Succ(zzz160300)), zzz1604, zzz1605, Branch(zzz16060, zzz16061, zzz16062, zzz16063, zzz16064), zzz1607, gc, gd) -> new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz16060, zzz16061, zzz16062, zzz16063, zzz16064, gc, gd) 130.57/78.24 new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Neg(Zero), zzz1604, zzz1605, zzz1606, zzz1607, gc, gd) -> new_intersectFM_C2IntersectFM_C145(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1604, gc, gd) 130.57/78.24 new_intersectFM_C2IntersectFM_C145(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1604, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Lts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1601, gc) 130.57/78.24 new_intersectFM_C2IntersectFM_C145(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1604, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Gts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1602, gc) 130.57/78.24 new_intersectFM_C2IntersectFM_C144(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, EmptyFM, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Gts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1602, gc) 130.57/78.24 new_intersectFM_C2IntersectFM_C133(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, Zero, Succ(zzz26430), ef, eg) -> new_intersectFM_C(new_intersectFM_C2Lts5(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, ef), zzz2635, ef) 130.57/78.24 new_intersectFM_C2IntersectFM_C133(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, Succ(zzz26420), Zero, ef, eg) -> new_intersectFM_C2IntersectFM_C134(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2641, ef, eg) 130.57/78.24 new_intersectFM_C2IntersectFM_C133(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, Zero, Zero, ef, eg) -> new_intersectFM_C2IntersectFM_C136(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, ef, eg) 130.57/78.24 new_intersectFM_C2IntersectFM_C136(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, ef, eg) -> new_intersectFM_C(new_intersectFM_C2Lts5(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, ef), zzz2635, ef) 130.57/78.24 new_intersectFM_C2IntersectFM_C136(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, ef, eg) -> new_intersectFM_C(new_intersectFM_C2Gts5(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, ef), zzz2636, ef) 130.57/78.24 130.57/78.24 The TRS R consists of the following rules: 130.57/78.24 130.57/78.24 new_mkBalBranch6MkBalBranch41(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64470), gf, gg) -> new_mkBalBranch6MkBalBranch42(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234, bd) -> new_mkBalBranch(zzz5230, zzz5231, new_mkVBalBranch8(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, bd), zzz5234, ty_Int, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Succ(zzz6476000), Zero, gf, gg) -> new_mkBalBranch6MkBalBranch114(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch148(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bd) 130.57/78.24 new_mkBalBranch6MkBalBranch314(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, zzz6461, gf, gg) -> new_mkBalBranch6MkBalBranch36(zzz474034, zzz474030, zzz474031, zzz6373, zzz6461, zzz645200, gf, gg) 130.57/78.24 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.24 new_mkVBalBranch3MkVBalBranch230(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bbf) -> new_mkVBalBranch3MkVBalBranch240(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bbf) 130.57/78.24 new_mkBalBranch6MkBalBranch415(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Succ(zzz644300)), Pos(zzz64420), gf, gg) -> new_mkBalBranch6MkBalBranch410(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, new_primMulNat(zzz64420), gf, gg) 130.57/78.24 new_splitGT18(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, Succ(zzz45010), Zero, bcf) -> new_splitGT19(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, bcf) 130.57/78.24 new_splitLT216(Pos(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_splitLT217(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.24 new_splitLT217(zzz830, zzz831, zzz832, zzz833, zzz834, fg) -> new_splitLT9(zzz833, fg) 130.57/78.24 new_splitLT211(zzz31, zzz32, zzz33, zzz34, bd) -> zzz33 130.57/78.24 new_mkVBalBranch3MkVBalBranch239(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, he) -> new_mkVBalBranch3MkVBalBranch232(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, he) 130.57/78.24 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.57/78.24 new_mkBalBranch6MkBalBranch43(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBalBranch6MkBalBranch40(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch310(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64620), gf, gg) -> new_mkBalBranch6MkBalBranch38(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch44(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64510), gf, gg) -> new_mkBalBranch6MkBalBranch45(zzz474034, zzz474030, zzz474031, zzz6373, zzz64510, Zero, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch130(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Zero, bce) -> new_mkVBalBranch3MkVBalBranch153(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, bce) 130.57/78.24 new_mkBalBranch6MkBalBranch34(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, Succ(zzz64560), gf, gg) -> new_mkBalBranch6MkBalBranch37(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, zzz64560, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch31(zzz474034, zzz474030, zzz474031, EmptyFM, gf, gg) -> error([]) 130.57/78.24 new_mkBalBranch6MkBalBranch30(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64590), gf, gg) -> new_mkBalBranch6MkBalBranch31(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch019(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch014(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch126(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), bcd) -> new_mkBalBranch(zzz6020, zzz6021, zzz6023, new_mkVBalBranch5(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), bcd), ty_Int, bcd) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(zzz300), zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), ty_Int, bd) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234, bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(zzz300), zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234), ty_Int, bd) 130.57/78.24 new_primPlusNat2(Zero) -> Zero 130.57/78.24 new_intersectFM_C2Gts6(zzz884, zzz885, zzz886, zzz887, zzz888, eh) -> new_splitGT219(zzz884, zzz885, zzz886, zzz887, zzz888, eh) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Succ(zzz426200)), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch133(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz4260, zzz4261, zzz426200, zzz4263, zzz4264, Succ(zzz3000), zzz31, new_primPlusNat0(new_primMulNat0(zzz426200), Succ(zzz426200)), bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch239(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), he) -> new_mkVBalBranch3MkVBalBranch222(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, he) 130.57/78.24 new_splitGT229(zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, bbh) -> new_splitGT13(zzz16124, zzz1613, bbh) 130.57/78.24 new_addToFM_C11(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, Succ(zzz43100), Succ(zzz43110), bae) -> new_addToFM_C11(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, zzz43100, zzz43110, bae) 130.57/78.24 new_splitLT41(zzz4000, bd) -> new_emptyFM(bd) 130.57/78.24 new_mkVBalBranch12(zzz6130, zzz6131, EmptyFM, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, bcb) -> new_addToFM2(zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, zzz6130, zzz6131, bcb) 130.57/78.24 new_splitGT12(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, Succ(zzz44340), Zero, bbb) -> new_splitGT17(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, bbb) 130.57/78.24 new_splitGT42(zzz4000, bd) -> new_emptyFM(bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch142(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, bbf) -> new_mkVBalBranch3MkVBalBranch139(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Zero, bbf) 130.57/78.24 new_intersectFM_C2Lts7(zzz830, zzz831, zzz832, zzz833, zzz834, fg) -> new_splitLT217(zzz830, zzz831, zzz832, zzz833, zzz834, fg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch136(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, he) -> new_mkVBalBranch3MkVBalBranch130(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Zero, he) 130.57/78.24 new_splitGT12(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, Zero, Zero, bbb) -> new_splitGT17(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, bbb) 130.57/78.24 new_mkBalBranch6MkBalBranch413(zzz474034, zzz474030, zzz474031, zzz6373, zzz6442, gf, gg) -> new_mkBalBranch6MkBalBranch415(zzz474034, zzz474030, zzz474031, zzz6373, new_mkBalBranch6Size_r(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg), zzz6442, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch015(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Neg(Zero), Pos(zzz64550), gf, gg) -> new_mkBalBranch6MkBalBranch0111(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, new_primMulNat8(zzz64550), gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch137(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bd) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch235(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bd) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch8(Zero, zzz31, zzz3530, zzz3531, Neg(Succ(zzz353200)), zzz3533, zzz3534, zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch143(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bac) -> new_mkVBalBranch3MkVBalBranch145(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bac) 130.57/78.24 new_mkVBalBranch3MkVBalBranch140(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, bbd) -> new_mkVBalBranch3MkVBalBranch126(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), bbd) 130.57/78.24 new_splitGT11(EmptyFM, dd) -> new_splitGT43(dd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch133(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), bd) -> new_mkVBalBranch3MkVBalBranch154(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch35(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Zero), Neg(zzz64530), gf, gg) -> new_mkBalBranch6MkBalBranch313(zzz474034, zzz474030, zzz474031, zzz6373, new_primMulNat(zzz64530), gf, gg) 130.57/78.24 new_splitLT15(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, Succ(zzz45100), Succ(zzz45110), ha) -> new_splitLT15(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, zzz45100, zzz45110, ha) 130.57/78.24 new_primMulNat(Succ(zzz633700)) -> new_primPlusNat0(new_primMulNat0(zzz633700), Succ(zzz633700)) 130.57/78.24 new_mkBalBranch6MkBalBranch117(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Succ(zzz64840), gf, gg) -> new_mkBalBranch6MkBalBranch118(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_splitGT217(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd) -> new_splitGT11(zzz1196, dd) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, zzz2502, zzz2503, zzz2504), EmptyFM, bd) -> new_addToFM3(Branch(zzz2500, zzz2501, zzz2502, zzz2503, zzz2504), zzz300, zzz31, bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch149(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, bcb) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(zzz6130), zzz6131, Branch(zzz6120, zzz6121, Pos(Succ(zzz6122)), zzz6123, zzz6124), Branch(zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129), ty_Int, bcb) 130.57/78.24 new_addToFM_C3(Branch(Neg(Zero), zzz9821, zzz9822, zzz9823, zzz9824), Zero, zzz31, bd) -> Branch(Neg(Zero), new_addToFM0(zzz9821, zzz31, bd), zzz9822, zzz9823, zzz9824) 130.57/78.24 new_mkVBalBranch3MkVBalBranch232(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, he) -> new_mkVBalBranch3MkVBalBranch136(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), he) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Zero), zzz31, Branch(zzz3530, zzz3531, Neg(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Int, bd) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch147(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bd) 130.57/78.24 new_splitGT224(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, bbg) -> new_splitGT18(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Succ(zzz3494), Succ(zzz3499), bbg) 130.57/78.24 new_addToFM_C25(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, hh) -> new_addToFM_C11(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Succ(zzz3186), Succ(zzz3181), hh) 130.57/78.24 new_mkBalBranch6MkBalBranch49(zzz474034, zzz474030, zzz474031, zzz6373, Zero, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch43(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch48(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, zzz6444, gf, gg) -> new_mkBalBranch6MkBalBranch45(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, zzz6444, gf, gg) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(zzz300), zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Int, bd) 130.57/78.24 new_primPlusInt2(Pos(zzz63770), zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_primPlusInt0(zzz63770, new_sizeFM(zzz474034, gf, gg)) 130.57/78.24 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.57/78.24 new_mkBalBranch6MkBalBranch011(zzz4740340, zzz4740341, zzz4740342, Branch(zzz47403430, zzz47403431, zzz47403432, zzz47403433, zzz47403434), zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), zzz47403430, zzz47403431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), zzz474030, zzz474031, zzz6373, zzz47403433, gf, gg), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4740340, zzz4740341, zzz47403434, zzz4740344, gf, gg), gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch224(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), hf) -> new_mkBalBranch(zzz3880, zzz3881, new_mkVBalBranch5(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, hf), zzz3884, ty_Int, hf) 130.57/78.24 new_mkVBalBranch7(zzz31, EmptyFM, zzz34, bd) -> new_addToFM(zzz34, zzz31, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch017(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBranch(Succ(Succ(Zero)), zzz4740340, zzz4740341, new_mkBranch(Succ(Succ(Succ(Zero))), zzz474030, zzz474031, zzz6373, zzz4740343, gf, gg), zzz4740344, gf, gg) 130.57/78.24 new_splitGT215(zzz31, zzz32, zzz33, zzz34, bd) -> zzz34 130.57/78.24 new_mkVBalBranch3MkVBalBranch143(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bac) -> new_mkVBalBranch3MkVBalBranch145(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bac) 130.57/78.24 new_mkVBalBranch3MkVBalBranch146(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bd) 130.57/78.24 new_mkBalBranch6MkBalBranch37(zzz474034, zzz474030, zzz474031, zzz6373, Zero, Succ(zzz645600), gf, gg) -> new_mkBalBranch6MkBalBranch38(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Succ(Succ(Zero))), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch230(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz4260, zzz4261, Succ(Zero), zzz4263, zzz4264, Succ(zzz3000), zzz31, Zero, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch133(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, bd) -> new_mkVBalBranch3MkVBalBranch154(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch016(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Succ(zzz6454000), Succ(zzz647200), gf, gg) -> new_mkBalBranch6MkBalBranch016(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, zzz6454000, zzz647200, gf, gg) 130.57/78.24 new_splitLT42(zzz4000, bd) -> new_emptyFM(bd) 130.57/78.24 new_mkVBalBranch11(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, bd) -> new_mkVBalBranch30(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, bd) 130.57/78.24 new_primPlusInt2(Neg(zzz63770), zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_primPlusInt1(zzz63770, new_sizeFM(zzz474034, gf, gg)) 130.57/78.24 new_mkVBalBranch3MkVBalBranch227(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bac) -> new_mkVBalBranch3MkVBalBranch228(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bac) 130.57/78.24 new_splitLT12(EmptyFM, zzz1975, gh) -> new_splitLT42(zzz1975, gh) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch133(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), bd) 130.57/78.24 new_mkBalBranch6MkBalBranch38(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBalBranch6MkBalBranch39(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_splitLT13(Branch(Pos(zzz74500), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, df) -> new_splitLT214(zzz74500, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, df) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Pos(Zero), Pos(zzz64770), gf, gg) -> new_mkBalBranch6MkBalBranch1112(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, new_primMulNat8(zzz64770), gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch228(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bac) -> new_mkVBalBranch3MkVBalBranch143(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primMulNat3(zzz5096), bac) 130.57/78.24 new_addToFM_C23(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Succ(zzz33930), Zero, bca) -> new_addToFM_C26(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, bca) 130.57/78.24 new_primPlusInt0(zzz58960, Neg(zzz59000)) -> new_primMinusNat0(zzz58960, zzz59000) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch137(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat6, bd) 130.57/78.24 new_intersectFM_C2Lts5(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, ed) -> new_splitLT13(Branch(Neg(Succ(zzz2143)), zzz2144, zzz2145, zzz2146, zzz2147), zzz2148, ed) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Succ(Succ(zzz3532000))), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch230(zzz3530, zzz3531, zzz3532000, zzz3533, zzz3534, zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, Zero, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz3532000), Succ(zzz3532000))), Succ(zzz3532000))), Succ(zzz3532000)), zzz3532000))), bd) 130.57/78.24 new_splitLT214(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df) -> new_splitLT13(zzz745, zzz747, df) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, bd) -> new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch10(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, bd), ty_Int, bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch150(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), bcc) -> new_mkVBalBranch3MkVBalBranch130(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), bcc) 130.57/78.24 new_intersectFM_C2Lts6(zzz884, zzz885, zzz886, zzz887, zzz888, eh) -> new_splitLT13(Branch(Neg(Zero), zzz884, zzz885, zzz886, zzz887), zzz888, eh) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_primMinusNat0(Succ(zzz482800), Zero) -> Pos(Succ(zzz482800)) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Zero), zzz31, Branch(zzz3530, zzz3531, Pos(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Int, bd) 130.57/78.24 new_splitLT29(Neg(zzz19700), zzz1971, zzz1972, Branch(zzz19730, zzz19731, zzz19732, zzz19733, zzz19734), Branch(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744), zzz1975, gh) -> new_mkVBalBranch8(zzz19700, zzz1971, zzz19730, zzz19731, zzz19732, zzz19733, zzz19734, new_splitLT31(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744, zzz1975, gh), gh) 130.57/78.24 new_mkBalBranch6MkBalBranch37(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz6452000), Zero, gf, gg) -> new_mkBalBranch6MkBalBranch31(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_primMulNat8(Zero) -> Zero 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch148(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat7, bd) 130.57/78.24 new_splitGT8(zzz4000, bd) -> new_splitGT41(zzz4000, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch311(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64580), gf, gg) -> new_mkBalBranch6MkBalBranch36(zzz474034, zzz474030, zzz474031, zzz6373, Zero, zzz64580, gf, gg) 130.57/78.24 new_splitGT222(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Succ(zzz35000), Zero, bbg) -> new_splitGT16(zzz3498, zzz3499, bbg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch225(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, hf) -> new_mkVBalBranch3MkVBalBranch236(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, hf) 130.57/78.24 new_mkBalBranch6MkBalBranch49(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz6443000), Succ(zzz644400), gf, gg) -> new_mkBalBranch6MkBalBranch49(zzz474034, zzz474030, zzz474031, zzz6373, zzz6443000, zzz644400, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch230(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bbf) -> new_mkVBalBranch3MkVBalBranch230(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bbf) 130.57/78.24 new_mkBalBranch6MkBalBranch1115(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Succ(zzz64850), gf, gg) -> new_mkBalBranch6MkBalBranch112(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz64850, Zero, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch1111(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, zzz6478, gf, gg) -> new_mkBalBranch6MkBalBranch112(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, zzz6478, gf, gg) 130.57/78.24 new_splitLT9(Branch(zzz8330, zzz8331, zzz8332, zzz8333, zzz8334), fg) -> new_splitLT216(zzz8330, zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.24 new_splitLT216(Neg(Zero), zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_splitLT222(zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(zzz300), zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Int, bd) 130.57/78.24 new_splitGT30(Neg(Zero), zzz7451, zzz7452, zzz7453, zzz7454, zzz747, df) -> new_splitGT219(zzz7451, zzz7452, zzz7453, zzz7454, zzz747, df) 130.57/78.24 new_splitGT17(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, bbb) -> zzz4432 130.57/78.24 new_addToFM_C11(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, Succ(zzz43100), Zero, bae) -> new_mkBalBranch(Pos(Succ(zzz4303)), zzz4304, zzz4306, new_addToFM_C4(zzz4307, Succ(zzz4308), zzz4309, bae), ty_Int, bae) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, EmptyFM, zzz426, bd) -> new_addToFM1(zzz426, zzz3000, zzz31, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch313(zzz474034, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch32(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBranch(zzz6231, zzz6232, zzz6233, zzz6234, zzz6235, hb, hc) -> Branch(zzz6232, zzz6233, new_primPlusInt(new_primPlusInt0(Succ(Zero), new_sizeFM(zzz6234, hb, hc)), zzz6234, zzz6235, zzz6232, hb, hc), zzz6234, zzz6235) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Neg(Zero), Neg(zzz64770), gf, gg) -> new_mkBalBranch6MkBalBranch1115(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, new_primMulNat8(zzz64770), gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch152(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, bcd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(zzz6030), zzz6031, Branch(zzz6020, zzz6021, Pos(Succ(zzz6022)), zzz6023, zzz6024), Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ty_Int, bcd) 130.57/78.24 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.57/78.24 new_splitGT216(zzz31, zzz32, zzz33, zzz34, bd) -> zzz34 130.57/78.24 new_mkVBalBranch3MkVBalBranch146(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bd) 130.57/78.24 new_splitGT13(EmptyFM, zzz1613, bbh) -> new_splitGT42(zzz1613, bbh) 130.57/78.24 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.57/78.24 new_mkVBalBranch3MkVBalBranch231(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bbc) -> new_mkVBalBranch3MkVBalBranch242(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bbc) 130.57/78.24 new_mkVBalBranch3MkVBalBranch144(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch135(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(zzz300), zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234), ty_Int, bd) 130.57/78.24 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.57/78.24 new_addToFM2(zzz330, zzz331, zzz332, zzz333, zzz334, zzz300, zzz31, bd) -> new_addToFM_C3(Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz300, zzz31, bd) 130.57/78.24 new_splitGT225(Neg(zzz161200), zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, bbh) -> new_splitGT13(zzz16124, zzz1613, bbh) 130.57/78.24 new_mkVBalBranch3MkVBalBranch226(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, bab) -> new_mkVBalBranch3MkVBalBranch131(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primMulNat3(zzz5000), bab) 130.57/78.24 new_mkVBalBranch3MkVBalBranch130(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Zero, bce) -> new_mkVBalBranch3MkVBalBranch153(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, bce) 130.57/78.24 new_intersectFM_C2Lts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc) -> new_splitLT9(Branch(Neg(Succ(zzz1594)), zzz1595, zzz1596, zzz1597, zzz1598), gc) 130.57/78.24 new_mkBalBranch6MkBalBranch40(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBalBranch6MkBalBranch35(zzz474034, zzz474030, zzz474031, zzz6373, new_mkBalBranch6Size_l(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg), new_mkBalBranch6Size_r(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg), gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch5(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Zero), gf, gg) -> new_mkBalBranch6MkBalBranch51(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_splitLT216(Neg(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_splitLT221(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.24 new_splitGT18(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, Succ(zzz45010), Succ(zzz45020), bcf) -> new_splitGT18(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, zzz45010, zzz45020, bcf) 130.57/78.24 new_sizeFM(EmptyFM, bah, bba) -> Pos(Zero) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_splitLT5(bd) -> new_splitLT40(bd) 130.57/78.24 new_mkVBalBranch8(zzz300, zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, Branch(zzz5230, zzz5231, zzz5232, zzz5233, zzz5234), bd) -> new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, zzz5230, zzz5231, zzz5232, zzz5233, zzz5234, bd) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Succ(Succ(Succ(zzz42620000)))), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch230(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz4260, zzz4261, Succ(Succ(zzz42620000)), zzz4263, zzz4264, Succ(zzz3000), zzz31, Succ(zzz42620000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), bd) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch135(zzz3530, zzz3531, zzz3533, zzz3534, zzz340, zzz341, zzz34200, zzz343, zzz344, Zero, zzz31, new_primMulNat3(zzz34200), bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch237(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, bcc) -> new_mkVBalBranch3MkVBalBranch241(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, bcc) 130.57/78.24 new_splitLT7(zzz31, zzz32, zzz34, zzz4000, bd) -> new_splitLT16(zzz4000, bd) 130.57/78.24 new_addToFM_C13(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, Succ(zzz45450), Succ(zzz45460), bag) -> new_addToFM_C13(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, zzz45450, zzz45460, bag) 130.57/78.24 new_primPlusInt1(zzz58960, Neg(zzz59010)) -> Neg(new_primPlusNat0(zzz58960, zzz59010)) 130.57/78.24 new_mkVBalBranch3MkVBalBranch242(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bbc) -> new_mkVBalBranch3MkVBalBranch138(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primMulNat3(zzz5253), bbc) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkBalBranch(zzz2500, zzz2501, zzz2503, new_mkVBalBranch5(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd), ty_Int, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch49(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz6443000), Zero, gf, gg) -> new_mkBalBranch6MkBalBranch42(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch018(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Succ(zzz64640), gf, gg) -> new_mkBalBranch6MkBalBranch0110(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Zero, zzz64640, gf, gg) 130.57/78.24 new_splitLT17(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, Zero, Succ(zzz41850), baf) -> new_splitLT18(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, baf) 130.57/78.24 new_mkBalBranch6MkBalBranch015(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Neg(Succ(zzz645400)), Neg(zzz64550), gf, gg) -> new_mkBalBranch6MkBalBranch0110(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, new_primMulNat8(zzz64550), zzz645400, gf, gg) 130.57/78.24 new_splitGT218(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, bad) -> new_splitGT12(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Succ(zzz3401), Succ(zzz3396), bad) 130.57/78.24 new_splitGT230(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_splitGT15(zzz8334, fg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch139(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), bbe) -> new_mkVBalBranch3MkVBalBranch139(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, bbe) 130.57/78.24 new_mkBalBranch6MkBalBranch412(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64500), gf, gg) -> new_mkBalBranch6MkBalBranch411(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch311(zzz474034, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch32(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch32(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBalBranch6MkBalBranch39(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Succ(Succ(Zero))), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch231(zzz330, zzz331, zzz333, zzz334, zzz4260, zzz4261, Succ(Zero), zzz4263, zzz4264, Succ(zzz3000), zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch151(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), hf) -> new_mkVBalBranch3MkVBalBranch126(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), hf) 130.57/78.24 new_splitGT220(zzz830, zzz831, zzz832, zzz833, zzz834, fg) -> new_mkVBalBranch5(Succ(zzz830), zzz831, new_splitGT15(zzz833, fg), zzz834, fg) 130.57/78.24 new_splitGT30(Neg(Succ(zzz745000)), zzz7451, zzz7452, zzz7453, zzz7454, zzz747, df) -> new_splitGT222(zzz745000, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, zzz745000, zzz747, df) 130.57/78.24 new_addToFM_C3(Branch(Neg(Succ(zzz982000)), zzz9821, zzz9822, zzz9823, zzz9824), Succ(zzz3000), zzz31, bd) -> new_addToFM_C23(zzz982000, zzz9821, zzz9822, zzz9823, zzz9824, zzz3000, zzz31, zzz982000, zzz3000, bd) 130.57/78.24 new_primMinusNat0(Succ(zzz482800), Succ(zzz47700)) -> new_primMinusNat0(zzz482800, zzz47700) 130.57/78.24 new_intersectFM_C2Lts4(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df) -> new_splitLT214(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df) 130.57/78.24 new_mkVBalBranch3MkVBalBranch139(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), bbe) -> new_mkBalBranch(zzz6294, zzz6295, zzz6297, new_mkVBalBranch11(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, bbe), ty_Int, bbe) 130.57/78.24 new_mkVBalBranch3MkVBalBranch154(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, bd) -> new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch11(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, bd), ty_Int, bd) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) -> new_mkBalBranch(zzz2500, zzz2501, zzz2503, new_mkVBalBranch5(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd), ty_Int, bd) 130.57/78.24 new_addToFM_C4(Branch(Pos(Zero), zzz341, zzz342, zzz343, zzz344), Succ(zzz3000), zzz31, bd) -> new_mkBalBranch(Pos(Zero), zzz341, zzz343, new_addToFM_C4(zzz344, Succ(zzz3000), zzz31, bd), ty_Int, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch37(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz6452000), Succ(zzz645600), gf, gg) -> new_mkBalBranch6MkBalBranch37(zzz474034, zzz474030, zzz474031, zzz6373, zzz6452000, zzz645600, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch147(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch125(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bd) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Succ(Zero)), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch231(zzz3530, zzz3531, zzz3533, zzz3534, zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, Zero, zzz31, Succ(zzz3420000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), bd) 130.57/78.24 new_addToFM_C23(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Zero, Succ(zzz33940), bca) -> new_mkBalBranch(Neg(Succ(zzz3386)), zzz3387, new_addToFM_C3(zzz3389, Succ(zzz3391), zzz3392, bca), zzz3390, ty_Int, bca) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch238(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), bd) 130.57/78.24 new_mkBalBranch6MkBalBranch35(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Zero), Pos(zzz64530), gf, gg) -> new_mkBalBranch6MkBalBranch311(zzz474034, zzz474030, zzz474031, zzz6373, new_primMulNat(zzz64530), gf, gg) 130.57/78.24 new_addToFM0(zzz341, zzz31, bd) -> zzz31 130.57/78.24 new_splitLT220(zzz618, zzz619, zzz620, zzz621, zzz622, db) -> new_splitLT19(zzz621, db) 130.57/78.24 new_mkBalBranch6MkBalBranch015(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Neg(Succ(zzz645400)), Pos(zzz64550), gf, gg) -> new_mkBalBranch6MkBalBranch017(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.57/78.24 new_mkVBalBranch3MkVBalBranch150(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, bcc) -> new_mkVBalBranch3MkVBalBranch130(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Zero, bcc) 130.57/78.24 new_mkVBalBranch12(zzz6130, zzz6131, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, bcb) -> new_mkVBalBranch30(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bcb) 130.57/78.24 new_splitLT218(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Succ(zzz35090), Succ(zzz35100), hg) -> new_splitLT218(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, zzz35090, zzz35100, hg) 130.57/78.24 new_mkBalBranch6MkBalBranch45(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch42(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_splitLT13(Branch(Neg(Succ(zzz745000)), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, df) -> new_splitLT218(zzz745000, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, zzz745000, zzz747, df) 130.57/78.24 new_mkVBalBranch3MkVBalBranch132(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, bd) -> new_mkVBalBranch3MkVBalBranch145(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), bd) 130.57/78.24 new_addToFM_C13(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, Succ(zzz45450), Zero, bag) -> new_mkBalBranch(Neg(Succ(zzz4538)), zzz4539, zzz4541, new_addToFM_C3(zzz4542, Succ(zzz4543), zzz4544, bag), ty_Int, bag) 130.57/78.24 new_splitLT216(Pos(Zero), zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_splitLT219(zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.24 new_splitGT16(Branch(zzz7450, zzz7451, zzz7452, zzz7453, zzz7454), zzz747, df) -> new_splitGT30(zzz7450, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, df) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) -> new_mkBalBranch(zzz3530, zzz3531, zzz3533, new_mkVBalBranch7(zzz31, zzz3534, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd), ty_Int, bd) 130.57/78.24 new_splitGT14(zzz618, zzz619, zzz620, zzz621, zzz622, db) -> new_splitGT228(zzz618, zzz619, zzz620, zzz621, zzz622, db) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Succ(Succ(zzz3532000))), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch229(zzz3530, zzz3531, zzz3532000, zzz3533, zzz3534, zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, Zero, zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz3532000), Succ(zzz3532000))), Succ(zzz3532000))), Succ(zzz3532000)), zzz3532000))), zzz342000, bd) 130.57/78.24 new_splitLT212(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Succ(zzz31390), Succ(zzz31400), ge) -> new_splitLT212(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, zzz31390, zzz31400, ge) 130.57/78.24 new_splitGT222(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Zero, Succ(zzz35010), bbg) -> new_splitGT224(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, bbg) 130.57/78.24 new_mkBalBranch6MkBalBranch39(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBranch(Succ(Zero), zzz474030, zzz474031, zzz6373, zzz474034, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch139(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Zero, bbe) -> new_mkVBalBranch3MkVBalBranch141(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, bbe) 130.57/78.24 new_mkVBalBranch3MkVBalBranch230(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bbf) -> new_mkVBalBranch3MkVBalBranch240(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bbf) 130.57/78.24 new_splitGT11(Branch(Pos(Zero), zzz11961, zzz11962, zzz11963, zzz11964), dd) -> new_splitGT213(zzz11961, zzz11962, zzz11963, zzz11964, dd) 130.57/78.24 new_addToFM_C3(Branch(Pos(zzz98200), zzz9821, zzz9822, zzz9823, zzz9824), Succ(zzz3000), zzz31, bd) -> new_mkBalBranch(Pos(zzz98200), zzz9821, new_addToFM_C3(zzz9823, Succ(zzz3000), zzz31, bd), zzz9824, ty_Int, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch416(zzz474034, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch43(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_splitGT7(bd) -> new_splitGT43(bd) 130.57/78.24 new_intersectFM_C2Lts2(zzz618, zzz619, zzz620, zzz621, zzz622, db) -> new_splitLT220(zzz618, zzz619, zzz620, zzz621, zzz622, db) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), bd) -> new_mkBalBranch(zzz4260, zzz4261, new_mkVBalBranch8(Succ(zzz3000), zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz4263, bd), zzz4264, ty_Int, bd) 130.57/78.24 new_splitLT29(Pos(Zero), zzz1971, zzz1972, zzz1973, zzz1974, zzz1975, gh) -> new_mkVBalBranch5(Zero, zzz1971, zzz1973, new_splitLT12(zzz1974, zzz1975, gh), gh) 130.57/78.24 new_primMulNat(Zero) -> Zero 130.57/78.24 new_splitLT219(zzz31, zzz32, zzz33, zzz34, bd) -> zzz33 130.57/78.24 new_mkBalBranch6MkBalBranch015(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Pos(Succ(zzz645400)), Pos(zzz64550), gf, gg) -> new_mkBalBranch6MkBalBranch013(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, zzz645400, new_primMulNat8(zzz64550), gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch019(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Succ(zzz64660), gf, gg) -> new_mkBalBranch6MkBalBranch010(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_splitGT223(Pos(Zero), zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_splitGT215(zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.24 new_primPlusInt(Neg(zzz62420), zzz6234, zzz6235, zzz6232, hb, hc) -> new_primPlusInt1(zzz62420, new_sizeFM(zzz6235, hb, hc)) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Succ(zzz426200)), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch135(zzz330, zzz331, zzz333, zzz334, zzz4260, zzz4261, zzz426200, zzz4263, zzz4264, Succ(zzz3000), zzz31, new_primMulNat3(zzz426200), bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch239(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, he) -> new_mkVBalBranch3MkVBalBranch232(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, he) 130.57/78.24 new_mkVBalBranch3MkVBalBranch141(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, bbe) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(zzz6304), zzz6305, Branch(zzz6294, zzz6295, Neg(Succ(zzz6296)), zzz6297, zzz6298), Branch(zzz6299, zzz6300, Neg(Succ(zzz6301)), zzz6302, zzz6303), ty_Int, bbe) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Succ(zzz426200)), zzz4263, zzz4264), bd) -> new_mkBalBranch(zzz4260, zzz4261, new_mkVBalBranch8(Succ(zzz3000), zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz4263, bd), zzz4264, ty_Int, bd) 130.57/78.24 new_addToFM_C4(Branch(Pos(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), Succ(zzz3000), zzz31, bd) -> new_addToFM_C24(zzz34000, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, zzz3000, zzz34000, bd) 130.57/78.24 new_splitLT29(Pos(Succ(zzz197000)), zzz1971, zzz1972, zzz1973, zzz1974, zzz1975, gh) -> new_splitLT212(zzz197000, zzz1971, zzz1972, zzz1973, zzz1974, zzz1975, zzz1975, zzz197000, gh) 130.57/78.24 new_addToFM_C4(Branch(Neg(Zero), zzz341, zzz342, zzz343, zzz344), Zero, zzz31, bd) -> Branch(Pos(Zero), new_addToFM0(zzz341, zzz31, bd), zzz342, zzz343, zzz344) 130.57/78.24 new_splitLT218(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Zero, Succ(zzz35100), hg) -> new_splitLT13(zzz3506, zzz3508, hg) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_intersectFM_C2Lts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd) -> new_splitLT19(Branch(Neg(Succ(zzz1192)), zzz1193, zzz1194, zzz1195, zzz1196), dd) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch8(Zero, zzz31, zzz3530, zzz3531, Neg(Zero), zzz3533, zzz3534, zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_splitGT11(Branch(Neg(Zero), zzz11961, zzz11962, zzz11963, zzz11964), dd) -> new_splitGT214(zzz11961, zzz11962, zzz11963, zzz11964, dd) 130.57/78.24 new_mkBalBranch6MkBalBranch1113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch111(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch129(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), baa) -> new_mkVBalBranch3MkVBalBranch130(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), baa) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Succ(zzz3000)), zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), ty_Int, bd) 130.57/78.24 new_splitGT227(zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, bbh) -> new_splitGT229(zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, bbh) 130.57/78.24 new_splitGT15(Branch(zzz8330, zzz8331, zzz8332, zzz8333, zzz8334), fg) -> new_splitGT223(zzz8330, zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.24 new_mkBalBranch6MkBalBranch110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, EmptyFM, gf, gg) -> error([]) 130.57/78.24 new_primPlusInt(Pos(zzz62420), zzz6234, zzz6235, zzz6232, hb, hc) -> new_primPlusInt0(zzz62420, new_sizeFM(zzz6235, hb, hc)) 130.57/78.24 new_mkVBalBranch3MkVBalBranch126(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Zero, bcd) -> new_mkVBalBranch3MkVBalBranch152(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, bcd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch227(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bac) -> new_mkVBalBranch3MkVBalBranch227(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bac) 130.57/78.24 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.24 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.24 new_splitLT18(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, baf) -> zzz4181 130.57/78.24 new_mkVBalBranch3MkVBalBranch132(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), bd) -> new_mkVBalBranch3MkVBalBranch145(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), bd) 130.57/78.24 new_mkBalBranch6MkBalBranch42(Branch(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344), zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBalBranch6MkBalBranch015(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, new_sizeFM(zzz4740343, gf, gg), new_sizeFM(zzz4740344, gf, gg), gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch235(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, bbd) -> new_mkVBalBranch3MkVBalBranch234(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, bbd) 130.57/78.24 new_mkBalBranch6MkBalBranch35(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Zero), Pos(zzz64530), gf, gg) -> new_mkBalBranch6MkBalBranch310(zzz474034, zzz474030, zzz474031, zzz6373, new_primMulNat(zzz64530), gf, gg) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch221(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bd) 130.57/78.24 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.57/78.24 new_splitLT212(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Zero, Zero, ge) -> new_splitLT213(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, ge) 130.57/78.24 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.24 new_mkBalBranch6MkBalBranch315(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, zzz6457, gf, gg) -> new_mkBalBranch6MkBalBranch31(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch010(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBalBranch6MkBalBranch011(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch223(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, hf) -> new_mkVBalBranch3MkVBalBranch225(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, hf) 130.57/78.24 new_addToFM_C3(Branch(Pos(Succ(zzz982000)), zzz9821, zzz9822, zzz9823, zzz9824), Zero, zzz31, bd) -> new_mkBalBranch(Pos(Succ(zzz982000)), zzz9821, new_addToFM_C3(zzz9823, Zero, zzz31, bd), zzz9824, ty_Int, bd) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch135(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), bd) 130.57/78.24 new_mkBalBranch6MkBalBranch35(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Succ(zzz645200)), Pos(zzz64530), gf, gg) -> new_mkBalBranch6MkBalBranch33(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, new_primMulNat(zzz64530), gf, gg) 130.57/78.24 new_addToFM_C11(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, Zero, Zero, bae) -> new_addToFM_C12(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, bae) 130.57/78.24 new_mkVBalBranch3MkVBalBranch229(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), bab) -> new_mkVBalBranch3MkVBalBranch229(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, bab) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Succ(Zero)), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch132(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz4260, zzz4261, zzz4263, zzz4264, Succ(zzz3000), zzz31, new_primMulNat3(Zero), bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch130(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bce) -> new_mkVBalBranch3MkVBalBranch130(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bce) 130.57/78.24 new_mkBalBranch6MkBalBranch46(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, zzz6449, gf, gg) -> new_mkBalBranch6MkBalBranch47(zzz474034, zzz474030, zzz474031, zzz6373, zzz6449, zzz644300, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch313(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64630), gf, gg) -> new_mkBalBranch6MkBalBranch34(zzz474034, zzz474030, zzz474031, zzz6373, zzz64630, Zero, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch153(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, bce) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(zzz6333), zzz6334, Branch(zzz6323, zzz6324, Neg(Succ(zzz6325)), zzz6326, zzz6327), Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), ty_Int, bce) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Succ(Zero)), zzz4263, zzz4264), bd) -> new_mkBalBranch(zzz4260, zzz4261, new_mkVBalBranch8(Succ(zzz3000), zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz4263, bd), zzz4264, ty_Int, bd) 130.57/78.24 new_splitGT40(bd) -> new_emptyFM(bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch238(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz41140), zzz4455, he) -> new_mkVBalBranch3MkVBalBranch239(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz41140, zzz4455, he) 130.57/78.24 new_mkVBalBranch3MkVBalBranch151(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, hf) -> new_mkVBalBranch3MkVBalBranch126(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), hf) 130.57/78.24 new_mkBalBranch6MkBalBranch5(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Succ(Zero)), gf, gg) -> new_mkBalBranch6MkBalBranch51(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch132(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(Zero), bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch231(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bbc) -> new_mkBalBranch(zzz5251, zzz5252, new_mkVBalBranch8(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bbc), zzz5255, ty_Int, bbc) 130.57/78.24 new_primPlusInt0(zzz58960, Pos(zzz59000)) -> Pos(new_primPlusNat0(zzz58960, zzz59000)) 130.57/78.24 new_splitLT215(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, hg) -> new_splitLT15(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Succ(zzz3503), Succ(zzz3508), hg) 130.57/78.24 new_splitGT18(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, Zero, Zero, bcf) -> new_splitGT19(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, bcf) 130.57/78.24 new_mkVBalBranch3MkVBalBranch237(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, bcc) -> new_mkVBalBranch3MkVBalBranch241(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, bcc) 130.57/78.24 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.57/78.24 new_addToFM_C24(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Zero, Succ(zzz31890), hh) -> new_mkBalBranch(Pos(Succ(zzz3181)), zzz3182, new_addToFM_C4(zzz3184, Succ(zzz3186), zzz3187, hh), zzz3185, ty_Int, hh) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch8(Zero, zzz31, zzz3530, zzz3531, Neg(Succ(zzz353200)), zzz3533, zzz3534, zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch1115(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch111(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch36(zzz474034, zzz474030, zzz474031, zzz6373, Zero, zzz645200, gf, gg) -> new_mkBalBranch6MkBalBranch38(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch221(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, hd) -> new_mkBalBranch(zzz3893, zzz3894, new_mkVBalBranch5(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, hd), zzz3897, ty_Int, hd) 130.57/78.24 new_mkVBalBranch8(zzz300, zzz31, zzz330, zzz331, zzz332, zzz333, zzz334, EmptyFM, bd) -> new_addToFM2(zzz330, zzz331, zzz332, zzz333, zzz334, zzz300, zzz31, bd) 130.57/78.24 new_splitLT218(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Succ(zzz35090), Zero, hg) -> new_splitLT215(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, hg) 130.57/78.24 new_intersectFM_C2Lts(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, h) -> new_splitLT12(Branch(Pos(Succ(zzz2078)), zzz2079, zzz2080, zzz2081, zzz2082), zzz2083, h) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch227(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz5232000, bd) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, EmptyFM, zzz34, bd) -> new_addToFM3(zzz34, zzz300, zzz31, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch50(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBalBranch6MkBalBranch413(zzz474034, zzz474030, zzz474031, zzz6373, new_mkBalBranch6Size_l(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg), gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch131(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), bab) -> new_mkVBalBranch3MkVBalBranch145(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), bab) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch231(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), bd) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkBalBranch(zzz2500, zzz2501, zzz2503, new_mkVBalBranch5(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd), ty_Int, bd) 130.57/78.24 new_splitLT40(bd) -> new_emptyFM(bd) 130.57/78.24 new_mkBalBranch6MkBalBranch5(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Succ(Succ(Zero))), gf, gg) -> new_mkBalBranch6MkBalBranch50(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch015(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Neg(Zero), Neg(zzz64550), gf, gg) -> new_mkBalBranch6MkBalBranch012(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, new_primMulNat8(zzz64550), gf, gg) 130.57/78.24 new_splitLT29(Neg(zzz19700), zzz1971, zzz1972, EmptyFM, zzz1974, zzz1975, gh) -> new_addToFM_C3(new_splitLT12(zzz1974, zzz1975, gh), zzz19700, zzz1971, gh) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Zero), zzz4263, zzz4264), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Succ(zzz3000)), zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Zero), zzz4263, zzz4264), ty_Int, bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch148(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bd) 130.57/78.24 new_splitLT15(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, Zero, Succ(zzz45110), ha) -> new_splitLT14(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, ha) 130.57/78.24 new_emptyFM(bd) -> EmptyFM 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch134(zzz3530, zzz3531, zzz3533, zzz3534, zzz340, zzz341, zzz34200, zzz343, zzz344, Zero, zzz31, new_primMulNat3(zzz34200), bd) 130.57/78.24 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch8(Zero, zzz31, zzz3530, zzz3531, Neg(Succ(zzz353200)), zzz3533, zzz3534, zzz343, bd), zzz344, ty_Int, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Neg(Succ(zzz647600)), Pos(zzz64770), gf, gg) -> new_mkBalBranch6MkBalBranch1114(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, new_primMulNat8(zzz64770), gf, gg) 130.57/78.24 new_mkVBalBranch3MkVBalBranch142(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bbf) -> new_mkVBalBranch3MkVBalBranch139(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bbf) 130.57/78.24 new_splitLT19(Branch(Neg(Succ(zzz621000)), zzz6211, zzz6212, zzz6213, zzz6214), db) -> new_mkVBalBranch6(zzz621000, zzz6211, zzz6213, new_splitLT19(zzz6214, db), db) 130.57/78.24 new_mkVBalBranch3MkVBalBranch224(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), hf) -> new_mkVBalBranch3MkVBalBranch224(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, hf) 130.57/78.24 new_mkVBalBranch3MkVBalBranch227(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bac) -> new_mkVBalBranch3MkVBalBranch228(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bac) 130.57/78.24 new_mkBalBranch6MkBalBranch42(EmptyFM, zzz474030, zzz474031, zzz6373, gf, gg) -> error([]) 130.57/78.24 new_mkBalBranch6MkBalBranch113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Zero, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch111(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_addToFM_C4(Branch(Pos(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), Zero, zzz31, bd) -> new_mkBalBranch(Pos(Succ(zzz34000)), zzz341, new_addToFM_C4(zzz343, Zero, zzz31, bd), zzz344, ty_Int, bd) 130.57/78.24 new_addToFM1(zzz426, zzz3000, zzz31, bd) -> new_addToFM_C3(zzz426, Succ(zzz3000), zzz31, bd) 130.57/78.24 new_splitGT41(zzz4000, bd) -> new_emptyFM(bd) 130.57/78.24 new_splitGT30(Pos(zzz74500), zzz7451, zzz7452, zzz7453, zzz7454, zzz747, df) -> new_splitGT221(zzz74500, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, df) 130.57/78.24 new_mkBalBranch6MkBalBranch415(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Zero), Neg(zzz64420), gf, gg) -> new_mkBalBranch6MkBalBranch41(zzz474034, zzz474030, zzz474031, zzz6373, new_primMulNat(zzz64420), gf, gg) 130.57/78.24 new_splitLT8(zzz31, zzz32, zzz33, zzz34, bd) -> new_splitLT219(zzz31, zzz32, zzz33, zzz34, bd) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch233(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bd) 130.57/78.24 new_mkBalBranch6MkBalBranch016(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Succ(zzz6454000), Zero, gf, gg) -> new_mkBalBranch6MkBalBranch010(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_addToFM_C13(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, Zero, Zero, bag) -> new_addToFM_C14(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, bag) 130.57/78.24 new_splitGT15(EmptyFM, fg) -> new_splitGT40(fg) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Pos(Zero), Neg(zzz64770), gf, gg) -> new_mkBalBranch6MkBalBranch1113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, new_primMulNat8(zzz64770), gf, gg) 130.57/78.24 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.24 new_mkBalBranch6MkBalBranch116(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Succ(zzz64830), zzz647600, gf, gg) -> new_mkBalBranch6MkBalBranch113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz64830, zzz647600, gf, gg) 130.57/78.24 new_splitGT223(Neg(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_splitGT230(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.24 new_splitGT43(bd) -> new_emptyFM(bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch231(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bbc) -> new_mkVBalBranch3MkVBalBranch242(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bbc) 130.57/78.24 new_mkBalBranch6MkBalBranch0110(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Succ(zzz64740), zzz645400, gf, gg) -> new_mkBalBranch6MkBalBranch016(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, zzz64740, zzz645400, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Neg(Succ(zzz647600)), Neg(zzz64770), gf, gg) -> new_mkBalBranch6MkBalBranch115(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, new_primMulNat8(zzz64770), gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch415(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Succ(zzz644300)), Neg(zzz64420), gf, gg) -> new_mkBalBranch6MkBalBranch414(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, new_primMulNat(zzz64420), gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Zero, Succ(zzz647800), gf, gg) -> new_mkBalBranch6MkBalBranch118(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234, bd) -> new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch9(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, bd), ty_Int, bd) 130.57/78.24 new_splitLT9(EmptyFM, fg) -> new_emptyFM(fg) 130.57/78.24 new_mkBalBranch6MkBalBranch1112(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch111(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), bd) -> new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch6(zzz3000, zzz31, zzz334, Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), bd), ty_Int, bd) 130.57/78.24 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.24 new_splitLT15(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, Zero, Zero, ha) -> new_splitLT14(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, ha) 130.57/78.24 new_mkVBalBranch3MkVBalBranch130(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bce) -> new_mkBalBranch(zzz6323, zzz6324, zzz6326, new_mkVBalBranch5(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bce), ty_Int, bce) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch238(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), bd) 130.57/78.24 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(zzz42620), zzz4263, zzz4264), bd) -> new_mkBalBranch(zzz4260, zzz4261, new_mkVBalBranch8(Succ(zzz3000), zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz4263, bd), zzz4264, ty_Int, bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch237(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), bcc) -> new_mkBalBranch(zzz5117, zzz5118, new_mkVBalBranch5(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, bcc), zzz5121, ty_Int, bcc) 130.57/78.24 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.57/78.24 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.57/78.24 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch144(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bd) 130.57/78.24 new_mkVBalBranch3MkVBalBranch147(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bd) 130.57/78.24 new_mkBalBranch6MkBalBranch1110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Pos(Succ(zzz647600)), Pos(zzz64770), gf, gg) -> new_mkBalBranch6MkBalBranch1111(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, new_primMulNat8(zzz64770), gf, gg) 130.57/78.24 new_addToFM_C13(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, Zero, Succ(zzz45460), bag) -> new_addToFM_C14(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, bag) 130.57/78.24 new_mkBalBranch6MkBalBranch013(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, zzz645400, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch010(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkBalBranch6MkBalBranch310(zzz474034, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch32(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.24 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234, bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(zzz300), zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234), ty_Int, bd) 130.57/78.24 new_splitLT19(Branch(Pos(Zero), zzz6211, zzz6212, zzz6213, zzz6214), db) -> new_splitLT210(zzz6211, zzz6212, zzz6213, zzz6214, db) 130.57/78.24 new_mkBalBranch6MkBalBranch0111(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch014(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(zzz300), zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), ty_Int, bd) 130.57/78.25 new_splitLT218(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Zero, Zero, hg) -> new_splitLT215(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, hg) 130.57/78.25 new_mkBalBranch6MkBalBranch415(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Succ(zzz644300)), Neg(zzz64420), gf, gg) -> new_mkBalBranch6MkBalBranch46(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, new_primMulNat(zzz64420), gf, gg) 130.57/78.25 new_intersectFM_C2Gts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd) -> new_splitGT217(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd) 130.57/78.25 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Succ(zzz3000)), zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Zero), zzz4263, zzz4264), ty_Int, bd) 130.57/78.25 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Zero), zzz4263, zzz4264), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Succ(zzz3000)), zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Zero), zzz4263, zzz4264), ty_Int, bd) 130.57/78.25 new_splitGT18(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, Zero, Succ(zzz45020), bcf) -> new_mkVBalBranch6(zzz4495, zzz4496, new_splitGT16(zzz4498, zzz4500, bcf), zzz4499, bcf) 130.57/78.25 new_mkVBalBranch3MkVBalBranch227(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bac) -> new_mkBalBranch(zzz5094, zzz5095, new_mkVBalBranch8(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bac), zzz5098, ty_Int, bac) 130.57/78.25 new_mkVBalBranch10(zzz300, zzz31, EmptyFM, zzz5230, zzz5231, zzz5233, zzz5234, bd) -> new_addToFM2(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, zzz300, zzz31, bd) 130.57/78.25 new_mkVBalBranch3MkVBalBranch236(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, hf) -> new_mkVBalBranch3MkVBalBranch151(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), hf) 130.57/78.25 new_mkVBalBranch3MkVBalBranch127(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bd) -> new_mkVBalBranch3MkVBalBranch128(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bd) 130.57/78.25 new_addToFM_C24(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Succ(zzz31880), Zero, hh) -> new_addToFM_C25(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, hh) 130.57/78.25 new_intersectFM_C2Gts5(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, ed) -> new_splitGT16(Branch(Neg(Succ(zzz2143)), zzz2144, zzz2145, zzz2146, zzz2147), zzz2148, ed) 130.57/78.25 new_mkBalBranch6MkBalBranch0111(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Succ(zzz64680), gf, gg) -> new_mkBalBranch6MkBalBranch017(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_mkVBalBranch3MkVBalBranch126(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Zero, bcd) -> new_mkVBalBranch3MkVBalBranch152(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, bcd) 130.57/78.25 new_intersectFM_C2Gts(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, h) -> new_splitGT13(Branch(Pos(Succ(zzz2078)), zzz2079, zzz2080, zzz2081, zzz2082), zzz2083, h) 130.57/78.25 new_mkBalBranch6MkBalBranch114(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) -> new_mkBalBranch6MkBalBranch110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.25 new_mkVBalBranch3MkVBalBranch235(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, bbd) -> new_mkVBalBranch3MkVBalBranch234(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, bbd) 130.57/78.25 new_mkBalBranch6MkBalBranch410(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, zzz6448, gf, gg) -> new_mkBalBranch6MkBalBranch411(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Succ(Succ(zzz4262000))), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch227(zzz330, zzz331, zzz333, zzz334, zzz4260, zzz4261, Succ(zzz4262000), zzz4263, zzz4264, Succ(zzz3000), zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz4262000, bd) 130.57/78.25 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.25 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, bd) -> new_mkBalBranch(zzz5230, zzz5231, new_mkVBalBranch8(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, bd), zzz5234, ty_Int, bd) 130.57/78.25 new_mkBalBranch6MkBalBranch1110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Neg(Zero), Pos(zzz64770), gf, gg) -> new_mkBalBranch6MkBalBranch117(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, new_primMulNat8(zzz64770), gf, gg) 130.57/78.25 new_primMulNat6 -> new_primPlusNat5(new_primMulNat4) 130.57/78.25 new_splitGT228(zzz618, zzz619, zzz620, zzz621, zzz622, db) -> new_mkVBalBranch5(Succ(zzz618), zzz619, new_splitGT11(zzz621, db), zzz622, db) 130.57/78.25 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch132(zzz3530, zzz3531, zzz353200, zzz3533, zzz3534, zzz340, zzz341, zzz343, zzz344, Zero, zzz31, new_primMulNat3(Zero), bd) 130.57/78.25 new_primMinusNat0(Zero, Zero) -> Pos(Zero) 130.57/78.25 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), EmptyFM, bd) -> new_addToFM1(Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz3000, zzz31, bd) 130.57/78.25 new_mkVBalBranch3MkVBalBranch131(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, bab) -> new_mkVBalBranch3MkVBalBranch145(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), bab) 130.57/78.25 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Succ(Succ(zzz3532000))), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch230(zzz3530, zzz3531, zzz3532000, zzz3533, zzz3534, zzz340, zzz341, Succ(Zero), zzz343, zzz344, Zero, zzz31, Zero, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz3532000), Succ(zzz3532000))), Succ(zzz3532000))), Succ(zzz3532000)), zzz3532000))), bd) 130.57/78.25 new_mkVBalBranch3MkVBalBranch235(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), bbd) -> new_mkVBalBranch3MkVBalBranch235(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, bbd) 130.57/78.25 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.25 new_mkVBalBranch3MkVBalBranch234(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, bbd) -> new_mkVBalBranch3MkVBalBranch140(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), bbd) 130.57/78.25 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch223(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bd) 130.57/78.25 new_intersectFM_C2Lts0(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, be) -> new_splitLT12(Branch(Pos(Zero), zzz2734, zzz2735, zzz2736, zzz2737), zzz2738, be) 130.57/78.25 new_mkVBalBranch3MkVBalBranch229(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), bab) -> new_mkBalBranch(zzz4998, zzz4999, new_mkVBalBranch8(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, bab), zzz5002, ty_Int, bab) 130.57/78.25 new_mkVBalBranch3MkVBalBranch229(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, bab) -> new_mkVBalBranch3MkVBalBranch226(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, bab) 130.57/78.25 new_mkBalBranch6MkBalBranch1112(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Succ(zzz64800), gf, gg) -> new_mkBalBranch6MkBalBranch116(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Zero, zzz64800, gf, gg) 130.57/78.25 new_addToFM_C12(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, bae) -> Branch(Pos(Succ(zzz4308)), new_addToFM0(zzz4304, zzz4309, bae), zzz4305, zzz4306, zzz4307) 130.57/78.25 new_mkBalBranch6MkBalBranch012(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch014(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_splitGT225(Pos(Zero), zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, bbh) -> new_splitGT227(zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, bbh) 130.57/78.25 new_splitLT17(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, Zero, Zero, baf) -> new_splitLT18(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, baf) 130.57/78.25 new_mkBalBranch6MkBalBranch015(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Pos(Zero), Pos(zzz64550), gf, gg) -> new_mkBalBranch6MkBalBranch018(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, new_primMulNat8(zzz64550), gf, gg) 130.57/78.25 new_splitLT12(Branch(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744), zzz1975, gh) -> new_splitLT31(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744, zzz1975, gh) 130.57/78.25 new_splitGT12(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, Succ(zzz44340), Succ(zzz44350), bbb) -> new_splitGT12(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, zzz44340, zzz44350, bbb) 130.57/78.25 new_mkBalBranch6MkBalBranch5(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Succ(zzz637500)), gf, gg) -> new_mkBalBranch6MkBalBranch51(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.57/78.25 new_splitLT213(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, ge) -> new_splitLT17(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Succ(zzz3138), Succ(zzz3133), ge) 130.57/78.25 new_mkVBalBranch3MkVBalBranch138(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bbc) -> new_mkVBalBranch3MkVBalBranch139(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bbc) 130.57/78.25 new_mkBalBranch6MkBalBranch47(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64490), zzz644300, gf, gg) -> new_mkBalBranch6MkBalBranch49(zzz474034, zzz474030, zzz474031, zzz6373, zzz64490, zzz644300, gf, gg) 130.57/78.25 new_splitGT223(Pos(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_splitGT220(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.25 new_splitGT226(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Zero, Succ(zzz34030), bad) -> new_splitGT218(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, bad) 130.57/78.25 new_splitGT11(Branch(Neg(Succ(zzz1196000)), zzz11961, zzz11962, zzz11963, zzz11964), dd) -> new_splitGT217(zzz1196000, zzz11961, zzz11962, zzz11963, zzz11964, dd) 130.57/78.25 new_splitGT226(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Succ(zzz34020), Zero, bad) -> new_splitGT13(zzz3400, zzz3401, bad) 130.57/78.25 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) -> new_mkBalBranch(zzz2500, zzz2501, zzz2503, new_mkVBalBranch5(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd), ty_Int, bd) 130.57/78.25 new_mkBalBranch6MkBalBranch115(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, zzz6483, gf, gg) -> new_mkBalBranch6MkBalBranch116(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz6483, zzz647600, gf, gg) 130.57/78.25 new_mkVBalBranch3MkVBalBranch127(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bd) -> new_mkVBalBranch3MkVBalBranch128(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bd) 130.57/78.25 new_addToFM(zzz34, zzz31, bd) -> new_addToFM_C3(zzz34, Zero, zzz31, bd) 130.57/78.25 new_mkBalBranch6MkBalBranch119(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, zzz6479, gf, gg) -> new_mkBalBranch6MkBalBranch114(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.25 new_mkBalBranch6MkBalBranch35(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Succ(zzz645200)), Pos(zzz64530), gf, gg) -> new_mkBalBranch6MkBalBranch312(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, new_primMulNat(zzz64530), gf, gg) 130.57/78.25 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch230(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), bd) 130.57/78.25 new_intersectFM_C2Gts4(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df) -> new_splitGT221(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df) 130.57/78.25 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(zzz300), zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Int, bd) 130.57/78.25 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(zzz300), zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Int, bd) 130.57/78.25 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch146(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Zero)))), bd) 130.57/78.25 new_addToFM3(zzz34, zzz300, zzz31, bd) -> new_addToFM_C4(zzz34, zzz300, zzz31, bd) 130.57/78.25 new_splitGT222(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Zero, Zero, bbg) -> new_splitGT224(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, bbg) 130.57/78.25 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Zero), zzz31, Branch(zzz3530, zzz3531, Pos(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Int, bd) 130.57/78.25 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Zero), zzz31, Branch(zzz3530, zzz3531, Neg(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Int, bd) 130.57/78.25 new_splitGT9(bd) -> new_splitGT40(bd) 130.57/78.25 new_mkBalBranch6MkBalBranch415(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Zero), Neg(zzz64420), gf, gg) -> new_mkBalBranch6MkBalBranch44(zzz474034, zzz474030, zzz474031, zzz6373, new_primMulNat(zzz64420), gf, gg) 130.57/78.25 new_mkBalBranch6MkBalBranch415(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Zero), Pos(zzz64420), gf, gg) -> new_mkBalBranch6MkBalBranch416(zzz474034, zzz474030, zzz474031, zzz6373, new_primMulNat(zzz64420), gf, gg) 130.57/78.25 new_splitLT17(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, Succ(zzz41840), Zero, baf) -> new_mkVBalBranch5(Succ(zzz4178), zzz4179, zzz4181, new_splitLT12(zzz4182, zzz4183, baf), baf) 130.57/78.25 new_mkVBalBranch3MkVBalBranch145(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Zero, bcb) -> new_mkVBalBranch3MkVBalBranch149(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, bcb) 130.57/78.25 new_splitLT19(Branch(Neg(Zero), zzz6211, zzz6212, zzz6213, zzz6214), db) -> new_splitLT211(zzz6211, zzz6212, zzz6213, zzz6214, db) 130.57/78.25 new_mkBalBranch6MkBalBranch117(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch111(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.25 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.25 new_mkBalBranch6MkBalBranch112(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, Succ(zzz64780), gf, gg) -> new_mkBalBranch6MkBalBranch113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, zzz64780, gf, gg) 130.57/78.25 new_mkVBalBranch3MkVBalBranch140(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), bbd) -> new_mkVBalBranch3MkVBalBranch126(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), bbd) 130.57/78.25 new_mkVBalBranch9(zzz300, zzz31, EmptyFM, zzz5230, zzz5231, zzz5233, zzz5234, bd) -> new_addToFM2(zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234, zzz300, zzz31, bd) 130.57/78.25 new_mkBalBranch6MkBalBranch36(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64610), zzz645200, gf, gg) -> new_mkBalBranch6MkBalBranch37(zzz474034, zzz474030, zzz474031, zzz6373, zzz64610, zzz645200, gf, gg) 130.57/78.25 new_mkBalBranch6MkBalBranch41(zzz474034, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch43(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_mkBalBranch6MkBalBranch312(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, zzz6460, gf, gg) -> new_mkBalBranch6MkBalBranch38(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Zero), zzz4263, zzz4264), bd) -> new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch6(zzz3000, zzz31, zzz334, Branch(zzz4260, zzz4261, Pos(Zero), zzz4263, zzz4264), bd), ty_Int, bd) 130.57/78.25 new_splitLT16(zzz4000, bd) -> new_splitLT41(zzz4000, bd) 130.57/78.25 new_intersectFM_C2Gts1(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, cc) -> new_splitGT13(Branch(Neg(zzz1382), zzz1383, zzz1384, zzz1385, zzz1386), zzz1387, cc) 130.57/78.25 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Succ(Succ(zzz4262000))), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch229(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz4260, zzz4261, Succ(zzz4262000), zzz4263, zzz4264, Succ(zzz3000), zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz4262000, bd) 130.57/78.25 new_mkBalBranch6Size_r(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_sizeFM(zzz474034, gf, gg) 130.57/78.25 new_mkBalBranch6MkBalBranch110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, Branch(zzz637340, zzz637341, zzz637342, zzz637343, zzz637344), gf, gg) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), zzz637340, zzz637341, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), zzz63730, zzz63731, zzz63733, zzz637343, gf, gg), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), zzz474030, zzz474031, zzz637344, zzz474034, gf, gg), gf, gg) 130.57/78.25 new_mkVBalBranch3MkVBalBranch233(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, baa) -> new_mkVBalBranch3MkVBalBranch129(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primMulNat3(zzz3745), baa) 130.57/78.25 new_mkBalBranch6MkBalBranch018(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch014(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_mkBalBranch6MkBalBranch34(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch31(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.57/78.25 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch229(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz5232000, bd) 130.57/78.25 new_primMulNat2(zzz4739) -> Zero 130.57/78.25 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch134(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), bd) 130.57/78.25 new_mkVBalBranch3MkVBalBranch137(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bd) 130.57/78.25 new_intersectFM_C2Gts7(zzz830, zzz831, zzz832, zzz833, zzz834, fg) -> new_splitGT220(zzz830, zzz831, zzz832, zzz833, zzz834, fg) 130.57/78.25 new_splitGT223(Neg(Zero), zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_splitGT216(zzz8331, zzz8332, zzz8333, zzz8334, fg) 130.57/78.25 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch133(zzz3530, zzz3531, zzz353200, zzz3533, zzz3534, zzz340, zzz341, zzz34200, zzz343, zzz344, Zero, zzz31, new_primPlusNat0(new_primMulNat0(zzz34200), Succ(zzz34200)), bd) 130.57/78.25 new_mkVBalBranch3MkVBalBranch144(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bd) 130.57/78.25 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Neg(Succ(Zero)), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch231(zzz3530, zzz3531, zzz3533, zzz3534, zzz340, zzz341, Succ(Zero), zzz343, zzz344, Zero, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), bd) 130.57/78.25 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, zzz3532, zzz3533, zzz3534), EmptyFM, bd) -> new_addToFM(Branch(zzz3530, zzz3531, zzz3532, zzz3533, zzz3534), zzz31, bd) 130.57/78.25 new_mkBalBranch6MkBalBranch49(zzz474034, zzz474030, zzz474031, zzz6373, Zero, Succ(zzz644400), gf, gg) -> new_mkBalBranch6MkBalBranch411(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Succ(zzz426200)), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch134(zzz330, zzz331, zzz333, zzz334, zzz4260, zzz4261, zzz426200, zzz4263, zzz4264, Succ(zzz3000), zzz31, new_primMulNat3(zzz426200), bd) 130.57/78.25 new_mkBalBranch6MkBalBranch35(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Succ(zzz645200)), Neg(zzz64530), gf, gg) -> new_mkBalBranch6MkBalBranch314(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, new_primMulNat(zzz64530), gf, gg) 130.57/78.25 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.57/78.25 new_addToFM_C11(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, Zero, Succ(zzz43110), bae) -> new_addToFM_C12(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, bae) 130.57/78.25 new_splitLT212(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Succ(zzz31390), Zero, ge) -> new_splitLT213(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, ge) 130.57/78.25 new_mkBalBranch6MkBalBranch016(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Zero, Succ(zzz647200), gf, gg) -> new_mkBalBranch6MkBalBranch017(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_sizeFM(Branch(zzz34900, zzz34901, zzz34902, zzz34903, zzz34904), bah, bba) -> zzz34902 130.57/78.25 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.57/78.25 new_splitLT13(Branch(Neg(Zero), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, df) -> new_splitLT13(zzz7453, zzz747, df) 130.57/78.25 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch230(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), bd) 130.57/78.25 new_splitGT226(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Zero, Zero, bad) -> new_splitGT218(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, bad) 130.57/78.25 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, bd) -> new_mkBalBranch(zzz5230, zzz5231, new_mkVBalBranch8(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, bd), zzz5234, ty_Int, bd) 130.57/78.25 new_mkVBalBranch11(zzz300, zzz31, EmptyFM, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, bd) -> new_addToFM2(zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, zzz300, zzz31, bd) 130.57/78.25 new_mkBalBranch6MkBalBranch416(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz64460), gf, gg) -> new_mkBalBranch6MkBalBranch47(zzz474034, zzz474030, zzz474031, zzz6373, Zero, zzz64460, gf, gg) 130.57/78.25 new_mkVBalBranch3MkVBalBranch224(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, hf) -> new_mkVBalBranch3MkVBalBranch236(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, hf) 130.57/78.25 new_mkBalBranch6MkBalBranch011(zzz4740340, zzz4740341, zzz4740342, EmptyFM, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) -> error([]) 130.57/78.25 new_mkBalBranch6MkBalBranch014(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBalBranch6MkBalBranch011(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_mkBalBranch6MkBalBranch016(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Zero, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch014(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_mkBalBranch6MkBalBranch013(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, zzz645400, Succ(zzz64720), gf, gg) -> new_mkBalBranch6MkBalBranch016(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, zzz645400, zzz64720, gf, gg) 130.57/78.25 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch129(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bd) 130.57/78.25 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334), Branch(zzz4260, zzz4261, Neg(Succ(Succ(Succ(zzz42620000)))), zzz4263, zzz4264), bd) -> new_mkVBalBranch3MkVBalBranch231(zzz330, zzz331, zzz333, zzz334, zzz4260, zzz4261, Succ(Succ(zzz42620000)), zzz4263, zzz4264, Succ(zzz3000), zzz31, Succ(zzz42620000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), bd) 130.57/78.25 new_addToFM_C3(Branch(Neg(Zero), zzz9821, zzz9822, zzz9823, zzz9824), Succ(zzz3000), zzz31, bd) -> new_mkBalBranch(Neg(Zero), zzz9821, new_addToFM_C3(zzz9823, Succ(zzz3000), zzz31, bd), zzz9824, ty_Int, bd) 130.57/78.25 new_intersectFM_C2Lts1(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, cc) -> new_splitLT29(Neg(zzz1382), zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, cc) 130.57/78.25 new_splitLT14(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, ha) -> zzz4507 130.57/78.25 new_splitLT6(zzz300, zzz31, zzz32, zzz34, zzz4000, bd) -> new_splitLT16(zzz4000, bd) 130.57/78.25 new_primMulNat8(Succ(zzz645500)) -> new_primPlusNat0(new_primMulNat1(zzz645500), Succ(zzz645500)) 130.57/78.25 new_mkVBalBranch3MkVBalBranch145(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bcb) -> new_mkBalBranch(zzz6120, zzz6121, zzz6123, new_mkVBalBranch12(zzz6130, zzz6131, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, bcb), ty_Int, bcb) 130.57/78.25 new_mkBalBranch6MkBalBranch111(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) -> new_mkBalBranch6MkBalBranch110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.25 new_splitGT222(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Succ(zzz35000), Succ(zzz35010), bbg) -> new_splitGT222(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, zzz35000, zzz35010, bbg) 130.57/78.25 new_mkBalBranch6MkBalBranch35(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Zero), Neg(zzz64530), gf, gg) -> new_mkBalBranch6MkBalBranch30(zzz474034, zzz474030, zzz474031, zzz6373, new_primMulNat(zzz64530), gf, gg) 130.57/78.25 new_mkVBalBranch3MkVBalBranch145(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bcb) -> new_mkVBalBranch3MkVBalBranch145(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bcb) 130.57/78.25 new_mkVBalBranch3MkVBalBranch136(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), he) -> new_mkVBalBranch3MkVBalBranch130(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), he) 130.57/78.25 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.25 new_mkBalBranch(zzz474030, zzz474031, zzz6373, zzz474034, gf, gg) -> new_mkBalBranch6MkBalBranch5(zzz474034, zzz474030, zzz474031, zzz6373, new_primPlusInt2(new_mkBalBranch6Size_l(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg), zzz474034, zzz474030, zzz474031, zzz6373, gf, gg), gf, gg) 130.57/78.25 new_splitLT210(zzz31, zzz32, zzz33, zzz34, bd) -> zzz33 130.57/78.25 new_intersectFM_C2Gts2(zzz618, zzz619, zzz620, zzz621, zzz622, db) -> new_splitGT14(zzz618, zzz619, zzz620, zzz621, zzz622, db) 130.57/78.25 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.57/78.25 new_mkVBalBranch3MkVBalBranch239(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), he) -> new_mkVBalBranch3MkVBalBranch239(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, he) 130.57/78.25 new_mkBalBranch6MkBalBranch45(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, Succ(zzz64440), gf, gg) -> new_mkBalBranch6MkBalBranch49(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, zzz64440, gf, gg) 130.57/78.25 new_mkVBalBranch3MkVBalBranch128(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bd) 130.57/78.25 new_mkVBalBranch3MkVBalBranch238(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, zzz4455, he) -> new_mkVBalBranch3MkVBalBranch222(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, he) 130.57/78.25 new_mkBalBranch6MkBalBranch30(zzz474034, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch32(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_mkVBalBranch3MkVBalBranch222(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, he) -> new_mkBalBranch(zzz4107, zzz4108, new_mkVBalBranch5(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, he), zzz4111, ty_Int, he) 130.57/78.25 new_mkBalBranch6MkBalBranch015(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Pos(Succ(zzz645400)), Neg(zzz64550), gf, gg) -> new_mkBalBranch6MkBalBranch010(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, bd) -> new_mkVBalBranch3MkVBalBranch231(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), bd) 130.57/78.25 new_splitLT17(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, Succ(zzz41840), Succ(zzz41850), baf) -> new_splitLT17(zzz4178, zzz4179, zzz4180, zzz4181, zzz4182, zzz4183, zzz41840, zzz41850, baf) 130.57/78.25 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Zero), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch8(Zero, zzz31, zzz3530, zzz3531, Pos(Zero), zzz3533, zzz3534, zzz343, bd), zzz344, ty_Int, bd) 130.57/78.25 new_mkBalBranch6MkBalBranch31(zzz474034, zzz474030, zzz474031, Branch(zzz63730, zzz63731, zzz63732, zzz63733, zzz63734), gf, gg) -> new_mkBalBranch6MkBalBranch1110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, new_sizeFM(zzz63734, gf, gg), new_sizeFM(zzz63733, gf, gg), gf, gg) 130.57/78.25 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch237(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000)))), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000))), bd) 130.57/78.25 new_mkBalBranch6MkBalBranch51(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBranch(Zero, zzz474030, zzz474031, zzz6373, zzz474034, gf, gg) 130.57/78.25 new_splitLT221(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, fg) -> new_mkVBalBranch6(zzz833000, zzz8331, zzz8333, new_splitLT9(zzz8334, fg), fg) 130.57/78.25 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(zzz523200)), zzz5233, zzz5234, bd) -> new_mkBalBranch(zzz5230, zzz5231, new_mkVBalBranch8(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5233, bd), zzz5234, ty_Int, bd) 130.57/78.25 new_splitLT222(zzz31, zzz32, zzz33, zzz34, bd) -> zzz33 130.57/78.25 new_splitGT225(Pos(Succ(zzz1612000)), zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, bbh) -> new_splitGT226(zzz1612000, zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, zzz1613, zzz1612000, bbh) 130.57/78.25 new_splitLT31(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744, zzz1975, gh) -> new_splitLT29(zzz19740, zzz19741, zzz19742, zzz19743, zzz19744, zzz1975, gh) 130.57/78.25 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), zzz343, bd), zzz344, ty_Int, bd) 130.57/78.25 new_mkBalBranch6MkBalBranch415(zzz474034, zzz474030, zzz474031, zzz6373, Neg(Zero), Pos(zzz64420), gf, gg) -> new_mkBalBranch6MkBalBranch412(zzz474034, zzz474030, zzz474031, zzz6373, new_primMulNat(zzz64420), gf, gg) 130.57/78.25 new_splitGT16(EmptyFM, zzz747, df) -> new_splitGT41(zzz747, df) 130.57/78.25 new_splitLT212(zzz3133, zzz3134, zzz3135, zzz3136, zzz3137, zzz3138, Zero, Succ(zzz31400), ge) -> new_splitLT12(zzz3136, zzz3138, ge) 130.57/78.25 new_mkBalBranch6MkBalBranch5(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Zero), gf, gg) -> new_mkBalBranch6MkBalBranch51(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_mkBalBranch6MkBalBranch1113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Succ(zzz64810), gf, gg) -> new_mkBalBranch6MkBalBranch114(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.25 new_mkVBalBranch3MkVBalBranch129(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Zero, baa) -> new_mkVBalBranch3MkVBalBranch130(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Zero, baa) 130.57/78.25 new_mkBalBranch6MkBalBranch112(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch114(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.25 new_mkVBalBranch30(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(zzz523200)), zzz5233, zzz5234, bd) -> new_mkBalBranch(zzz5230, zzz5231, new_mkVBalBranch8(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5233, bd), zzz5234, ty_Int, bd) 130.57/78.25 new_mkVBalBranch3MkVBalBranch229(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, bab) -> new_mkVBalBranch3MkVBalBranch226(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, bab) 130.57/78.25 new_mkVBalBranch3MkVBalBranch224(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, hf) -> new_mkVBalBranch3MkVBalBranch225(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, hf) 130.57/78.25 new_mkVBalBranch9(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz5233, zzz5234, bd) -> new_mkVBalBranch30(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234, bd) 130.57/78.25 new_addToFM_C23(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Zero, Zero, bca) -> new_addToFM_C26(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, bca) 130.57/78.25 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch237(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000)))), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000))), bd) 130.57/78.25 new_splitLT11(zzz31, zzz32, zzz33, zzz34, bd) -> new_splitLT222(zzz31, zzz32, zzz33, zzz34, bd) 130.57/78.25 new_mkVBalBranch3MkVBalBranch230(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bbf) -> new_mkBalBranch(zzz5135, zzz5136, new_mkVBalBranch8(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bbf), zzz5139, ty_Int, bbf) 130.57/78.25 new_splitLT29(Neg(zzz19700), zzz1971, zzz1972, Branch(zzz19730, zzz19731, zzz19732, zzz19733, zzz19734), EmptyFM, zzz1975, gh) -> new_mkVBalBranch8(zzz19700, zzz1971, zzz19730, zzz19731, zzz19732, zzz19733, zzz19734, new_splitLT42(zzz1975, gh), gh) 130.57/78.25 new_addToFM_C4(EmptyFM, zzz300, zzz31, bd) -> Branch(Pos(zzz300), zzz31, Pos(Succ(Zero)), new_emptyFM(bd), new_emptyFM(bd)) 130.57/78.25 new_primPlusNat3(Zero) -> Succ(Zero) 130.57/78.25 new_mkVBalBranch3MkVBalBranch145(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Zero, bcb) -> new_mkVBalBranch3MkVBalBranch149(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, bcb) 130.57/78.25 new_mkBalBranch6MkBalBranch411(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_mkBalBranch6MkBalBranch40(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_mkVBalBranch3MkVBalBranch139(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Zero, bbe) -> new_mkVBalBranch3MkVBalBranch141(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, bbe) 130.57/78.25 new_mkBalBranch6MkBalBranch5(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Succ(Succ(Succ(zzz63750000)))), gf, gg) -> new_mkBalBranch6MkBalBranch50(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_addToFM_C4(Branch(Neg(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), Zero, zzz31, bd) -> new_mkBalBranch(Neg(Succ(zzz34000)), zzz341, zzz343, new_addToFM_C4(zzz344, Zero, zzz31, bd), ty_Int, bd) 130.57/78.25 new_addToFM_C23(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Succ(zzz33930), Succ(zzz33940), bca) -> new_addToFM_C23(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, zzz33930, zzz33940, bca) 130.57/78.25 new_mkVBalBranch3MkVBalBranch240(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bbf) -> new_mkVBalBranch3MkVBalBranch142(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bbf) 130.57/78.25 new_mkVBalBranch3MkVBalBranch237(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), bcc) -> new_mkVBalBranch3MkVBalBranch237(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, bcc) 130.57/78.25 new_intersectFM_C2Gts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc) -> new_splitGT15(Branch(Neg(Succ(zzz1594)), zzz1595, zzz1596, zzz1597, zzz1598), gc) 130.57/78.25 new_splitGT19(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, bcf) -> zzz4499 130.57/78.25 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd) -> new_mkBalBranch(zzz3530, zzz3531, zzz3533, new_mkVBalBranch7(zzz31, zzz3534, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bd), ty_Int, bd) 130.57/78.25 new_mkVBalBranch10(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz5233, zzz5234, bd) -> new_mkVBalBranch30(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, bd) 130.57/78.25 new_splitGT214(zzz31, zzz32, zzz33, zzz34, bd) -> zzz34 130.57/78.25 new_mkVBalBranch3MkVBalBranch241(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, bcc) -> new_mkVBalBranch3MkVBalBranch150(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), bcc) 130.57/78.25 new_mkVBalBranch3MkVBalBranch134(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), bd) -> new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch11(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, bd), ty_Int, bd) 130.57/78.25 new_splitGT11(Branch(Pos(Succ(zzz1196000)), zzz11961, zzz11962, zzz11963, zzz11964), dd) -> new_splitGT228(zzz1196000, zzz11961, zzz11962, zzz11963, zzz11964, dd) 130.57/78.25 new_mkBalBranch6MkBalBranch116(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Zero, zzz647600, gf, gg) -> new_mkBalBranch6MkBalBranch118(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.25 new_splitLT15(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, Succ(zzz45100), Zero, ha) -> new_mkVBalBranch6(zzz4504, zzz4505, zzz4507, new_splitLT13(zzz4508, zzz4509, ha), ha) 130.57/78.25 new_mkBalBranch6MkBalBranch1114(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, zzz6482, gf, gg) -> new_mkBalBranch6MkBalBranch118(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) 130.57/78.25 new_primMinusNat0(Zero, Succ(zzz47700)) -> Neg(Succ(zzz47700)) 130.57/78.25 new_mkBalBranch6MkBalBranch113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Succ(zzz6476000), Succ(zzz647800), gf, gg) -> new_mkBalBranch6MkBalBranch113(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz6476000, zzz647800, gf, gg) 130.57/78.25 new_mkBalBranch6MkBalBranch414(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, zzz6445, gf, gg) -> new_mkBalBranch6MkBalBranch42(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_mkBalBranch6MkBalBranch012(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Succ(zzz64700), gf, gg) -> new_mkBalBranch6MkBalBranch013(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, zzz64700, Zero, gf, gg) 130.57/78.25 new_addToFM_C26(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, bca) -> new_addToFM_C13(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Succ(zzz3386), Succ(zzz3391), bca) 130.57/78.25 new_mkBalBranch6MkBalBranch412(zzz474034, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch43(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_mkVBalBranch6(zzz3000, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz4260, zzz4261, Pos(Succ(zzz426200)), zzz4263, zzz4264), bd) -> new_mkBalBranch(zzz4260, zzz4261, new_mkVBalBranch8(Succ(zzz3000), zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz4263, bd), zzz4264, ty_Int, bd) 130.57/78.25 new_addToFM_C3(Branch(Neg(Succ(zzz982000)), zzz9821, zzz9822, zzz9823, zzz9824), Zero, zzz31, bd) -> new_mkBalBranch(Neg(Succ(zzz982000)), zzz9821, zzz9823, new_addToFM_C3(zzz9824, Zero, zzz31, bd), ty_Int, bd) 130.57/78.25 new_mkVBalBranch3MkVBalBranch134(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, bd) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(zzz300), zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234), ty_Int, bd) 130.57/78.25 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd) -> new_mkBalBranch(zzz2500, zzz2501, zzz2503, new_mkVBalBranch5(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bd), ty_Int, bd) 130.57/78.25 new_mkBalBranch6MkBalBranch35(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Succ(zzz645200)), Neg(zzz64530), gf, gg) -> new_mkBalBranch6MkBalBranch315(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, new_primMulNat(zzz64530), gf, gg) 130.57/78.25 new_addToFM_C24(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Zero, Zero, hh) -> new_addToFM_C25(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, hh) 130.57/78.25 new_splitLT19(EmptyFM, db) -> new_splitLT40(db) 130.57/78.25 new_mkBalBranch6MkBalBranch33(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, zzz6456, gf, gg) -> new_mkBalBranch6MkBalBranch34(zzz474034, zzz474030, zzz474031, zzz6373, zzz645200, zzz6456, gf, gg) 130.57/78.25 new_addToFM_C4(Branch(Neg(zzz3400), zzz341, zzz342, zzz343, zzz344), Succ(zzz3000), zzz31, bd) -> new_mkBalBranch(Neg(zzz3400), zzz341, zzz343, new_addToFM_C4(zzz344, Succ(zzz3000), zzz31, bd), ty_Int, bd) 130.57/78.25 new_splitGT12(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, Zero, Succ(zzz44350), bbb) -> new_mkVBalBranch5(Succ(zzz4428), zzz4429, new_splitGT13(zzz4431, zzz4433, bbb), zzz4432, bbb) 130.57/78.25 new_mkVBalBranch3MkVBalBranch126(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), bcd) -> new_mkVBalBranch3MkVBalBranch126(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, bcd) 130.57/78.25 new_mkBalBranch6MkBalBranch118(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, gf, gg) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), zzz63730, zzz63731, zzz63733, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), zzz474030, zzz474031, zzz63734, zzz474034, gf, gg), gf, gg) 130.57/78.25 new_mkVBalBranch3MkVBalBranch125(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bd) -> new_mkVBalBranch3MkVBalBranch126(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bd) 130.57/78.25 new_addToFM_C4(Branch(Pos(Zero), zzz341, zzz342, zzz343, zzz344), Zero, zzz31, bd) -> Branch(Pos(Zero), new_addToFM0(zzz341, zzz31, bd), zzz342, zzz343, zzz344) 130.57/78.25 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.57/78.25 new_addToFM_C3(EmptyFM, zzz300, zzz31, bd) -> Branch(Neg(zzz300), zzz31, Pos(Succ(Zero)), new_emptyFM(bd), new_emptyFM(bd)) 130.57/78.25 new_mkBalBranch6MkBalBranch015(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Pos(Zero), Neg(zzz64550), gf, gg) -> new_mkBalBranch6MkBalBranch019(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, new_primMulNat8(zzz64550), gf, gg) 130.57/78.25 new_mkVBalBranch3MkVBalBranch138(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, bbc) -> new_mkVBalBranch3MkVBalBranch139(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Zero, bbc) 130.57/78.25 new_splitGT219(zzz884, zzz885, zzz886, zzz887, zzz888, eh) -> new_mkVBalBranch7(zzz884, new_splitGT16(zzz886, zzz888, eh), zzz887, eh) 130.57/78.25 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch127(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat4, bd) 130.57/78.25 new_splitGT221(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df) -> new_mkVBalBranch5(zzz742, zzz743, new_splitGT16(zzz745, zzz747, df), zzz746, df) 130.57/78.25 new_mkBalBranch6MkBalBranch47(zzz474034, zzz474030, zzz474031, zzz6373, Zero, zzz644300, gf, gg) -> new_mkBalBranch6MkBalBranch411(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_addToFM_C3(Branch(Pos(Zero), zzz9821, zzz9822, zzz9823, zzz9824), Zero, zzz31, bd) -> Branch(Neg(Zero), new_addToFM0(zzz9821, zzz31, bd), zzz9822, zzz9823, zzz9824) 130.57/78.25 new_mkVBalBranch3MkVBalBranch223(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Succ(zzz388700), hf) -> new_mkVBalBranch3MkVBalBranch224(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, zzz388700, hf) 130.57/78.25 new_mkBalBranch6MkBalBranch37(zzz474034, zzz474030, zzz474031, zzz6373, Zero, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch32(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_mkBalBranch6MkBalBranch1110(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, Pos(Succ(zzz647600)), Neg(zzz64770), gf, gg) -> new_mkBalBranch6MkBalBranch119(zzz474034, zzz474030, zzz474031, zzz63730, zzz63731, zzz63732, zzz63733, zzz63734, zzz647600, new_primMulNat8(zzz64770), gf, gg) 130.57/78.25 new_splitGT6(zzz4000, bd) -> new_splitGT42(zzz4000, bd) 130.57/78.25 new_mkVBalBranch7(zzz31, Branch(zzz3530, zzz3531, Pos(Succ(Zero)), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch227(zzz3530, zzz3531, zzz3533, zzz3534, zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, Zero, zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz342000, bd) 130.57/78.25 new_mkBalBranch6Size_l(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) -> new_sizeFM(zzz6373, gf, gg) 130.57/78.25 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.25 new_mkBalBranch6MkBalBranch0110(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Zero, zzz645400, gf, gg) -> new_mkBalBranch6MkBalBranch017(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_intersectFM_C2Gts0(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, be) -> new_splitGT13(Branch(Pos(Zero), zzz2734, zzz2735, zzz2736, zzz2737), zzz2738, be) 130.57/78.25 new_mkVBalBranch5(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bd) -> new_mkVBalBranch3MkVBalBranch125(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bd) 130.57/78.25 new_splitGT226(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Succ(zzz34020), Succ(zzz34030), bad) -> new_splitGT226(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, zzz34020, zzz34030, bad) 130.57/78.25 new_splitGT13(Branch(zzz16120, zzz16121, zzz16122, zzz16123, zzz16124), zzz1613, bbh) -> new_splitGT225(zzz16120, zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, bbh) 130.57/78.25 new_mkVBalBranch3MkVBalBranch235(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), bbd) -> new_mkBalBranch(zzz4706, zzz4707, new_mkVBalBranch5(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, bbd), zzz4710, ty_Int, bbd) 130.57/78.25 new_mkVBalBranch3MkVBalBranch135(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), bd) -> new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch11(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, bd), ty_Int, bd) 130.57/78.25 new_mkBalBranch6MkBalBranch44(zzz474034, zzz474030, zzz474031, zzz6373, Zero, gf, gg) -> new_mkBalBranch6MkBalBranch43(zzz474034, zzz474030, zzz474031, zzz6373, gf, gg) 130.57/78.25 new_addToFM_C24(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Succ(zzz31880), Succ(zzz31890), hh) -> new_addToFM_C24(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, zzz31880, zzz31890, hh) 130.57/78.25 new_primPlusInt1(zzz58960, Pos(zzz59010)) -> new_primMinusNat0(zzz59010, zzz58960) 130.57/78.25 new_splitGT213(zzz31, zzz32, zzz33, zzz34, bd) -> zzz34 130.57/78.25 new_mkBalBranch6MkBalBranch415(zzz474034, zzz474030, zzz474031, zzz6373, Pos(Succ(zzz644300)), Pos(zzz64420), gf, gg) -> new_mkBalBranch6MkBalBranch48(zzz474034, zzz474030, zzz474031, zzz6373, zzz644300, new_primMulNat(zzz64420), gf, gg) 130.57/78.25 new_splitLT19(Branch(Pos(Succ(zzz621000)), zzz6211, zzz6212, zzz6213, zzz6214), db) -> new_splitLT220(zzz621000, zzz6211, zzz6212, zzz6213, zzz6214, db) 130.57/78.25 new_mkVBalBranch3MkVBalBranch231(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bbc) -> new_mkVBalBranch3MkVBalBranch231(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bbc) 130.57/78.25 new_splitLT13(EmptyFM, zzz747, df) -> new_splitLT41(zzz747, df) 130.57/78.25 new_addToFM_C14(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, bag) -> Branch(Neg(Succ(zzz4543)), new_addToFM0(zzz4539, zzz4544, bag), zzz4540, zzz4541, zzz4542) 130.57/78.25 130.57/78.25 The set Q consists of the following terms: 130.57/78.25 130.57/78.25 new_intersectFM_C2Lts8(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_splitGT15(Branch(x0, x1, x2, x3, x4), x5) 130.57/78.25 new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Zero, x4, x5) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Zero), x4, x5, x6, x7, Neg(Zero), x8, x9, x10) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Zero), x4, x5, x6, x7, Pos(Zero), x8, x9, x10) 130.57/78.25 new_splitGT14(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_splitLT213(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_mkVBalBranch3MkVBalBranch238(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11, x12) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Zero), x4, x5, x6, x7, Neg(Zero), x8, x9, x10) 130.57/78.25 new_splitLT41(x0, x1) 130.57/78.25 new_mkVBalBranch5(x0, x1, EmptyFM, x2, x3) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Succ(Zero)), x3, x4), Branch(x5, x6, Neg(Succ(Succ(Zero))), x7, x8), x9) 130.57/78.25 new_splitLT18(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_mkVBalBranch3MkVBalBranch130(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13) 130.57/78.25 new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13) 130.57/78.25 new_splitLT216(Neg(Succ(x0)), x1, x2, x3, x4, x5) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Succ(Zero))), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Succ(Succ(Succ(x8)))))), x9, x10), x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.25 new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, Succ(x5), x6, x7) 130.57/78.25 new_splitLT218(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) 130.57/78.25 new_intersectFM_C2Lts6(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.25 new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Zero, x4, x5) 130.57/78.25 new_primPlusNat8(Zero, x0) 130.57/78.25 new_primPlusInt1(x0, Neg(x1)) 130.57/78.25 new_addToFM_C24(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8) 130.57/78.25 new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12) 130.57/78.25 new_primMulNat1(x0) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Zero), x4, x5, x6, x7, Pos(Zero), x8, x9, x10) 130.57/78.25 new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10) 130.57/78.25 new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Succ(x4), x5, x6) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(Succ(Succ(x4)))), x5, x6), Branch(x7, x8, Pos(Succ(Succ(Succ(Succ(x9))))), x10, x11), x12) 130.57/78.25 new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13) 130.57/78.25 new_splitGT12(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch231(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13) 130.57/78.25 new_intersectFM_C2Lts2(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkBalBranch6MkBalBranch31(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9) 130.57/78.25 new_primMinusNat0(Zero, Zero) 130.57/78.25 new_addToFM3(x0, x1, x2, x3) 130.57/78.25 new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14) 130.57/78.25 new_primMulNat8(Succ(x0)) 130.57/78.25 new_mkVBalBranch3MkVBalBranch136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.25 new_primMulNat7 130.57/78.25 new_splitGT30(Pos(x0), x1, x2, x3, x4, x5, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch41(x0, x1, x2, x3, Zero, x4, x5) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10) 130.57/78.25 new_primMulNat3(x0) 130.57/78.25 new_splitGT18(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) 130.57/78.25 new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, Zero, x5, x6) 130.57/78.25 new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.25 new_mkVBalBranch12(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9, x10, x11, x12) 130.57/78.25 new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14) 130.57/78.25 new_primPlusInt1(x0, Pos(x1)) 130.57/78.25 new_splitGT18(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) 130.57/78.25 new_addToFM_C24(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8) 130.57/78.25 new_addToFM_C3(Branch(Neg(Succ(x0)), x1, x2, x3, x4), Zero, x5, x6) 130.57/78.25 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.25 new_primPlusInt2(Pos(x0), x1, x2, x3, x4, x5, x6) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Succ(Zero))), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Succ(Succ(Zero))))), x8, x9), x10) 130.57/78.25 new_splitLT19(Branch(Neg(Zero), x0, x1, x2, x3), x4) 130.57/78.25 new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Succ(x4), x5, x6) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, Pos(x9), x10, x11), x12) 130.57/78.25 new_mkVBalBranch3MkVBalBranch222(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, Pos(Zero), x9, x10), x11) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13) 130.57/78.25 new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.25 new_splitGT18(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) 130.57/78.25 new_splitLT216(Neg(Zero), x0, x1, x2, x3, x4) 130.57/78.25 new_splitGT6(x0, x1) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Succ(Zero)), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Zero))), x8, x9), x10) 130.57/78.25 new_addToFM_C4(Branch(Pos(Succ(x0)), x1, x2, x3, x4), Zero, x5, x6) 130.57/78.25 new_addToFM_C4(Branch(Neg(Succ(x0)), x1, x2, x3, x4), Zero, x5, x6) 130.57/78.25 new_primPlusNat2(Zero) 130.57/78.25 new_mkVBalBranch3MkVBalBranch221(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.25 new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Succ(x4), x5, x6) 130.57/78.25 new_mkVBalBranch3MkVBalBranch240(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Succ(Succ(x4))), x5, x6, x7, x8, Pos(Succ(Succ(x9))), x10, x11, x12) 130.57/78.25 new_addToFM_C3(Branch(Pos(Succ(x0)), x1, x2, x3, x4), Zero, x5, x6) 130.57/78.25 new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.25 new_primPlusNat6(x0, Succ(x1)) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Succ(Zero)), x3, x4), Branch(x5, x6, Pos(Succ(Succ(x7))), x8, x9), x10) 130.57/78.25 new_intersectFM_C2Lts0(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_splitLT11(x0, x1, x2, x3, x4) 130.57/78.25 new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, Succ(x4), x5, x6) 130.57/78.25 new_splitGT30(Neg(Zero), x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11) 130.57/78.25 new_mkBalBranch6MkBalBranch011(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9, x10, x11, x12, x13) 130.57/78.25 new_splitLT218(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) 130.57/78.25 new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9) 130.57/78.25 new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10) 130.57/78.25 new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10) 130.57/78.25 new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) 130.57/78.25 new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.25 new_intersectFM_C2Lts3(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10) 130.57/78.25 new_splitGT226(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) 130.57/78.25 new_splitLT15(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) 130.57/78.25 new_primPlusNat4(Zero) 130.57/78.25 new_primPlusNat2(Succ(x0)) 130.57/78.25 new_addToFM_C4(Branch(Pos(Zero), x0, x1, x2, x3), Zero, x4, x5) 130.57/78.25 new_mkVBalBranch3MkVBalBranch223(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13) 130.57/78.25 new_mkBalBranch6MkBalBranch41(x0, x1, x2, x3, Succ(x4), x5, x6) 130.57/78.25 new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.25 new_primPlusNat1(Succ(x0)) 130.57/78.25 new_splitGT16(Branch(x0, x1, x2, x3, x4), x5, x6) 130.57/78.25 new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10) 130.57/78.25 new_splitLT212(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11) 130.57/78.25 new_splitLT29(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12) 130.57/78.25 new_splitGT219(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_primMulNat8(Zero) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10) 130.57/78.25 new_mkBalBranch(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_splitLT218(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Succ(Succ(x4))), x5, x6, x7, x8, Neg(Succ(Succ(Succ(x9)))), x10, x11, x12) 130.57/78.25 new_addToFM_C25(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.25 new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.25 new_primPlusInt2(Neg(x0), x1, x2, x3, x4, x5, x6) 130.57/78.25 new_splitLT19(Branch(Pos(Zero), x0, x1, x2, x3), x4) 130.57/78.25 new_intersectFM_C2Lts5(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, Succ(x4), x5, x6, x7) 130.57/78.25 new_splitGT226(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10) 130.57/78.25 new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Zero), x4, x5, x6, x7, Neg(Succ(x8)), x9, x10, x11) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Zero), x4, x5, x6, x7, Pos(Succ(x8)), x9, x10, x11) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Succ(Succ(x3))), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Succ(x8)))), x9, x10), x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10) 130.57/78.25 new_addToFM2(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.25 new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9) 130.57/78.25 new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10) 130.57/78.25 new_addToFM_C13(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Succ(Succ(x4))), x5, x6, x7, x8, Neg(Succ(Succ(Zero))), x9, x10, x11) 130.57/78.25 new_addToFM_C13(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8) 130.57/78.25 new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8) 130.57/78.25 new_intersectFM_C2Gts2(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13) 130.57/78.25 new_mkBalBranch6MkBalBranch42(EmptyFM, x0, x1, x2, x3, x4) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10) 130.57/78.25 new_mkVBalBranch3MkVBalBranch227(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, Neg(Zero), x9, x10), x11) 130.57/78.25 new_primPlusNat8(Succ(x0), x1) 130.57/78.25 new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7) 130.57/78.25 new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.25 new_splitGT220(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Succ(x4), x5, x6, x7) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10) 130.57/78.25 new_splitLT15(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) 130.57/78.25 new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13) 130.57/78.25 new_mkVBalBranch3MkVBalBranch227(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12) 130.57/78.25 new_splitGT9(x0) 130.57/78.25 new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7) 130.57/78.25 new_primPlusNat4(Succ(x0)) 130.57/78.25 new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, Zero, x4, x5, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, Pos(x8), x9, x10), x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch241(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.25 new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7) 130.57/78.25 new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7) 130.57/78.25 new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Zero, Succ(x4), x5, x6) 130.57/78.25 new_primPlusNat7(x0, Succ(x1)) 130.57/78.25 new_addToFM_C13(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8) 130.57/78.25 new_mkVBalBranch9(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9, x10, x11) 130.57/78.25 new_addToFM_C11(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7) 130.57/78.25 new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14) 130.57/78.25 new_splitGT213(x0, x1, x2, x3, x4) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10) 130.57/78.25 new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch227(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11) 130.57/78.25 new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Succ(x4), Zero, x5, x6) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Succ(Zero)), x4, x5, x6, x7, Neg(Succ(Succ(Zero))), x8, x9, x10) 130.57/78.25 new_mkBalBranch6MkBalBranch1112(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10) 130.57/78.25 new_addToFM_C13(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9) 130.57/78.25 new_splitGT225(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(Succ(Zero))), x4, x5), Branch(x6, x7, Pos(Succ(Succ(Succ(Succ(x8))))), x9, x10), x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch129(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.25 new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, Zero, x4, x5) 130.57/78.25 new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13) 130.57/78.25 new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9) 130.57/78.25 new_splitGT18(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.25 new_splitLT13(Branch(Neg(Zero), x0, x1, x2, x3), x4, x5) 130.57/78.25 new_splitGT12(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Zero, Zero, x4, x5) 130.57/78.25 new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.25 new_addToFM_C3(Branch(Neg(Zero), x0, x1, x2, x3), Zero, x4, x5) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6) 130.57/78.25 new_primPlusNat5(Succ(x0)) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11) 130.57/78.25 new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Zero, Zero, x4, x5) 130.57/78.25 new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13) 130.57/78.25 new_mkVBalBranch8(x0, x1, x2, x3, x4, x5, x6, EmptyFM, x7) 130.57/78.25 new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.25 new_splitLT5(x0) 130.57/78.25 new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.25 new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.25 new_splitGT222(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) 130.57/78.25 new_mkBalBranch6MkBalBranch1112(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Succ(Succ(x4)))), x5, x6), Branch(x7, x8, Neg(Succ(Succ(Succ(Succ(Zero))))), x9, x10), x11) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Zero)), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Succ(Succ(Succ(Succ(x8))))))), x9, x10), x11) 130.57/78.25 new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.25 new_addToFM_C4(Branch(Pos(Zero), x0, x1, x2, x3), Succ(x4), x5, x6) 130.57/78.25 new_splitGT222(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Zero), x4, x5, x6, x7, Neg(Succ(x8)), x9, x10, x11) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11) 130.57/78.25 new_mkVBalBranch10(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9, x10, x11) 130.57/78.25 new_intersectFM_C2Gts(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Succ(Zero)), x4, x5) 130.57/78.25 new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), x12, x13) 130.57/78.25 new_addToFM_C3(EmptyFM, x0, x1, x2) 130.57/78.25 new_emptyFM(x0) 130.57/78.25 new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10) 130.57/78.25 new_sizeFM(EmptyFM, x0, x1) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(Zero)), x4, x5), Branch(x6, x7, Pos(Succ(Succ(Succ(Succ(Zero))))), x8, x9), x10) 130.57/78.25 new_splitLT17(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Zero)), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Succ(Succ(Zero))))), x8, x9), x10) 130.57/78.25 new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14) 130.57/78.25 new_splitLT217(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_splitLT218(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) 130.57/78.25 new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.25 new_addToFM_C14(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6, x7, x8, Pos(x9), x10, x11, x12) 130.57/78.25 new_splitLT214(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_splitGT43(x0) 130.57/78.25 new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_splitGT230(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, Neg(Zero), x9, x10), x11) 130.57/78.25 new_splitLT211(x0, x1, x2, x3, x4) 130.57/78.25 new_splitLT6(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14) 130.57/78.25 new_splitLT212(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) 130.57/78.25 new_mkVBalBranch8(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), x12) 130.57/78.25 new_splitLT216(Pos(Zero), x0, x1, x2, x3, x4) 130.57/78.25 new_primMulNat5 130.57/78.25 new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Zero, Succ(x4), x5, x6) 130.57/78.25 new_splitGT214(x0, x1, x2, x3, x4) 130.57/78.25 new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9) 130.57/78.25 new_addToFM_C26(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.25 new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8) 130.57/78.25 new_splitGT222(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) 130.57/78.25 new_intersectFM_C2Lts(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Zero, x4, x5, x6) 130.57/78.25 new_addToFM_C12(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.25 new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) 130.57/78.25 new_splitGT222(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) 130.57/78.25 new_primPlusNat3(Succ(x0)) 130.57/78.25 new_splitGT11(EmptyFM, x0) 130.57/78.25 new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11) 130.57/78.25 new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6) 130.57/78.25 new_splitGT16(EmptyFM, x0, x1) 130.57/78.25 new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7) 130.57/78.25 new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.25 new_addToFM(x0, x1, x2) 130.57/78.25 new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10) 130.57/78.25 new_addToFM_C11(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9) 130.57/78.25 new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13) 130.57/78.25 new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Succ(x4), Zero, x5, x6) 130.57/78.25 new_addToFM_C4(Branch(Neg(x0), x1, x2, x3, x4), Succ(x5), x6, x7) 130.57/78.25 new_primPlusNat3(Zero) 130.57/78.25 new_intersectFM_C2Gts0(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, Neg(Succ(x9)), x10, x11), x12) 130.57/78.25 new_splitGT11(Branch(Neg(Succ(x0)), x1, x2, x3, x4), x5) 130.57/78.25 new_splitGT224(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_splitLT16(x0, x1) 130.57/78.25 new_mkVBalBranch3MkVBalBranch133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13) 130.57/78.25 new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10) 130.57/78.25 new_splitGT223(Neg(Succ(x0)), x1, x2, x3, x4, x5) 130.57/78.25 new_mkVBalBranch3MkVBalBranch239(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11) 130.57/78.25 new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7) 130.57/78.25 new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, Neg(Succ(Zero)), x8, x9), x10) 130.57/78.25 new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Neg(Zero), x4, x5) 130.57/78.25 new_primMulNat0(x0) 130.57/78.25 new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_splitGT19(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, Neg(Succ(x9)), x10, x11), x12) 130.57/78.25 new_splitGT225(Neg(x0), x1, x2, x3, x4, x5, x6) 130.57/78.25 new_mkVBalBranch3MkVBalBranch131(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13) 130.57/78.25 new_splitGT223(Pos(Succ(x0)), x1, x2, x3, x4, x5) 130.57/78.25 new_splitLT13(EmptyFM, x0, x1) 130.57/78.25 new_mkVBalBranch3MkVBalBranch127(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.25 new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Zero), x4, x5) 130.57/78.25 new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6) 130.57/78.25 new_primMinusNat0(Succ(x0), Zero) 130.57/78.25 new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7) 130.57/78.25 new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7) 130.57/78.25 new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch125(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Succ(x4)), x5, x6, x7, x8, Neg(Zero), x9, x10, x11) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(Succ(x4))), x5, x6), Branch(x7, x8, Pos(Succ(Succ(Succ(Zero)))), x9, x10), x11) 130.57/78.25 new_splitLT42(x0, x1) 130.57/78.25 new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10) 130.57/78.25 new_intersectFM_C2Gts4(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7) 130.57/78.25 new_addToFM_C3(Branch(Pos(x0), x1, x2, x3, x4), Succ(x5), x6, x7) 130.57/78.25 new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12) 130.57/78.25 new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Succ(x4)), x5, x6, x7, x8, Pos(Zero), x9, x10, x11) 130.57/78.25 new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Succ(Succ(x3))), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Zero))), x8, x9), x10) 130.57/78.25 new_splitGT227(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.25 new_mkVBalBranch3MkVBalBranch126(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13) 130.57/78.25 new_splitGT15(EmptyFM, x0) 130.57/78.25 new_splitLT15(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) 130.57/78.25 new_mkVBalBranch3MkVBalBranch130(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6, x7, x8, Neg(Succ(Zero)), x9, x10, x11) 130.57/78.25 new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12) 130.57/78.25 new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11) 130.57/78.25 new_splitLT221(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_splitGT228(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch239(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12) 130.57/78.25 new_splitLT14(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_splitGT217(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9) 130.57/78.25 new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10) 130.57/78.25 new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10) 130.57/78.25 new_primMulNat4 130.57/78.25 new_mkVBalBranch7(x0, EmptyFM, x1, x2) 130.57/78.25 new_splitGT11(Branch(Pos(Zero), x0, x1, x2, x3), x4) 130.57/78.25 new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Zero, x4, x5) 130.57/78.25 new_splitLT19(EmptyFM, x0) 130.57/78.25 new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10) 130.57/78.25 new_primPlusNat5(Zero) 130.57/78.25 new_primMinusNat0(Zero, Succ(x0)) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Succ(x4)), x5, x6, x7, x8, Pos(Succ(Zero)), x9, x10, x11) 130.57/78.25 new_primPlusInt0(x0, Pos(x1)) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Zero)), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), x8, x9), x10) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Succ(x4))), x5, x6), Branch(x7, x8, Neg(Succ(Succ(Succ(Zero)))), x9, x10), x11) 130.57/78.25 new_splitLT29(Neg(x0), x1, x2, EmptyFM, x3, x4, x5) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, Pos(Succ(Zero)), x8, x9), x10) 130.57/78.25 new_mkVBalBranch3MkVBalBranch223(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12) 130.57/78.25 new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7) 130.57/78.25 new_primPlusNat0(Zero, Zero) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Succ(x4)), x5, x6, x7, x8, Neg(Succ(x9)), x10, x11, x12) 130.57/78.25 new_mkVBalBranch10(x0, x1, EmptyFM, x2, x3, x4, x5, x6) 130.57/78.25 new_splitGT221(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.25 new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12) 130.57/78.25 new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14) 130.57/78.25 new_mkBalBranch6MkBalBranch011(x0, x1, x2, EmptyFM, x3, x4, x5, x6, x7, x8) 130.57/78.25 new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10) 130.57/78.25 new_primPlusNat1(Zero) 130.57/78.25 new_primPlusInt(Neg(x0), x1, x2, x3, x4, x5) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Succ(x4))), x5, x6), Branch(x7, x8, Neg(Succ(Succ(Zero))), x9, x10), x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch131(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12) 130.57/78.25 new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13) 130.57/78.25 new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6) 130.57/78.25 new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13) 130.57/78.25 new_splitLT210(x0, x1, x2, x3, x4) 130.57/78.25 new_addToFM_C4(EmptyFM, x0, x1, x2) 130.57/78.25 new_mkVBalBranch3MkVBalBranch126(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13) 130.57/78.25 new_mkVBalBranch3MkVBalBranch130(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9) 130.57/78.25 new_splitGT30(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6) 130.57/78.25 new_splitLT19(Branch(Neg(Succ(x0)), x1, x2, x3, x4), x5) 130.57/78.25 new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, x4, Succ(x5), x6, x7) 130.57/78.25 new_splitLT19(Branch(Pos(Succ(x0)), x1, x2, x3, x4), x5) 130.57/78.25 new_primPlusInt(Pos(x0), x1, x2, x3, x4, x5) 130.57/78.25 new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10) 130.57/78.25 new_splitGT223(Neg(Zero), x0, x1, x2, x3, x4) 130.57/78.25 new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6) 130.57/78.25 new_addToFM_C3(Branch(Neg(Succ(x0)), x1, x2, x3, x4), Succ(x5), x6, x7) 130.57/78.25 new_splitLT212(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, Succ(x4), x5, x6) 130.57/78.25 new_splitGT12(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) 130.57/78.25 new_splitGT13(Branch(x0, x1, x2, x3, x4), x5, x6) 130.57/78.25 new_mkVBalBranch3MkVBalBranch225(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, Pos(Succ(Zero)), x9, x10), x11) 130.57/78.25 new_splitGT13(EmptyFM, x0, x1) 130.57/78.25 new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13) 130.57/78.25 new_primPlusInt0(x0, Neg(x1)) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Succ(Zero)), x3, x4), Branch(x5, x6, Neg(Succ(Succ(Succ(x7)))), x8, x9), x10) 130.57/78.25 new_splitLT17(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) 130.57/78.25 new_primMulNat6 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(Zero)), x4, x5), Branch(x6, x7, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x8, x9), x10) 130.57/78.25 new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.25 new_mkVBalBranch3MkVBalBranch154(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.25 new_mkVBalBranch3MkVBalBranch239(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13) 130.57/78.25 new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_mkVBalBranch3MkVBalBranch231(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7) 130.57/78.25 new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Zero)), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Succ(Zero)))), x8, x9), x10) 130.57/78.25 new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, Zero, x4, x5) 130.57/78.25 new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.25 new_intersectFM_C2Gts6(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkVBalBranch3MkVBalBranch231(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12) 130.57/78.25 new_mkVBalBranch3MkVBalBranch233(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.25 new_splitLT17(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) 130.57/78.25 new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, EmptyFM, x7, x8) 130.57/78.25 new_mkVBalBranch3MkVBalBranch227(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13) 130.57/78.25 new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9) 130.57/78.25 new_primMulNat2(x0) 130.57/78.25 new_primPlusNat0(Succ(x0), Zero) 130.57/78.25 new_mkBalBranch6MkBalBranch31(x0, x1, x2, EmptyFM, x3, x4) 130.57/78.25 new_splitGT215(x0, x1, x2, x3, x4) 130.57/78.25 new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Succ(Succ(Succ(x4)))), x5, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch119(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.25 new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, Succ(x4), x5, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10) 130.57/78.25 new_splitLT29(Pos(Zero), x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7) 130.57/78.25 new_mkVBalBranch3MkVBalBranch126(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12) 130.57/78.25 new_mkVBalBranch11(x0, x1, EmptyFM, x2, x3, x4, x5, x6, x7) 130.57/78.25 new_splitGT229(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11) 130.57/78.25 new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11) 130.57/78.25 new_addToFM_C3(Branch(Neg(Zero), x0, x1, x2, x3), Succ(x4), x5, x6) 130.57/78.25 new_splitGT225(Pos(Zero), x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkBranch(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, Pos(Zero), x9, x10), x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch232(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.25 new_addToFM_C24(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10) 130.57/78.25 new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, x4, Zero, x5, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10) 130.57/78.25 new_splitLT215(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_splitGT7(x0) 130.57/78.25 new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.25 new_intersectFM_C2Gts7(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Succ(Zero)), x4, x5), Branch(x6, x7, Pos(Succ(Succ(x8))), x9, x10), x11) 130.57/78.25 new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) 130.57/78.25 new_addToFM_C24(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7) 130.57/78.25 new_splitLT219(x0, x1, x2, x3, x4) 130.57/78.25 new_splitLT212(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) 130.57/78.25 new_splitGT12(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) 130.57/78.25 new_splitLT8(x0, x1, x2, x3, x4) 130.57/78.25 new_intersectFM_C2Lts1(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.25 new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Zero, x4, x5) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, Pos(Succ(Zero)), x9, x10), x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12) 130.57/78.25 new_addToFM_C11(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Succ(Succ(x4))), x5, x6), Branch(x7, x8, Pos(Succ(Succ(x9))), x10, x11), x12) 130.57/78.25 new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13) 130.57/78.25 new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch129(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(Zero)), x4, x5), Branch(x6, x7, Pos(Succ(Succ(Succ(Succ(Succ(Succ(x8))))))), x9, x10), x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12) 130.57/78.25 new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, Neg(Zero), x9, x10), x11) 130.57/78.25 new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) 130.57/78.25 new_splitLT7(x0, x1, x2, x3, x4) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Succ(Succ(x4)))), x5, x6), Branch(x7, x8, Neg(Succ(Succ(Succ(Succ(Succ(x9)))))), x10, x11), x12) 130.57/78.25 new_splitLT220(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkVBalBranch9(x0, x1, EmptyFM, x2, x3, x4, x5, x6) 130.57/78.25 new_splitGT11(Branch(Pos(Succ(x0)), x1, x2, x3, x4), x5) 130.57/78.25 new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_splitLT17(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch33(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.25 new_mkVBalBranch12(x0, x1, EmptyFM, x2, x3, x4, x5, x6, x7) 130.57/78.25 new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.25 new_intersectFM_C2Gts8(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(Zero)), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Zero))), x8, x9), x10) 130.57/78.25 new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12) 130.57/78.25 new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(Succ(x4))), x5, x6), Branch(x7, x8, Pos(Succ(Succ(Zero))), x9, x10), x11) 130.57/78.25 new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9) 130.57/78.25 new_mkVBalBranch3MkVBalBranch126(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14) 130.57/78.25 new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Succ(Succ(Zero))), x4, x5) 130.57/78.25 new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10) 130.57/78.25 new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9) 130.57/78.25 new_splitGT42(x0, x1) 130.57/78.25 new_addToFM_C11(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8) 130.57/78.25 new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13) 130.57/78.25 new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10) 130.57/78.25 new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.25 new_primPlusNat7(x0, Zero) 130.57/78.25 new_intersectFM_C2Lts4(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_splitLT12(Branch(x0, x1, x2, x3, x4), x5, x6) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Succ(Succ(x3))), x4, x5), Branch(x6, x7, Pos(Succ(Succ(x8))), x9, x10), x11) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, Neg(Succ(Zero)), x9, x10), x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch231(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10) 130.57/78.25 new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10) 130.57/78.25 new_mkVBalBranch3MkVBalBranch239(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12) 130.57/78.25 new_splitLT40(x0) 130.57/78.25 new_splitLT9(EmptyFM, x0) 130.57/78.25 new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10) 130.57/78.25 new_splitLT15(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) 130.57/78.25 new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9) 130.57/78.25 new_splitGT226(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) 130.57/78.25 new_splitGT11(Branch(Neg(Zero), x0, x1, x2, x3), x4) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, Pos(x9), x10, x11), x12) 130.57/78.25 new_splitGT223(Pos(Zero), x0, x1, x2, x3, x4) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, Neg(Zero), x9, x10), x11) 130.57/78.25 new_addToFM0(x0, x1, x2) 130.57/78.25 new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch242(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.25 new_mkBalBranch6MkBalBranch42(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8, x9) 130.57/78.25 new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch127(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11) 130.57/78.25 new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10) 130.57/78.25 new_addToFM_C4(Branch(Neg(Zero), x0, x1, x2, x3), Zero, x4, x5) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Succ(Succ(x4))), x5, x6), Branch(x7, x8, Neg(Succ(Succ(Zero))), x9, x10), x11) 130.57/78.25 new_splitGT216(x0, x1, x2, x3, x4) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Succ(Zero)), x4, x5), Branch(x6, x7, Neg(Succ(Succ(Succ(x8)))), x9, x10), x11) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Zero), x4, x5, x6, x7, Pos(Succ(x8)), x9, x10, x11) 130.57/78.25 new_addToFM_C4(Branch(Pos(Succ(x0)), x1, x2, x3, x4), Succ(x5), x6, x7) 130.57/78.25 new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.25 new_primPlusNat6(x0, Zero) 130.57/78.25 new_primMulNat(Succ(x0)) 130.57/78.25 new_intersectFM_C2Gts5(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10) 130.57/78.25 new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.25 new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10) 130.57/78.25 new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12) 130.57/78.25 new_splitLT29(Neg(x0), x1, x2, Branch(x3, x4, x5, x6, x7), EmptyFM, x8, x9) 130.57/78.25 new_splitLT13(Branch(Pos(x0), x1, x2, x3, x4), x5, x6) 130.57/78.25 new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12) 130.57/78.25 new_splitLT29(Neg(x0), x1, x2, Branch(x3, x4, x5, x6, x7), Branch(x8, x9, x10, x11, x12), x13, x14) 130.57/78.25 new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch238(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12, x13) 130.57/78.25 new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(Zero)), x4, x5), Branch(x6, x7, Pos(Succ(Succ(Succ(Zero)))), x8, x9), x10) 130.57/78.25 new_splitGT40(x0) 130.57/78.25 new_intersectFM_C2Gts1(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Pos(Succ(Zero)), x4, x5, x6, x7, Pos(Succ(Succ(x8))), x9, x10, x11) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10) 130.57/78.25 new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11) 130.57/78.25 new_mkVBalBranch5(x0, x1, Branch(x2, x3, Pos(Succ(Zero)), x4, x5), Branch(x6, x7, Pos(Succ(Succ(Zero))), x8, x9), x10) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Succ(Succ(x4))), x5, x6), Branch(x7, x8, Neg(Succ(Succ(Succ(x9)))), x10, x11), x12) 130.57/78.25 new_splitLT31(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_splitLT9(Branch(x0, x1, x2, x3, x4), x5) 130.57/78.25 new_splitLT13(Branch(Neg(Succ(x0)), x1, x2, x3, x4), x5, x6) 130.57/78.25 new_splitGT17(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10) 130.57/78.25 new_primMinusNat0(Succ(x0), Succ(x1)) 130.57/78.25 new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, Neg(Succ(Zero)), x9, x10), x11) 130.57/78.25 new_primMulNat(Zero) 130.57/78.25 new_splitGT226(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) 130.57/78.25 new_splitGT41(x0, x1) 130.57/78.25 new_splitGT218(x0, x1, x2, x3, x4, x5, x6) 130.57/78.25 new_addToFM1(x0, x1, x2, x3) 130.57/78.25 new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Succ(Zero)), x4, x5, x6, x7, Neg(Succ(Succ(Succ(x8)))), x9, x10, x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10) 130.57/78.25 new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13) 130.57/78.25 new_intersectFM_C2Lts7(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, x4, x5, x6, x7) 130.57/78.25 new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13) 130.57/78.25 new_mkVBalBranch3MkVBalBranch125(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10) 130.57/78.25 new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Succ(x4), x5, x6) 130.57/78.25 new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11) 130.57/78.25 new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.25 new_mkVBalBranch3MkVBalBranch130(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13) 130.57/78.25 new_splitGT8(x0, x1) 130.57/78.25 new_splitLT222(x0, x1, x2, x3, x4) 130.57/78.25 new_mkVBalBranch3MkVBalBranch128(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 130.57/78.25 new_addToFM_C3(Branch(Pos(Zero), x0, x1, x2, x3), Zero, x4, x5) 130.57/78.25 new_splitLT216(Pos(Succ(x0)), x1, x2, x3, x4, x5) 130.57/78.25 new_mkVBalBranch30(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6, x7, x8, Neg(Zero), x9, x10, x11) 130.57/78.25 new_splitLT12(EmptyFM, x0, x1) 130.57/78.25 new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, Zero, x4, x5) 130.57/78.25 new_intersectFM_C2Gts3(x0, x1, x2, x3, x4, x5) 130.57/78.25 new_mkVBalBranch11(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9, x10, x11, x12) 130.57/78.25 new_mkVBalBranch6(x0, x1, EmptyFM, x2, x3) 130.57/78.25 130.57/78.25 We have to consider all minimal (P,Q,R)-chains. 130.57/78.25 ---------------------------------------- 130.57/78.25 130.57/78.25 (53) QDPSizeChangeProof (EQUIVALENT) 130.57/78.25 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. 130.57/78.25 130.57/78.25 From the DPs we obtained the following set of size-change graphs: 130.57/78.25 *new_intersectFM_C2IntersectFM_C135(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, ed, ee) -> new_intersectFM_C2IntersectFM_C133(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, Succ(zzz2153), Succ(zzz2148), ed, ee) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 16 >= 18, 17 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C133(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, Succ(zzz26420), Succ(zzz26430), ef, eg) -> new_intersectFM_C2IntersectFM_C133(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, zzz26420, zzz26430, ef, eg) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 16 > 16, 17 > 17, 18 >= 18, 19 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, Zero, Zero, ed, ee) -> new_intersectFM_C2IntersectFM_C135(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, ed, ee) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 18 >= 16, 19 >= 17 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, Succ(zzz21580), Zero, ed, ee) -> new_intersectFM_C2IntersectFM_C133(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, Succ(zzz2153), Succ(zzz2148), ed, ee) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 18 >= 18, 19 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Neg(Succ(zzz3000)), zzz31, zzz32, zzz33, zzz34), Branch(Neg(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C19(zzz3000, zzz31, zzz32, zzz33, zzz34, zzz4000, zzz41, zzz42, zzz43, zzz44, zzz3000, zzz31, zzz32, zzz33, zzz34, zzz3000, zzz4000, bd, bd) 130.57/78.25 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 > 6, 2 > 7, 2 > 8, 2 > 9, 2 > 10, 1 > 11, 1 > 12, 1 > 13, 1 > 14, 1 > 15, 1 > 16, 2 > 17, 3 >= 18, 3 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Neg(Succ(zzz3000)), zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C113(zzz3000, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, bd, bd) 130.57/78.25 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 > 6, 2 > 7, 2 > 8, 2 > 9, 1 > 10, 1 > 11, 1 > 12, 1 > 13, 1 > 14, 3 >= 15, 3 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Pos(Succ(zzz160300)), zzz1604, zzz1605, Branch(zzz16060, zzz16061, zzz16062, zzz16063, zzz16064), zzz1607, gc, gd) -> new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz16060, zzz16061, zzz16062, zzz16063, zzz16064, gc, gd) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 13 > 10, 13 > 11, 13 > 12, 13 > 13, 13 > 14, 15 >= 15, 16 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C144(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Branch(zzz16060, zzz16061, zzz16062, zzz16063, zzz16064), gc, gd) -> new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz16060, zzz16061, zzz16062, zzz16063, zzz16064, gc, gd) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 > 10, 10 > 11, 10 > 12, 10 > 13, 10 > 14, 11 >= 15, 12 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Pos(Succ(zzz3000)), zzz31, zzz32, EmptyFM, zzz34), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C111(zzz3000, zzz31, zzz32, EmptyFM, zzz34, zzz41, zzz42, zzz43, zzz44, bd, bd) 130.57/78.25 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 > 6, 2 > 7, 2 > 8, 2 > 9, 3 >= 10, 3 >= 11 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Pos(Zero), zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(Pos(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C14(zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz4000, zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, bd, bd) 130.57/78.25 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 2 > 5, 2 > 6, 2 > 7, 2 > 8, 2 > 9, 1 > 10, 1 > 11, 1 > 12, 1 > 13, 1 > 14, 3 >= 15, 3 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, Neg(zzz27430), zzz2744, zzz2745, zzz2746, Branch(zzz27470, zzz27471, zzz27472, zzz27473, zzz27474), be, bf) -> new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, zzz27470, zzz27471, zzz27472, zzz27473, zzz27474, be, bf) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 14 > 10, 14 > 11, 14 > 12, 14 > 13, 14 > 14, 15 >= 15, 16 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C115(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, Branch(zzz27470, zzz27471, zzz27472, zzz27473, zzz27474), be, bf) -> new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, zzz27470, zzz27471, zzz27472, zzz27473, zzz27474, be, bf) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 > 10, 10 > 11, 10 > 12, 10 > 13, 10 > 14, 11 >= 15, 12 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, Branch(Neg(Succ(zzz2156000)), zzz21561, zzz21562, zzz21563, zzz21564), ed, ee) -> new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2156000, zzz21561, zzz21562, zzz21563, zzz21564, zzz2156000, zzz2148, ed, ee) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 > 11, 11 > 12, 11 > 13, 11 > 14, 11 > 15, 11 > 16, 6 >= 17, 12 >= 18, 13 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Neg(Zero), zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(Neg(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C110(zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz4000, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, bd, bd) 130.57/78.25 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 2 > 5, 2 > 6, 2 > 7, 2 > 8, 2 > 9, 1 > 10, 1 > 11, 1 > 12, 1 > 13, 1 > 14, 3 >= 15, 3 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, Pos(zzz8930), zzz894, zzz895, Branch(zzz8960, zzz8961, zzz8962, zzz8963, zzz8964), zzz897, eh, fa) -> new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz8960, zzz8961, zzz8962, zzz8963, zzz8964, eh, fa) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 13 > 10, 13 > 11, 13 > 12, 13 > 13, 13 > 14, 15 >= 15, 16 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C138(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, Branch(zzz8960, zzz8961, zzz8962, zzz8963, zzz8964), eh, fa) -> new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz8960, zzz8961, zzz8962, zzz8963, zzz8964, eh, fa) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 > 10, 10 > 11, 10 > 12, 10 > 13, 10 > 14, 11 >= 15, 12 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, Neg(Zero), zzz894, zzz895, zzz896, zzz897, eh, fa) -> new_intersectFM_C2IntersectFM_C138(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz896, eh, fa) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 13 >= 10, 15 >= 11, 16 >= 12 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, Neg(Succ(zzz89300)), zzz894, zzz895, zzz896, zzz897, eh, fa) -> new_intersectFM_C2IntersectFM_C137(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz89300, zzz894, zzz895, zzz896, zzz897, zzz89300, zzz888, eh, fa) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 > 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 10 > 15, 5 >= 16, 15 >= 17, 16 >= 18 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Pos(Succ(zzz3000)), zzz31, zzz32, zzz33, zzz34), Branch(Pos(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C1(zzz3000, zzz31, zzz32, zzz33, zzz34, zzz4000, zzz41, zzz42, zzz43, zzz44, zzz3000, zzz31, zzz32, zzz33, zzz34, zzz4000, zzz3000, bd, bd) 130.57/78.25 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 > 6, 2 > 7, 2 > 8, 2 > 9, 2 > 10, 1 > 11, 1 > 12, 1 > 13, 1 > 14, 1 > 15, 2 > 16, 1 > 17, 3 >= 18, 3 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, Branch(Pos(Succ(zzz2091000)), zzz20911, zzz20912, zzz20913, zzz20914), h, ba) -> new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2091000, zzz20911, zzz20912, zzz20913, zzz20914, zzz2083, zzz2091000, h, ba) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 > 11, 11 > 12, 11 > 13, 11 > 14, 11 > 15, 6 >= 16, 11 > 17, 12 >= 18, 13 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Pos(Succ(zzz90800)), zzz909, zzz910, EmptyFM, zzz912, ga, gb) -> new_intersectFM_C2IntersectFM_C111(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, ga, gb) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 15 >= 10, 16 >= 11 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C142(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, EmptyFM, ga, gb) -> new_intersectFM_C2IntersectFM_C111(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, ga, gb) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 11 >= 10, 12 >= 11 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Pos(Succ(zzz3000)), zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C112(zzz3000, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, bd, bd) 130.57/78.25 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 > 6, 2 > 7, 2 > 8, 2 > 9, 1 > 10, 1 > 11, 1 > 12, 1 > 13, 1 > 14, 3 >= 15, 3 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Pos(Succ(zzz90800)), zzz909, zzz910, Branch(zzz9110, zzz9111, zzz9112, zzz9113, zzz9114), zzz912, ga, gb) -> new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz9110, zzz9111, zzz9112, zzz9113, zzz9114, ga, gb) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 13 > 10, 13 > 11, 13 > 12, 13 > 13, 13 > 14, 15 >= 15, 16 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C142(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Branch(zzz9110, zzz9111, zzz9112, zzz9113, zzz9114), ga, gb) -> new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz9110, zzz9111, zzz9112, zzz9113, zzz9114, ga, gb) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 > 10, 10 > 11, 10 > 12, 10 > 13, 10 > 14, 11 >= 15, 12 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Neg(zzz300), zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(Pos(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C15(zzz300, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz4000, zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, bd, bd) 130.57/78.25 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 > 6, 2 > 7, 2 > 8, 2 > 9, 2 > 10, 1 > 11, 1 > 12, 1 > 13, 1 > 14, 1 > 15, 3 >= 16, 3 >= 17 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, Neg(zzz13920), zzz1393, zzz1394, zzz1395, Branch(zzz13960, zzz13961, zzz13962, zzz13963, zzz13964), cc, cd) -> new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, zzz13960, zzz13961, zzz13962, zzz13963, zzz13964, cc, cd) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 15 > 11, 15 > 12, 15 > 13, 15 > 14, 15 > 15, 16 >= 16, 17 >= 17 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C120(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, Branch(zzz13960, zzz13961, zzz13962, zzz13963, zzz13964), cc, cd) -> new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, zzz13960, zzz13961, zzz13962, zzz13963, zzz13964, cc, cd) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 > 11, 11 > 12, 11 > 13, 11 > 14, 11 > 15, 12 >= 16, 13 >= 17 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, Pos(Zero), zzz1393, zzz1394, zzz1395, zzz1396, cc, cd) -> new_intersectFM_C2IntersectFM_C120(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, zzz1396, cc, cd) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 15 >= 11, 16 >= 12, 17 >= 13 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, Pos(Succ(zzz139200)), zzz1393, zzz1394, zzz1395, zzz1396, cc, cd) -> new_intersectFM_C2IntersectFM_C119(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, zzz139200, zzz1393, zzz1394, zzz1395, zzz1396, zzz1387, zzz139200, cc, cd) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 > 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 6 >= 16, 11 > 17, 16 >= 18, 17 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Pos(zzz300), zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(Neg(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C18(zzz300, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz4000, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, bd, bd) 130.57/78.25 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 > 6, 2 > 7, 2 > 8, 2 > 9, 2 > 10, 1 > 11, 1 > 12, 1 > 13, 1 > 14, 1 > 15, 3 >= 16, 3 >= 17 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, Pos(zzz7520), zzz753, zzz754, Branch(zzz7550, zzz7551, zzz7552, zzz7553, zzz7554), zzz756, df, dg) -> new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, zzz7550, zzz7551, zzz7552, zzz7553, zzz7554, df, dg) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 14 > 11, 14 > 12, 14 > 13, 14 > 14, 14 > 15, 16 >= 16, 17 >= 17 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C129(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, Branch(zzz7550, zzz7551, zzz7552, zzz7553, zzz7554), df, dg) -> new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, zzz7550, zzz7551, zzz7552, zzz7553, zzz7554, df, dg) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 > 11, 11 > 12, 11 > 13, 11 > 14, 11 > 15, 12 >= 16, 13 >= 17 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, Neg(Zero), zzz753, zzz754, zzz755, zzz756, df, dg) -> new_intersectFM_C2IntersectFM_C129(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, zzz755, df, dg) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 14 >= 11, 16 >= 12, 17 >= 13 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, Neg(Succ(zzz75200)), zzz753, zzz754, zzz755, zzz756, df, dg) -> new_intersectFM_C2IntersectFM_C128(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, zzz75200, zzz753, zzz754, zzz755, zzz756, zzz75200, zzz747, df, dg) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 > 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 11 > 16, 6 >= 17, 16 >= 18, 17 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Neg(Succ(zzz3000)), zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C17(zzz3000, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, bd, bd) 130.57/78.25 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 > 6, 2 > 7, 2 > 8, 2 > 9, 1 > 10, 1 > 11, 1 > 12, 1 > 13, 1 > 14, 3 >= 15, 3 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Pos(Succ(zzz3000)), zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C2IntersectFM_C16(zzz3000, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, bd, bd) 130.57/78.25 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 > 6, 2 > 7, 2 > 8, 2 > 9, 1 > 10, 1 > 11, 1 > 12, 1 > 13, 1 > 14, 3 >= 15, 3 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Pos(Succ(zzz120100)), zzz1202, zzz1203, Branch(zzz12040, zzz12041, zzz12042, zzz12043, zzz12044), zzz1205, dd, de) -> new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, zzz12040, zzz12041, zzz12042, zzz12043, zzz12044, dd, de) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 13 > 10, 13 > 11, 13 > 12, 13 > 13, 13 > 14, 15 >= 15, 16 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C126(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Branch(zzz12040, zzz12041, zzz12042, zzz12043, zzz12044), dd, de) -> new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, zzz12040, zzz12041, zzz12042, zzz12043, zzz12044, dd, de) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 > 10, 10 > 11, 10 > 12, 10 > 13, 10 > 14, 11 >= 15, 12 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Neg(Zero), zzz1202, zzz1203, zzz1204, zzz1205, dd, de) -> new_intersectFM_C2IntersectFM_C127(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, zzz1202, dd, de) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 11 >= 10, 15 >= 11, 16 >= 12 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Neg(Succ(zzz120100)), zzz1202, zzz1203, zzz1204, zzz1205, dd, de) -> new_intersectFM_C2IntersectFM_C126(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, zzz1205, dd, de) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 14 >= 10, 15 >= 11, 16 >= 12 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Pos(Succ(zzz62700)), zzz628, zzz629, Branch(zzz6300, zzz6301, zzz6302, zzz6303, zzz6304), zzz631, db, dc) -> new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, db, dc) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 13 > 10, 13 > 11, 13 > 12, 13 > 13, 13 > 14, 15 >= 15, 16 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C124(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Branch(zzz6300, zzz6301, zzz6302, zzz6303, zzz6304), db, dc) -> new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, db, dc) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 > 10, 10 > 11, 10 > 12, 10 > 13, 10 > 14, 11 >= 15, 12 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Neg(Succ(zzz62700)), zzz628, zzz629, zzz630, zzz631, db, dc) -> new_intersectFM_C2IntersectFM_C124(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, zzz631, db, dc) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 14 >= 10, 15 >= 11, 16 >= 12 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Neg(Zero), zzz628, zzz629, zzz630, zzz631, db, dc) -> new_intersectFM_C2IntersectFM_C125(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, zzz628, db, dc) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 11 >= 10, 15 >= 11, 16 >= 12 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C128(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, Zero, Succ(zzz14140), dh, ea) -> new_intersectFM_C2IntersectFM_C129(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1411, dh, ea) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 14 >= 11, 18 >= 12, 19 >= 13 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C130(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, Succ(zzz27700), Zero, eb, ec) -> new_intersectFM_C2IntersectFM_C129(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2769, eb, ec) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 15 >= 11, 18 >= 12, 19 >= 13 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C128(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, Succ(zzz14130), Succ(zzz14140), dh, ea) -> new_intersectFM_C2IntersectFM_C128(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, zzz14130, zzz14140, dh, ea) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 16 > 16, 17 > 17, 18 >= 18, 19 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C130(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, Succ(zzz27700), Succ(zzz27710), eb, ec) -> new_intersectFM_C2IntersectFM_C130(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, zzz27700, zzz27710, eb, ec) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 16 > 16, 17 > 17, 18 >= 18, 19 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C128(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, Succ(zzz14130), Zero, dh, ea) -> new_intersectFM_C2IntersectFM_C130(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, Succ(zzz1408), Succ(zzz1403), dh, ea) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 18 >= 18, 19 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C128(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, Zero, Zero, dh, ea) -> new_intersectFM_C2IntersectFM_C131(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, dh, ea) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 18 >= 16, 19 >= 17 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C130(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, Zero, Zero, eb, ec) -> new_intersectFM_C2IntersectFM_C132(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, eb, ec) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 18 >= 16, 19 >= 17 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C131(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, dh, ea) -> new_intersectFM_C2IntersectFM_C130(zzz1398, zzz1399, zzz1400, zzz1401, zzz1402, zzz1403, zzz1404, zzz1405, zzz1406, zzz1407, zzz1408, zzz1409, zzz1410, zzz1411, zzz1412, Succ(zzz1408), Succ(zzz1403), dh, ea) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 16 >= 18, 17 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C119(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, Zero, Succ(zzz19930), ce, cf) -> new_intersectFM_C2IntersectFM_C120(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1990, ce, cf) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 14 >= 11, 18 >= 12, 19 >= 13 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C121(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, Succ(zzz31780), Zero, cg, da) -> new_intersectFM_C2IntersectFM_C120(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3177, cg, da) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 15 >= 11, 18 >= 12, 19 >= 13 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C119(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, Succ(zzz19920), Succ(zzz19930), ce, cf) -> new_intersectFM_C2IntersectFM_C119(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz19920, zzz19930, ce, cf) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 16 > 16, 17 > 17, 18 >= 18, 19 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C121(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, Succ(zzz31780), Succ(zzz31790), cg, da) -> new_intersectFM_C2IntersectFM_C121(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, zzz31780, zzz31790, cg, da) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 16 > 16, 17 > 17, 18 >= 18, 19 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C119(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, Succ(zzz19920), Zero, ce, cf) -> new_intersectFM_C2IntersectFM_C121(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, Succ(zzz1982), Succ(zzz1987), ce, cf) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 18 >= 18, 19 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C119(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, Zero, Zero, ce, cf) -> new_intersectFM_C2IntersectFM_C122(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, ce, cf) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 18 >= 16, 19 >= 17 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C121(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, Zero, Zero, cg, da) -> new_intersectFM_C2IntersectFM_C123(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, cg, da) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 18 >= 16, 19 >= 17 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C122(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, ce, cf) -> new_intersectFM_C2IntersectFM_C121(zzz1977, zzz1978, zzz1979, zzz1980, zzz1981, zzz1982, zzz1983, zzz1984, zzz1985, zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, Succ(zzz1982), Succ(zzz1987), ce, cf) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 16 >= 18, 17 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Neg(Succ(zzz90800)), zzz909, zzz910, zzz911, zzz912, ga, gb) -> new_intersectFM_C2IntersectFM_C142(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz912, ga, gb) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 14 >= 10, 15 >= 11, 16 >= 12 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Neg(Zero), zzz909, zzz910, zzz911, zzz912, ga, gb) -> new_intersectFM_C2IntersectFM_C143(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz909, ga, gb) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 11 >= 10, 15 >= 11, 16 >= 12 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C12(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, h, ba) -> new_intersectFM_C2IntersectFM_C10(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, Succ(zzz2083), Succ(zzz2088), h, ba) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 16 >= 18, 17 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, Zero, Zero, h, ba) -> new_intersectFM_C2IntersectFM_C12(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, h, ba) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 18 >= 16, 19 >= 17 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C10(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, Succ(zzz26240), Succ(zzz26250), bb, bc) -> new_intersectFM_C2IntersectFM_C10(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, zzz26240, zzz26250, bb, bc) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 16 > 16, 17 > 17, 18 >= 18, 19 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, Succ(zzz20930), Zero, h, ba) -> new_intersectFM_C2IntersectFM_C10(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, Succ(zzz2083), Succ(zzz2088), h, ba) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 18 >= 18, 19 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C10(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, Zero, Zero, bb, bc) -> new_intersectFM_C2IntersectFM_C13(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, bb, bc) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 18 >= 16, 19 >= 17 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C10(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, Succ(zzz26240), Zero, bb, bc) -> new_intersectFM_C2IntersectFM_C11(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2623, bb, bc) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 15 >= 11, 18 >= 12, 19 >= 13 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C137(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, Zero, Succ(zzz15920), fb, fc) -> new_intersectFM_C2IntersectFM_C138(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1589, fb, fc) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 13 >= 10, 17 >= 11, 18 >= 12 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C139(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, Succ(zzz28980), Zero, fd, ff) -> new_intersectFM_C2IntersectFM_C138(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2897, fd, ff) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 14 >= 10, 17 >= 11, 18 >= 12 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C137(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, Succ(zzz15910), Succ(zzz15920), fb, fc) -> new_intersectFM_C2IntersectFM_C137(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, zzz15910, zzz15920, fb, fc) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 > 15, 16 > 16, 17 >= 17, 18 >= 18 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C139(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, Succ(zzz28980), Succ(zzz28990), fd, ff) -> new_intersectFM_C2IntersectFM_C139(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, zzz28980, zzz28990, fd, ff) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 > 15, 16 > 16, 17 >= 17, 18 >= 18 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C137(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, Succ(zzz15910), Zero, fb, fc) -> new_intersectFM_C2IntersectFM_C139(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, Succ(zzz1586), Succ(zzz1581), fb, fc) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 17 >= 17, 18 >= 18 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C137(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, Zero, Zero, fb, fc) -> new_intersectFM_C2IntersectFM_C140(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, fb, fc) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 17 >= 15, 18 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C139(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, Zero, Zero, fd, ff) -> new_intersectFM_C2IntersectFM_C141(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, fd, ff) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 17 >= 15, 18 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C140(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, fb, fc) -> new_intersectFM_C2IntersectFM_C139(zzz1577, zzz1578, zzz1579, zzz1580, zzz1581, zzz1582, zzz1583, zzz1584, zzz1585, zzz1586, zzz1587, zzz1588, zzz1589, zzz1590, Succ(zzz1586), Succ(zzz1581), fb, fc) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 17, 16 >= 18 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C133(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, Succ(zzz26420), Zero, ef, eg) -> new_intersectFM_C2IntersectFM_C134(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2641, ef, eg) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 15 >= 11, 18 >= 12, 19 >= 13 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C133(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, Zero, Zero, ef, eg) -> new_intersectFM_C2IntersectFM_C136(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, ef, eg) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 18 >= 16, 19 >= 17 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, Pos(Succ(zzz274300)), zzz2744, zzz2745, zzz2746, zzz2747, be, bf) -> new_intersectFM_C2IntersectFM_C114(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, zzz274300, zzz2744, zzz2745, zzz2746, zzz2747, zzz2738, zzz274300, be, bf) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 > 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 5 >= 15, 10 > 16, 15 >= 17, 16 >= 18 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, Pos(Zero), zzz2744, zzz2745, zzz2746, zzz2747, be, bf) -> new_intersectFM_C2IntersectFM_C115(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, zzz2747, be, bf) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 14 >= 10, 15 >= 11, 16 >= 12 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C114(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, Succ(zzz30820), Succ(zzz30830), bg, bh) -> new_intersectFM_C2IntersectFM_C114(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, zzz30820, zzz30830, bg, bh) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 > 15, 16 > 16, 17 >= 17, 18 >= 18 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C114(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, Zero, Succ(zzz30830), bg, bh) -> new_intersectFM_C2IntersectFM_C115(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3080, bg, bh) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 13 >= 10, 17 >= 11, 18 >= 12 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C116(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, Succ(zzz35390), Zero, ca, cb) -> new_intersectFM_C2IntersectFM_C115(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3538, ca, cb) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 14 >= 10, 17 >= 11, 18 >= 12 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C117(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, bg, bh) -> new_intersectFM_C2IntersectFM_C116(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, Succ(zzz3072), Succ(zzz3077), bg, bh) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 17, 16 >= 18 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C114(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, Zero, Zero, bg, bh) -> new_intersectFM_C2IntersectFM_C117(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, bg, bh) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 17 >= 15, 18 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C114(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, Succ(zzz30820), Zero, bg, bh) -> new_intersectFM_C2IntersectFM_C116(zzz3068, zzz3069, zzz3070, zzz3071, zzz3072, zzz3073, zzz3074, zzz3075, zzz3076, zzz3077, zzz3078, zzz3079, zzz3080, zzz3081, Succ(zzz3072), Succ(zzz3077), bg, bh) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 17 >= 17, 18 >= 18 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C116(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, Succ(zzz35390), Succ(zzz35400), ca, cb) -> new_intersectFM_C2IntersectFM_C116(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, zzz35390, zzz35400, ca, cb) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 > 15, 16 > 16, 17 >= 17, 18 >= 18 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C116(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, Zero, Zero, ca, cb) -> new_intersectFM_C2IntersectFM_C118(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, ca, cb) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 17 >= 15, 18 >= 16 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Neg(Succ(zzz160300)), zzz1604, zzz1605, zzz1606, zzz1607, gc, gd) -> new_intersectFM_C2IntersectFM_C144(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1607, gc, gd) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 14 >= 10, 15 >= 11, 16 >= 12 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Neg(Zero), zzz1604, zzz1605, zzz1606, zzz1607, gc, gd) -> new_intersectFM_C2IntersectFM_C145(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1604, gc, gd) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 11 >= 10, 15 >= 11, 16 >= 12 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, Succ(zzz21580), Succ(zzz21590), ed, ee) -> new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, zzz2156, zzz2157, zzz21580, zzz21590, ed, ee) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 16 > 16, 17 > 17, 18 >= 18, 19 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, Branch(Neg(Succ(zzz2156000)), zzz21561, zzz21562, zzz21563, zzz21564), zzz2157, Zero, Succ(zzz21590), ed, ee) -> new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2156000, zzz21561, zzz21562, zzz21563, zzz21564, zzz2156000, zzz2148, ed, ee) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 14 > 11, 14 > 12, 14 > 13, 14 > 14, 14 > 15, 14 > 16, 6 >= 17, 18 >= 18, 19 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C133(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, Zero, Succ(zzz26430), ef, eg) -> new_intersectFM_C(new_intersectFM_C2Gts5(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, ef), zzz2636, ef) 130.57/78.25 The graph contains the following edges 10 >= 2, 18 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C133(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, Zero, Succ(zzz26430), ef, eg) -> new_intersectFM_C(new_intersectFM_C2Lts5(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, ef), zzz2635, ef) 130.57/78.25 The graph contains the following edges 9 >= 2, 18 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Neg(Succ(zzz3000)), zzz31, zzz32, zzz33, EmptyFM), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_mkVBalBranch6(zzz3000, zzz31, zzz33, new_splitLT5(bd), bd), zzz43, bd) 130.57/78.25 The graph contains the following edges 2 > 2, 3 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Pos(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT210(zzz31, zzz32, zzz33, zzz34, bd), zzz43, bd) 130.57/78.25 The graph contains the following edges 2 > 2, 3 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Neg(zzz300), zzz31, zzz32, zzz33, EmptyFM), Branch(Pos(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT29(Neg(zzz300), zzz31, zzz32, zzz33, EmptyFM, zzz4000, bd), zzz43, bd) 130.57/78.25 The graph contains the following edges 2 > 2, 3 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Neg(Succ(zzz3000)), zzz31, zzz32, zzz33, EmptyFM), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_mkVBalBranch6(zzz3000, zzz31, zzz33, new_splitLT9(EmptyFM, bd), bd), zzz43, bd) 130.57/78.25 The graph contains the following edges 2 > 2, 3 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Pos(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT8(zzz31, zzz32, zzz33, zzz34, bd), zzz43, bd) 130.57/78.25 The graph contains the following edges 2 > 2, 3 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Pos(zzz300), zzz31, zzz32, EmptyFM, zzz34), Branch(Neg(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_mkVBalBranch5(zzz300, zzz31, new_splitGT8(zzz4000, bd), zzz34, bd), zzz44, bd) 130.57/78.25 The graph contains the following edges 2 > 2, 3 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Neg(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT211(zzz31, zzz32, zzz33, zzz34, bd), zzz43, bd) 130.57/78.25 The graph contains the following edges 2 > 2, 3 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Neg(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT11(zzz31, zzz32, zzz33, zzz34, bd), zzz43, bd) 130.57/78.25 The graph contains the following edges 2 > 2, 3 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Pos(Succ(zzz3000)), zzz31, zzz32, EmptyFM, zzz34), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_mkVBalBranch5(Succ(zzz3000), zzz31, new_splitGT7(bd), zzz34, bd), zzz44, bd) 130.57/78.25 The graph contains the following edges 2 > 2, 3 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Neg(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitGT214(zzz31, zzz32, zzz33, zzz34, bd), zzz44, bd) 130.57/78.25 The graph contains the following edges 2 > 2, 3 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Pos(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitGT215(zzz31, zzz32, zzz33, zzz34, bd), zzz44, bd) 130.57/78.25 The graph contains the following edges 2 > 2, 3 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Pos(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Pos(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitGT213(zzz31, zzz32, zzz33, zzz34, bd), zzz44, bd) 130.57/78.25 The graph contains the following edges 2 > 2, 3 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Neg(Zero), zzz31, zzz32, zzz33, zzz34), Branch(Neg(Zero), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitGT216(zzz31, zzz32, zzz33, zzz34, bd), zzz44, bd) 130.57/78.25 The graph contains the following edges 2 > 2, 3 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Neg(Zero), zzz31, zzz32, EmptyFM, zzz34), Branch(Neg(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_mkVBalBranch7(zzz31, new_splitGT8(zzz4000, bd), zzz34, bd), zzz44, bd) 130.57/78.25 The graph contains the following edges 2 > 2, 3 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C(Branch(Pos(Zero), zzz31, zzz32, zzz33, EmptyFM), Branch(Pos(Succ(zzz4000)), zzz41, zzz42, zzz43, zzz44), bd) -> new_intersectFM_C(new_splitLT29(Pos(Zero), zzz31, zzz32, zzz33, EmptyFM, zzz4000, bd), zzz43, bd) 130.57/78.25 The graph contains the following edges 2 > 2, 3 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Pos(Succ(zzz160300)), zzz1604, zzz1605, EmptyFM, zzz1607, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Gts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1602, gc) 130.57/78.25 The graph contains the following edges 9 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Pos(Zero), zzz1604, zzz1605, zzz1606, zzz1607, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Lts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1601, gc) 130.57/78.25 The graph contains the following edges 8 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Pos(Zero), zzz1604, zzz1605, zzz1606, zzz1607, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Gts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1602, gc) 130.57/78.25 The graph contains the following edges 9 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C113(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, Pos(Succ(zzz160300)), zzz1604, zzz1605, EmptyFM, zzz1607, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Lts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1601, gc) 130.57/78.25 The graph contains the following edges 8 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C111(zzz830, zzz831, zzz832, zzz833, zzz834, zzz835, zzz836, zzz837, zzz838, fg, fh) -> new_intersectFM_C(new_intersectFM_C2Gts7(zzz830, zzz831, zzz832, zzz833, zzz834, fg), zzz838, fg) 130.57/78.25 The graph contains the following edges 9 >= 2, 10 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C111(zzz830, zzz831, zzz832, zzz833, zzz834, zzz835, zzz836, zzz837, zzz838, fg, fh) -> new_intersectFM_C(new_intersectFM_C2Lts7(zzz830, zzz831, zzz832, zzz833, zzz834, fg), zzz837, fg) 130.57/78.25 The graph contains the following edges 8 >= 2, 10 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, Neg(zzz27430), zzz2744, zzz2745, zzz2746, EmptyFM, be, bf) -> new_intersectFM_C(new_intersectFM_C2Gts0(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, be), zzz2742, be) 130.57/78.25 The graph contains the following edges 9 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C14(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, Neg(zzz27430), zzz2744, zzz2745, zzz2746, EmptyFM, be, bf) -> new_intersectFM_C(new_intersectFM_C2Lts0(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, be), zzz2741, be) 130.57/78.25 The graph contains the following edges 8 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, EmptyFM, zzz2157, Zero, Succ(zzz21590), ed, ee) -> new_intersectFM_C(new_intersectFM_C2Gts5(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, ed), zzz2152, ed) 130.57/78.25 The graph contains the following edges 10 >= 2, 18 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, EmptyFM, zzz2157, Zero, Succ(zzz21590), ed, ee) -> new_intersectFM_C(new_intersectFM_C2Lts5(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, ed), zzz2151, ed) 130.57/78.25 The graph contains the following edges 9 >= 2, 18 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, Pos(zzz8930), zzz894, zzz895, EmptyFM, zzz897, eh, fa) -> new_intersectFM_C(new_intersectFM_C2Lts6(zzz884, zzz885, zzz886, zzz887, zzz888, eh), zzz891, eh) 130.57/78.25 The graph contains the following edges 8 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C110(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, Pos(zzz8930), zzz894, zzz895, EmptyFM, zzz897, eh, fa) -> new_intersectFM_C(new_intersectFM_C2Gts6(zzz884, zzz885, zzz886, zzz887, zzz888, eh), zzz892, eh) 130.57/78.25 The graph contains the following edges 9 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C138(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, EmptyFM, eh, fa) -> new_intersectFM_C(new_intersectFM_C2Lts6(zzz884, zzz885, zzz886, zzz887, zzz888, eh), zzz891, eh) 130.57/78.25 The graph contains the following edges 8 >= 2, 11 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C138(zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, EmptyFM, eh, fa) -> new_intersectFM_C(new_intersectFM_C2Gts6(zzz884, zzz885, zzz886, zzz887, zzz888, eh), zzz892, eh) 130.57/78.25 The graph contains the following edges 9 >= 2, 11 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, EmptyFM, zzz2092, Zero, Succ(zzz20940), h, ba) -> new_intersectFM_C(new_intersectFM_C2Gts(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, h), zzz2087, h) 130.57/78.25 The graph contains the following edges 10 >= 2, 18 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, EmptyFM, zzz2092, Zero, Succ(zzz20940), h, ba) -> new_intersectFM_C(new_intersectFM_C2Lts(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, h), zzz2086, h) 130.57/78.25 The graph contains the following edges 9 >= 2, 18 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Pos(Zero), zzz909, zzz910, zzz911, zzz912, ga, gb) -> new_intersectFM_C(new_intersectFM_C2Lts7(zzz899, zzz900, zzz901, zzz902, zzz903, ga), zzz906, ga) 130.57/78.25 The graph contains the following edges 8 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C112(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, Pos(Zero), zzz909, zzz910, zzz911, zzz912, ga, gb) -> new_intersectFM_C(new_intersectFM_C2Gts7(zzz899, zzz900, zzz901, zzz902, zzz903, ga), zzz907, ga) 130.57/78.25 The graph contains the following edges 9 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, Neg(zzz13920), zzz1393, zzz1394, zzz1395, EmptyFM, cc, cd) -> new_intersectFM_C(new_intersectFM_C2Gts1(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, cc), zzz1391, cc) 130.57/78.25 The graph contains the following edges 10 >= 2, 16 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C15(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, Neg(zzz13920), zzz1393, zzz1394, zzz1395, EmptyFM, cc, cd) -> new_intersectFM_C(new_intersectFM_C2Lts1(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, cc), zzz1390, cc) 130.57/78.25 The graph contains the following edges 9 >= 2, 16 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C120(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, EmptyFM, cc, cd) -> new_intersectFM_C(new_intersectFM_C2Lts1(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, cc), zzz1390, cc) 130.57/78.25 The graph contains the following edges 9 >= 2, 12 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C120(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, zzz1388, zzz1389, zzz1390, zzz1391, EmptyFM, cc, cd) -> new_intersectFM_C(new_intersectFM_C2Gts1(zzz1382, zzz1383, zzz1384, zzz1385, zzz1386, zzz1387, cc), zzz1391, cc) 130.57/78.25 The graph contains the following edges 10 >= 2, 12 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, Pos(zzz7520), zzz753, zzz754, EmptyFM, zzz756, df, dg) -> new_intersectFM_C(new_intersectFM_C2Lts4(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df), zzz750, df) 130.57/78.25 The graph contains the following edges 9 >= 2, 16 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C18(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, Pos(zzz7520), zzz753, zzz754, EmptyFM, zzz756, df, dg) -> new_intersectFM_C(new_intersectFM_C2Gts4(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df), zzz751, df) 130.57/78.25 The graph contains the following edges 10 >= 2, 16 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C129(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, EmptyFM, df, dg) -> new_intersectFM_C(new_intersectFM_C2Lts4(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df), zzz750, df) 130.57/78.25 The graph contains the following edges 9 >= 2, 12 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C129(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, zzz748, zzz749, zzz750, zzz751, EmptyFM, df, dg) -> new_intersectFM_C(new_intersectFM_C2Gts4(zzz742, zzz743, zzz744, zzz745, zzz746, zzz747, df), zzz751, df) 130.57/78.25 The graph contains the following edges 10 >= 2, 12 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Pos(Succ(zzz120100)), zzz1202, zzz1203, EmptyFM, zzz1205, dd, de) -> new_intersectFM_C(new_intersectFM_C2Lts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1199, dd) 130.57/78.25 The graph contains the following edges 8 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Pos(Zero), zzz1202, zzz1203, zzz1204, zzz1205, dd, de) -> new_intersectFM_C(new_intersectFM_C2Lts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1199, dd) 130.57/78.25 The graph contains the following edges 8 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Pos(Zero), zzz1202, zzz1203, zzz1204, zzz1205, dd, de) -> new_intersectFM_C(new_intersectFM_C2Gts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1200, dd) 130.57/78.25 The graph contains the following edges 9 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C17(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, Pos(Succ(zzz120100)), zzz1202, zzz1203, EmptyFM, zzz1205, dd, de) -> new_intersectFM_C(new_intersectFM_C2Gts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1200, dd) 130.57/78.25 The graph contains the following edges 9 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C127(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, zzz1202, dd, de) -> new_intersectFM_C(new_intersectFM_C2Gts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1200, dd) 130.57/78.25 The graph contains the following edges 9 >= 2, 11 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C127(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, zzz1202, dd, de) -> new_intersectFM_C(new_intersectFM_C2Lts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1199, dd) 130.57/78.25 The graph contains the following edges 8 >= 2, 11 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Pos(Zero), zzz628, zzz629, zzz630, zzz631, db, dc) -> new_intersectFM_C(new_intersectFM_C2Lts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz625, db) 130.57/78.25 The graph contains the following edges 8 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Pos(Succ(zzz62700)), zzz628, zzz629, EmptyFM, zzz631, db, dc) -> new_intersectFM_C(new_intersectFM_C2Gts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz626, db) 130.57/78.25 The graph contains the following edges 9 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Pos(Zero), zzz628, zzz629, zzz630, zzz631, db, dc) -> new_intersectFM_C(new_intersectFM_C2Gts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz626, db) 130.57/78.25 The graph contains the following edges 9 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C16(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, Pos(Succ(zzz62700)), zzz628, zzz629, EmptyFM, zzz631, db, dc) -> new_intersectFM_C(new_intersectFM_C2Lts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz625, db) 130.57/78.25 The graph contains the following edges 8 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C124(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, EmptyFM, db, dc) -> new_intersectFM_C(new_intersectFM_C2Lts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz625, db) 130.57/78.25 The graph contains the following edges 8 >= 2, 11 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C124(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, EmptyFM, db, dc) -> new_intersectFM_C(new_intersectFM_C2Gts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz626, db) 130.57/78.25 The graph contains the following edges 9 >= 2, 11 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C125(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, zzz628, db, dc) -> new_intersectFM_C(new_intersectFM_C2Gts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz626, db) 130.57/78.25 The graph contains the following edges 9 >= 2, 11 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C125(zzz618, zzz619, zzz620, zzz621, zzz622, zzz623, zzz624, zzz625, zzz626, zzz628, db, dc) -> new_intersectFM_C(new_intersectFM_C2Lts2(zzz618, zzz619, zzz620, zzz621, zzz622, db), zzz625, db) 130.57/78.25 The graph contains the following edges 8 >= 2, 11 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C126(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, EmptyFM, dd, de) -> new_intersectFM_C(new_intersectFM_C2Gts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1200, dd) 130.57/78.25 The graph contains the following edges 9 >= 2, 11 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C126(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, zzz1197, zzz1198, zzz1199, zzz1200, EmptyFM, dd, de) -> new_intersectFM_C(new_intersectFM_C2Lts3(zzz1192, zzz1193, zzz1194, zzz1195, zzz1196, dd), zzz1199, dd) 130.57/78.25 The graph contains the following edges 8 >= 2, 11 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C130(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, Zero, Succ(zzz27710), eb, ec) -> new_intersectFM_C(new_intersectFM_C2Lts4(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, eb), zzz2763, eb) 130.57/78.25 The graph contains the following edges 9 >= 2, 18 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C130(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, Zero, Succ(zzz27710), eb, ec) -> new_intersectFM_C(new_intersectFM_C2Gts4(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, eb), zzz2764, eb) 130.57/78.25 The graph contains the following edges 10 >= 2, 18 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C132(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, eb, ec) -> new_intersectFM_C(new_intersectFM_C2Gts4(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, eb), zzz2764, eb) 130.57/78.25 The graph contains the following edges 10 >= 2, 16 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C132(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, zzz2761, zzz2762, zzz2763, zzz2764, zzz2765, zzz2766, zzz2767, zzz2768, zzz2769, eb, ec) -> new_intersectFM_C(new_intersectFM_C2Lts4(zzz2755, zzz2756, zzz2757, zzz2758, zzz2759, zzz2760, eb), zzz2763, eb) 130.57/78.25 The graph contains the following edges 9 >= 2, 16 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C121(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, Zero, Succ(zzz31790), cg, da) -> new_intersectFM_C(new_intersectFM_C2Lts1(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, cg), zzz3171, cg) 130.57/78.25 The graph contains the following edges 9 >= 2, 18 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C121(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, Zero, Succ(zzz31790), cg, da) -> new_intersectFM_C(new_intersectFM_C2Gts1(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, cg), zzz3172, cg) 130.57/78.25 The graph contains the following edges 10 >= 2, 18 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C123(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, cg, da) -> new_intersectFM_C(new_intersectFM_C2Lts1(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, cg), zzz3171, cg) 130.57/78.25 The graph contains the following edges 9 >= 2, 16 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C123(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, zzz3169, zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz3175, zzz3176, zzz3177, cg, da) -> new_intersectFM_C(new_intersectFM_C2Gts1(zzz3163, zzz3164, zzz3165, zzz3166, zzz3167, zzz3168, cg), zzz3172, cg) 130.57/78.25 The graph contains the following edges 10 >= 2, 16 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C143(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz909, ga, gb) -> new_intersectFM_C(new_intersectFM_C2Lts7(zzz899, zzz900, zzz901, zzz902, zzz903, ga), zzz906, ga) 130.57/78.25 The graph contains the following edges 8 >= 2, 11 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C143(zzz899, zzz900, zzz901, zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz909, ga, gb) -> new_intersectFM_C(new_intersectFM_C2Gts7(zzz899, zzz900, zzz901, zzz902, zzz903, ga), zzz907, ga) 130.57/78.25 The graph contains the following edges 9 >= 2, 11 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C10(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, Zero, Succ(zzz26250), bb, bc) -> new_intersectFM_C(new_intersectFM_C2Gts(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, bb), zzz2618, bb) 130.57/78.25 The graph contains the following edges 10 >= 2, 18 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C10(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, Zero, Succ(zzz26250), bb, bc) -> new_intersectFM_C(new_intersectFM_C2Lts(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, bb), zzz2617, bb) 130.57/78.25 The graph contains the following edges 9 >= 2, 18 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C13(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, bb, bc) -> new_intersectFM_C(new_intersectFM_C2Lts(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, bb), zzz2617, bb) 130.57/78.25 The graph contains the following edges 9 >= 2, 16 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C13(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, zzz2615, zzz2616, zzz2617, zzz2618, zzz2619, zzz2620, zzz2621, zzz2622, zzz2623, bb, bc) -> new_intersectFM_C(new_intersectFM_C2Gts(zzz2609, zzz2610, zzz2611, zzz2612, zzz2613, zzz2614, bb), zzz2618, bb) 130.57/78.25 The graph contains the following edges 10 >= 2, 16 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, EmptyFM, h, ba) -> new_intersectFM_C(new_intersectFM_C2Lts(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, h), zzz2086, h) 130.57/78.25 The graph contains the following edges 9 >= 2, 12 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, EmptyFM, h, ba) -> new_intersectFM_C(new_intersectFM_C2Gts(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, h), zzz2087, h) 130.57/78.25 The graph contains the following edges 10 >= 2, 12 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C139(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, Zero, Succ(zzz28990), fd, ff) -> new_intersectFM_C(new_intersectFM_C2Lts6(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, fd), zzz2891, fd) 130.57/78.25 The graph contains the following edges 8 >= 2, 17 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C139(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, Zero, Succ(zzz28990), fd, ff) -> new_intersectFM_C(new_intersectFM_C2Gts6(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, fd), zzz2892, fd) 130.57/78.25 The graph contains the following edges 9 >= 2, 17 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C141(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, fd, ff) -> new_intersectFM_C(new_intersectFM_C2Gts6(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, fd), zzz2892, fd) 130.57/78.25 The graph contains the following edges 9 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C141(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, zzz2889, zzz2890, zzz2891, zzz2892, zzz2893, zzz2894, zzz2895, zzz2896, zzz2897, fd, ff) -> new_intersectFM_C(new_intersectFM_C2Lts6(zzz2884, zzz2885, zzz2886, zzz2887, zzz2888, fd), zzz2891, fd) 130.57/78.25 The graph contains the following edges 8 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, EmptyFM, ed, ee) -> new_intersectFM_C(new_intersectFM_C2Gts5(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, ed), zzz2152, ed) 130.57/78.25 The graph contains the following edges 10 >= 2, 12 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, EmptyFM, ed, ee) -> new_intersectFM_C(new_intersectFM_C2Lts5(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, ed), zzz2151, ed) 130.57/78.25 The graph contains the following edges 9 >= 2, 12 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C115(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, EmptyFM, be, bf) -> new_intersectFM_C(new_intersectFM_C2Gts0(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, be), zzz2742, be) 130.57/78.25 The graph contains the following edges 9 >= 2, 11 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C115(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, zzz2739, zzz2740, zzz2741, zzz2742, EmptyFM, be, bf) -> new_intersectFM_C(new_intersectFM_C2Lts0(zzz2734, zzz2735, zzz2736, zzz2737, zzz2738, be), zzz2741, be) 130.57/78.25 The graph contains the following edges 8 >= 2, 11 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C116(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, Zero, Succ(zzz35400), ca, cb) -> new_intersectFM_C(new_intersectFM_C2Lts0(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, ca), zzz3532, ca) 130.57/78.25 The graph contains the following edges 8 >= 2, 17 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C116(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, Zero, Succ(zzz35400), ca, cb) -> new_intersectFM_C(new_intersectFM_C2Gts0(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, ca), zzz3533, ca) 130.57/78.25 The graph contains the following edges 9 >= 2, 17 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C118(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, ca, cb) -> new_intersectFM_C(new_intersectFM_C2Lts0(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, ca), zzz3532, ca) 130.57/78.25 The graph contains the following edges 8 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C118(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, zzz3530, zzz3531, zzz3532, zzz3533, zzz3534, zzz3535, zzz3536, zzz3537, zzz3538, ca, cb) -> new_intersectFM_C(new_intersectFM_C2Gts0(zzz3525, zzz3526, zzz3527, zzz3528, zzz3529, ca), zzz3533, ca) 130.57/78.25 The graph contains the following edges 9 >= 2, 15 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C144(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, EmptyFM, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Lts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1601, gc) 130.57/78.25 The graph contains the following edges 8 >= 2, 11 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C144(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, EmptyFM, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Gts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1602, gc) 130.57/78.25 The graph contains the following edges 9 >= 2, 11 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C145(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1604, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Lts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1601, gc) 130.57/78.25 The graph contains the following edges 8 >= 2, 11 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C145(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, zzz1599, zzz1600, zzz1601, zzz1602, zzz1604, gc, gd) -> new_intersectFM_C(new_intersectFM_C2Gts8(zzz1594, zzz1595, zzz1596, zzz1597, zzz1598, gc), zzz1602, gc) 130.57/78.25 The graph contains the following edges 9 >= 2, 11 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C136(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, ef, eg) -> new_intersectFM_C(new_intersectFM_C2Lts5(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, ef), zzz2635, ef) 130.57/78.25 The graph contains the following edges 9 >= 2, 16 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C136(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz2635, zzz2636, zzz2637, zzz2638, zzz2639, zzz2640, zzz2641, ef, eg) -> new_intersectFM_C(new_intersectFM_C2Gts5(zzz2627, zzz2628, zzz2629, zzz2630, zzz2631, zzz2632, ef), zzz2636, ef) 130.57/78.25 The graph contains the following edges 10 >= 2, 16 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, Branch(Pos(zzz215600), zzz21561, zzz21562, zzz21563, zzz21564), zzz2157, Zero, Succ(zzz21590), ed, ee) -> new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz21563, ed, ee) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 14 > 11, 18 >= 12, 19 >= 13 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C19(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, Branch(Neg(Zero), zzz21561, zzz21562, zzz21563, zzz21564), zzz2157, Zero, Succ(zzz21590), ed, ee) -> new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz21563, ed, ee) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 14 > 11, 18 >= 12, 19 >= 13 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, Succ(zzz20930), Succ(zzz20940), h, ba) -> new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, zzz2091, zzz2092, zzz20930, zzz20940, h, ba) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 14, 15 >= 15, 16 > 16, 17 > 17, 18 >= 18, 19 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, Branch(Pos(Succ(zzz2091000)), zzz20911, zzz20912, zzz20913, zzz20914), zzz2092, Zero, Succ(zzz20940), h, ba) -> new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2091000, zzz20911, zzz20912, zzz20913, zzz20914, zzz2083, zzz2091000, h, ba) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 14 > 11, 14 > 12, 14 > 13, 14 > 14, 14 > 15, 6 >= 16, 14 > 17, 18 >= 18, 19 >= 19 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, Branch(Neg(zzz209100), zzz20911, zzz20912, zzz20913, zzz20914), zzz2092, Zero, Succ(zzz20940), h, ba) -> new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz20914, h, ba) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 14 > 11, 18 >= 12, 19 >= 13 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C1(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz2088, zzz2089, zzz2090, Branch(Pos(Zero), zzz20911, zzz20912, zzz20913, zzz20914), zzz2092, Zero, Succ(zzz20940), h, ba) -> new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz20914, h, ba) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 14 > 11, 18 >= 12, 19 >= 13 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, Branch(Neg(zzz209100), zzz20911, zzz20912, zzz20913, zzz20914), h, ba) -> new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz20914, h, ba) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 > 11, 12 >= 12, 13 >= 13 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, Branch(Pos(Zero), zzz20911, zzz20912, zzz20913, zzz20914), h, ba) -> new_intersectFM_C2IntersectFM_C11(zzz2078, zzz2079, zzz2080, zzz2081, zzz2082, zzz2083, zzz2084, zzz2085, zzz2086, zzz2087, zzz20914, h, ba) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 > 11, 12 >= 12, 13 >= 13 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, Branch(Neg(Zero), zzz21561, zzz21562, zzz21563, zzz21564), ed, ee) -> new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz21563, ed, ee) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 > 11, 12 >= 12, 13 >= 13 130.57/78.25 130.57/78.25 130.57/78.25 *new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, Branch(Pos(zzz215600), zzz21561, zzz21562, zzz21563, zzz21564), ed, ee) -> new_intersectFM_C2IntersectFM_C134(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz21563, ed, ee) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 > 11, 12 >= 12, 13 >= 13 130.57/78.25 130.57/78.25 130.57/78.25 ---------------------------------------- 130.57/78.25 130.57/78.25 (54) 130.57/78.25 YES 130.57/78.25 130.57/78.25 ---------------------------------------- 130.57/78.25 130.57/78.25 (55) 130.57/78.25 Obligation: 130.57/78.25 Q DP problem: 130.57/78.25 The TRS P consists of the following rules: 130.57/78.25 130.57/78.25 new_mkBalBranch6MkBalBranch01(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Succ(zzz6454000), Succ(zzz647200), h, ba) -> new_mkBalBranch6MkBalBranch01(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, zzz6454000, zzz647200, h, ba) 130.57/78.25 130.57/78.25 R is empty. 130.57/78.25 Q is empty. 130.57/78.25 We have to consider all minimal (P,Q,R)-chains. 130.57/78.25 ---------------------------------------- 130.57/78.25 130.57/78.25 (56) QDPSizeChangeProof (EQUIVALENT) 130.57/78.25 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. 130.57/78.25 130.57/78.25 From the DPs we obtained the following set of size-change graphs: 130.57/78.25 *new_mkBalBranch6MkBalBranch01(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, Succ(zzz6454000), Succ(zzz647200), h, ba) -> new_mkBalBranch6MkBalBranch01(zzz4740340, zzz4740341, zzz4740342, zzz4740343, zzz4740344, zzz474030, zzz474031, zzz6373, zzz6454000, zzz647200, h, ba) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 > 9, 10 > 10, 11 >= 11, 12 >= 12 130.57/78.25 130.57/78.25 130.57/78.25 ---------------------------------------- 130.57/78.25 130.57/78.25 (57) 130.57/78.25 YES 130.57/78.25 130.57/78.25 ---------------------------------------- 130.57/78.25 130.57/78.25 (58) 130.57/78.25 Obligation: 130.57/78.25 Q DP problem: 130.57/78.25 The TRS P consists of the following rules: 130.57/78.25 130.57/78.25 new_splitLT21(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, h) -> new_splitLT(zzz8334, h) 130.57/78.25 new_splitLT20(Pos(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334, h) -> new_splitLT2(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, h) 130.57/78.25 new_splitLT20(Neg(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334, h) -> new_splitLT(zzz8334, h) 130.57/78.25 new_splitLT(Branch(Neg(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), h) -> new_splitLT(zzz8334, h) 130.57/78.25 new_splitLT(Branch(Pos(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), h) -> new_splitLT2(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, h) 130.57/78.25 new_splitLT2(zzz830, zzz831, zzz832, Branch(Pos(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), zzz834, h) -> new_splitLT2(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, h) 130.57/78.25 new_splitLT2(zzz830, zzz831, zzz832, Branch(Neg(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), zzz834, h) -> new_splitLT(zzz8334, h) 130.57/78.25 130.57/78.25 R is empty. 130.57/78.25 Q is empty. 130.57/78.25 We have to consider all minimal (P,Q,R)-chains. 130.57/78.25 ---------------------------------------- 130.57/78.25 130.57/78.25 (59) DependencyGraphProof (EQUIVALENT) 130.57/78.25 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 130.57/78.25 ---------------------------------------- 130.57/78.25 130.57/78.25 (60) 130.57/78.25 Obligation: 130.57/78.25 Q DP problem: 130.57/78.25 The TRS P consists of the following rules: 130.57/78.25 130.57/78.25 new_splitLT(Branch(Pos(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), h) -> new_splitLT2(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, h) 130.57/78.25 new_splitLT2(zzz830, zzz831, zzz832, Branch(Pos(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), zzz834, h) -> new_splitLT2(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, h) 130.57/78.25 new_splitLT2(zzz830, zzz831, zzz832, Branch(Neg(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), zzz834, h) -> new_splitLT(zzz8334, h) 130.57/78.25 new_splitLT(Branch(Neg(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), h) -> new_splitLT(zzz8334, h) 130.57/78.25 130.57/78.25 R is empty. 130.57/78.25 Q is empty. 130.57/78.25 We have to consider all minimal (P,Q,R)-chains. 130.57/78.25 ---------------------------------------- 130.57/78.25 130.57/78.25 (61) QDPSizeChangeProof (EQUIVALENT) 130.57/78.25 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. 130.57/78.25 130.57/78.25 From the DPs we obtained the following set of size-change graphs: 130.57/78.25 *new_splitLT2(zzz830, zzz831, zzz832, Branch(Neg(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), zzz834, h) -> new_splitLT(zzz8334, h) 130.57/78.25 The graph contains the following edges 4 > 1, 6 >= 2 130.57/78.25 130.57/78.25 130.57/78.25 *new_splitLT2(zzz830, zzz831, zzz832, Branch(Pos(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), zzz834, h) -> new_splitLT2(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, h) 130.57/78.25 The graph contains the following edges 4 > 1, 4 > 2, 4 > 3, 4 > 4, 4 > 5, 6 >= 6 130.57/78.25 130.57/78.25 130.57/78.25 *new_splitLT(Branch(Neg(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), h) -> new_splitLT(zzz8334, h) 130.57/78.25 The graph contains the following edges 1 > 1, 2 >= 2 130.57/78.25 130.57/78.25 130.57/78.25 *new_splitLT(Branch(Pos(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), h) -> new_splitLT2(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, h) 130.57/78.25 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 >= 6 130.57/78.25 130.57/78.25 130.57/78.25 ---------------------------------------- 130.57/78.25 130.57/78.25 (62) 130.57/78.25 YES 130.57/78.25 130.57/78.25 ---------------------------------------- 130.57/78.25 130.57/78.25 (63) 130.57/78.25 Obligation: 130.57/78.25 Q DP problem: 130.57/78.25 The TRS P consists of the following rules: 130.57/78.25 130.57/78.25 new_splitLT1(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, Succ(zzz45100), Succ(zzz45110), h) -> new_splitLT1(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, zzz45100, zzz45110, h) 130.57/78.25 new_splitLT23(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Succ(zzz35090), Zero, bb) -> new_splitLT1(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Succ(zzz3503), Succ(zzz3508), bb) 130.57/78.25 new_splitLT0(Branch(Neg(Succ(zzz745000)), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, ba) -> new_splitLT23(zzz745000, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, zzz745000, zzz747, ba) 130.57/78.25 new_splitLT0(Branch(Pos(zzz74500), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, ba) -> new_splitLT22(zzz74500, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, ba) 130.57/78.25 new_splitLT22(zzz742, zzz743, zzz744, Branch(Neg(Zero), zzz7451, zzz7452, zzz7453, zzz7454), zzz746, zzz747, ba) -> new_splitLT0(zzz7453, zzz747, ba) 130.57/78.25 new_splitLT23(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Zero, Succ(zzz35100), bb) -> new_splitLT0(zzz3506, zzz3508, bb) 130.57/78.25 new_splitLT23(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Succ(zzz35090), Succ(zzz35100), bb) -> new_splitLT23(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, zzz35090, zzz35100, bb) 130.57/78.25 new_splitLT0(Branch(Neg(Zero), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, ba) -> new_splitLT0(zzz7453, zzz747, ba) 130.57/78.25 new_splitLT1(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, Succ(zzz45100), Zero, h) -> new_splitLT0(zzz4508, zzz4509, h) 130.57/78.25 new_splitLT22(zzz742, zzz743, zzz744, Branch(Neg(Succ(zzz745000)), zzz7451, zzz7452, zzz7453, zzz7454), zzz746, zzz747, ba) -> new_splitLT23(zzz745000, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, zzz745000, zzz747, ba) 130.57/78.25 new_splitLT23(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Zero, Zero, bb) -> new_splitLT24(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, bb) 130.57/78.25 new_splitLT22(zzz742, zzz743, zzz744, Branch(Pos(zzz74500), zzz7451, zzz7452, zzz7453, zzz7454), zzz746, zzz747, ba) -> new_splitLT22(zzz74500, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, ba) 130.57/78.25 new_splitLT24(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, bb) -> new_splitLT1(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Succ(zzz3503), Succ(zzz3508), bb) 130.57/78.25 130.57/78.25 R is empty. 130.57/78.25 Q is empty. 130.57/78.25 We have to consider all minimal (P,Q,R)-chains. 130.57/78.25 ---------------------------------------- 130.57/78.25 130.57/78.25 (64) QDPSizeChangeProof (EQUIVALENT) 130.57/78.25 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. 130.57/78.25 130.57/78.25 From the DPs we obtained the following set of size-change graphs: 130.57/78.25 *new_splitLT1(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, Succ(zzz45100), Succ(zzz45110), h) -> new_splitLT1(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, zzz45100, zzz45110, h) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9 130.57/78.25 130.57/78.25 130.57/78.25 *new_splitLT1(zzz4504, zzz4505, zzz4506, zzz4507, zzz4508, zzz4509, Succ(zzz45100), Zero, h) -> new_splitLT0(zzz4508, zzz4509, h) 130.57/78.25 The graph contains the following edges 5 >= 1, 6 >= 2, 9 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_splitLT23(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Succ(zzz35090), Zero, bb) -> new_splitLT1(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Succ(zzz3503), Succ(zzz3508), bb) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 9 130.57/78.25 130.57/78.25 130.57/78.25 *new_splitLT24(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, bb) -> new_splitLT1(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Succ(zzz3503), Succ(zzz3508), bb) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 9 130.57/78.25 130.57/78.25 130.57/78.25 *new_splitLT23(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Succ(zzz35090), Succ(zzz35100), bb) -> new_splitLT23(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, zzz35090, zzz35100, bb) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9 130.57/78.25 130.57/78.25 130.57/78.25 *new_splitLT23(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Zero, Succ(zzz35100), bb) -> new_splitLT0(zzz3506, zzz3508, bb) 130.57/78.25 The graph contains the following edges 4 >= 1, 6 >= 2, 9 >= 3 130.57/78.25 130.57/78.25 130.57/78.25 *new_splitLT23(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, Zero, Zero, bb) -> new_splitLT24(zzz3503, zzz3504, zzz3505, zzz3506, zzz3507, zzz3508, bb) 130.57/78.25 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 7 130.57/78.25 130.57/78.25 130.57/78.25 *new_splitLT22(zzz742, zzz743, zzz744, Branch(Neg(Succ(zzz745000)), zzz7451, zzz7452, zzz7453, zzz7454), zzz746, zzz747, ba) -> new_splitLT23(zzz745000, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, zzz745000, zzz747, ba) 130.57/78.25 The graph contains the following edges 4 > 1, 4 > 2, 4 > 3, 4 > 4, 4 > 5, 6 >= 6, 4 > 7, 6 >= 8, 7 >= 9 130.57/78.25 130.57/78.25 130.57/78.25 *new_splitLT0(Branch(Neg(Succ(zzz745000)), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, ba) -> new_splitLT23(zzz745000, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, zzz745000, zzz747, ba) 130.57/78.26 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 >= 6, 1 > 7, 2 >= 8, 3 >= 9 130.57/78.26 130.57/78.26 130.57/78.26 *new_splitLT22(zzz742, zzz743, zzz744, Branch(Neg(Zero), zzz7451, zzz7452, zzz7453, zzz7454), zzz746, zzz747, ba) -> new_splitLT0(zzz7453, zzz747, ba) 130.57/78.26 The graph contains the following edges 4 > 1, 6 >= 2, 7 >= 3 130.57/78.26 130.57/78.26 130.57/78.26 *new_splitLT0(Branch(Neg(Zero), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, ba) -> new_splitLT0(zzz7453, zzz747, ba) 130.57/78.26 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 130.57/78.26 130.57/78.26 130.57/78.26 *new_splitLT22(zzz742, zzz743, zzz744, Branch(Pos(zzz74500), zzz7451, zzz7452, zzz7453, zzz7454), zzz746, zzz747, ba) -> new_splitLT22(zzz74500, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, ba) 130.57/78.26 The graph contains the following edges 4 > 1, 4 > 2, 4 > 3, 4 > 4, 4 > 5, 6 >= 6, 7 >= 7 130.57/78.26 130.57/78.26 130.57/78.26 *new_splitLT0(Branch(Pos(zzz74500), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, ba) -> new_splitLT22(zzz74500, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, ba) 130.57/78.26 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 >= 6, 3 >= 7 130.57/78.26 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (65) 130.57/78.26 YES 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (66) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_addToFM_C(Branch(Pos(zzz98200), zzz9821, zzz9822, zzz9823, zzz9824), Succ(zzz3000), zzz31, h) -> new_addToFM_C(zzz9823, Succ(zzz3000), zzz31, h) 130.57/78.26 new_addToFM_C2(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Succ(zzz33930), Zero, ba) -> new_addToFM_C1(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Succ(zzz3386), Succ(zzz3391), ba) 130.57/78.26 new_addToFM_C(Branch(Neg(Succ(zzz982000)), zzz9821, zzz9822, zzz9823, zzz9824), Zero, zzz31, h) -> new_addToFM_C(zzz9824, Zero, zzz31, h) 130.57/78.26 new_addToFM_C2(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Zero, Succ(zzz33940), ba) -> new_addToFM_C(zzz3389, Succ(zzz3391), zzz3392, ba) 130.57/78.26 new_addToFM_C(Branch(Pos(Succ(zzz982000)), zzz9821, zzz9822, zzz9823, zzz9824), Zero, zzz31, h) -> new_addToFM_C(zzz9823, Zero, zzz31, h) 130.57/78.26 new_addToFM_C1(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, Succ(zzz45450), Zero, bb) -> new_addToFM_C(zzz4542, Succ(zzz4543), zzz4544, bb) 130.57/78.26 new_addToFM_C(Branch(Neg(Succ(zzz982000)), zzz9821, zzz9822, zzz9823, zzz9824), Succ(zzz3000), zzz31, h) -> new_addToFM_C2(zzz982000, zzz9821, zzz9822, zzz9823, zzz9824, zzz3000, zzz31, zzz982000, zzz3000, h) 130.57/78.26 new_addToFM_C1(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, Succ(zzz45450), Succ(zzz45460), bb) -> new_addToFM_C1(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, zzz45450, zzz45460, bb) 130.57/78.26 new_addToFM_C20(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, ba) -> new_addToFM_C1(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Succ(zzz3386), Succ(zzz3391), ba) 130.57/78.26 new_addToFM_C(Branch(Neg(Zero), zzz9821, zzz9822, zzz9823, zzz9824), Succ(zzz3000), zzz31, h) -> new_addToFM_C(zzz9823, Succ(zzz3000), zzz31, h) 130.57/78.26 new_addToFM_C2(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Zero, Zero, ba) -> new_addToFM_C20(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, ba) 130.57/78.26 new_addToFM_C2(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Succ(zzz33930), Succ(zzz33940), ba) -> new_addToFM_C2(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, zzz33930, zzz33940, ba) 130.57/78.26 130.57/78.26 R is empty. 130.57/78.26 Q is empty. 130.57/78.26 We have to consider all minimal (P,Q,R)-chains. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (67) DependencyGraphProof (EQUIVALENT) 130.57/78.26 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (68) 130.57/78.26 Complex Obligation (AND) 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (69) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_addToFM_C(Branch(Pos(Succ(zzz982000)), zzz9821, zzz9822, zzz9823, zzz9824), Zero, zzz31, h) -> new_addToFM_C(zzz9823, Zero, zzz31, h) 130.57/78.26 new_addToFM_C(Branch(Neg(Succ(zzz982000)), zzz9821, zzz9822, zzz9823, zzz9824), Zero, zzz31, h) -> new_addToFM_C(zzz9824, Zero, zzz31, h) 130.57/78.26 130.57/78.26 R is empty. 130.57/78.26 Q is empty. 130.57/78.26 We have to consider all minimal (P,Q,R)-chains. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (70) QDPSizeChangeProof (EQUIVALENT) 130.57/78.26 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. 130.57/78.26 130.57/78.26 From the DPs we obtained the following set of size-change graphs: 130.57/78.26 *new_addToFM_C(Branch(Pos(Succ(zzz982000)), zzz9821, zzz9822, zzz9823, zzz9824), Zero, zzz31, h) -> new_addToFM_C(zzz9823, Zero, zzz31, h) 130.57/78.26 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C(Branch(Neg(Succ(zzz982000)), zzz9821, zzz9822, zzz9823, zzz9824), Zero, zzz31, h) -> new_addToFM_C(zzz9824, Zero, zzz31, h) 130.57/78.26 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4 130.57/78.26 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (71) 130.57/78.26 YES 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (72) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_addToFM_C(Branch(Neg(Succ(zzz982000)), zzz9821, zzz9822, zzz9823, zzz9824), Succ(zzz3000), zzz31, h) -> new_addToFM_C2(zzz982000, zzz9821, zzz9822, zzz9823, zzz9824, zzz3000, zzz31, zzz982000, zzz3000, h) 130.57/78.26 new_addToFM_C2(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Succ(zzz33930), Zero, ba) -> new_addToFM_C1(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Succ(zzz3386), Succ(zzz3391), ba) 130.57/78.26 new_addToFM_C1(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, Succ(zzz45450), Succ(zzz45460), bb) -> new_addToFM_C1(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, zzz45450, zzz45460, bb) 130.57/78.26 new_addToFM_C1(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, Succ(zzz45450), Zero, bb) -> new_addToFM_C(zzz4542, Succ(zzz4543), zzz4544, bb) 130.57/78.26 new_addToFM_C(Branch(Pos(zzz98200), zzz9821, zzz9822, zzz9823, zzz9824), Succ(zzz3000), zzz31, h) -> new_addToFM_C(zzz9823, Succ(zzz3000), zzz31, h) 130.57/78.26 new_addToFM_C(Branch(Neg(Zero), zzz9821, zzz9822, zzz9823, zzz9824), Succ(zzz3000), zzz31, h) -> new_addToFM_C(zzz9823, Succ(zzz3000), zzz31, h) 130.57/78.26 new_addToFM_C2(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Zero, Succ(zzz33940), ba) -> new_addToFM_C(zzz3389, Succ(zzz3391), zzz3392, ba) 130.57/78.26 new_addToFM_C2(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Zero, Zero, ba) -> new_addToFM_C20(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, ba) 130.57/78.26 new_addToFM_C20(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, ba) -> new_addToFM_C1(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Succ(zzz3386), Succ(zzz3391), ba) 130.57/78.26 new_addToFM_C2(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Succ(zzz33930), Succ(zzz33940), ba) -> new_addToFM_C2(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, zzz33930, zzz33940, ba) 130.57/78.26 130.57/78.26 R is empty. 130.57/78.26 Q is empty. 130.57/78.26 We have to consider all minimal (P,Q,R)-chains. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (73) QDPSizeChangeProof (EQUIVALENT) 130.57/78.26 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. 130.57/78.26 130.57/78.26 From the DPs we obtained the following set of size-change graphs: 130.57/78.26 *new_addToFM_C2(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Zero, Succ(zzz33940), ba) -> new_addToFM_C(zzz3389, Succ(zzz3391), zzz3392, ba) 130.57/78.26 The graph contains the following edges 4 >= 1, 7 >= 3, 10 >= 4 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C2(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Succ(zzz33930), Succ(zzz33940), ba) -> new_addToFM_C2(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, zzz33930, zzz33940, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 9 > 9, 10 >= 10 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C1(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, Succ(zzz45450), Succ(zzz45460), bb) -> new_addToFM_C1(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, zzz45450, zzz45460, bb) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 9 > 9, 10 >= 10 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C(Branch(Neg(Succ(zzz982000)), zzz9821, zzz9822, zzz9823, zzz9824), Succ(zzz3000), zzz31, h) -> new_addToFM_C2(zzz982000, zzz9821, zzz9822, zzz9823, zzz9824, zzz3000, zzz31, zzz982000, zzz3000, h) 130.57/78.26 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 > 6, 3 >= 7, 1 > 8, 2 > 9, 4 >= 10 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C20(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, ba) -> new_addToFM_C1(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Succ(zzz3386), Succ(zzz3391), ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 10 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C2(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Succ(zzz33930), Zero, ba) -> new_addToFM_C1(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Succ(zzz3386), Succ(zzz3391), ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 10 >= 10 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C2(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, Zero, Zero, ba) -> new_addToFM_C20(zzz3386, zzz3387, zzz3388, zzz3389, zzz3390, zzz3391, zzz3392, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 10 >= 8 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C1(zzz4538, zzz4539, zzz4540, zzz4541, zzz4542, zzz4543, zzz4544, Succ(zzz45450), Zero, bb) -> new_addToFM_C(zzz4542, Succ(zzz4543), zzz4544, bb) 130.57/78.26 The graph contains the following edges 5 >= 1, 7 >= 3, 10 >= 4 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C(Branch(Pos(zzz98200), zzz9821, zzz9822, zzz9823, zzz9824), Succ(zzz3000), zzz31, h) -> new_addToFM_C(zzz9823, Succ(zzz3000), zzz31, h) 130.57/78.26 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C(Branch(Neg(Zero), zzz9821, zzz9822, zzz9823, zzz9824), Succ(zzz3000), zzz31, h) -> new_addToFM_C(zzz9823, Succ(zzz3000), zzz31, h) 130.57/78.26 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4 130.57/78.26 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (74) 130.57/78.26 YES 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (75) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_splitGT29(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Succ(zzz34020), Zero, ba) -> new_splitGT5(zzz3400, zzz3401, ba) 130.57/78.26 new_splitGT211(zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, h) -> new_splitGT5(zzz16124, zzz1613, h) 130.57/78.26 new_splitGT28(Neg(zzz161200), zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, h) -> new_splitGT5(zzz16124, zzz1613, h) 130.57/78.26 new_splitGT10(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, Succ(zzz44340), Succ(zzz44350), bb) -> new_splitGT10(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, zzz44340, zzz44350, bb) 130.57/78.26 new_splitGT5(Branch(Neg(zzz161200), zzz16121, zzz16122, zzz16123, zzz16124), zzz1613, h) -> new_splitGT5(zzz16124, zzz1613, h) 130.57/78.26 new_splitGT29(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Zero, Zero, ba) -> new_splitGT210(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, ba) 130.57/78.26 new_splitGT5(Branch(Pos(Succ(zzz1612000)), zzz16121, zzz16122, zzz16123, zzz16124), zzz1613, h) -> new_splitGT29(zzz1612000, zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, zzz1613, zzz1612000, h) 130.57/78.26 new_splitGT29(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Succ(zzz34020), Succ(zzz34030), ba) -> new_splitGT29(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, zzz34020, zzz34030, ba) 130.57/78.26 new_splitGT5(Branch(Pos(Zero), zzz16121, zzz16122, zzz16123, zzz16124), zzz1613, h) -> new_splitGT5(zzz16124, zzz1613, h) 130.57/78.26 new_splitGT29(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Zero, Succ(zzz34030), ba) -> new_splitGT10(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Succ(zzz3401), Succ(zzz3396), ba) 130.57/78.26 new_splitGT10(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, Zero, Succ(zzz44350), bb) -> new_splitGT5(zzz4431, zzz4433, bb) 130.57/78.26 new_splitGT210(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, ba) -> new_splitGT10(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Succ(zzz3401), Succ(zzz3396), ba) 130.57/78.26 new_splitGT28(Pos(Succ(zzz1612000)), zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, h) -> new_splitGT29(zzz1612000, zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, zzz1613, zzz1612000, h) 130.57/78.26 new_splitGT28(Pos(Zero), zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, h) -> new_splitGT5(zzz16124, zzz1613, h) 130.57/78.26 new_splitGT212(zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, h) -> new_splitGT5(zzz16124, zzz1613, h) 130.57/78.26 130.57/78.26 R is empty. 130.57/78.26 Q is empty. 130.57/78.26 We have to consider all minimal (P,Q,R)-chains. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (76) DependencyGraphProof (EQUIVALENT) 130.57/78.26 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (77) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_splitGT5(Branch(Neg(zzz161200), zzz16121, zzz16122, zzz16123, zzz16124), zzz1613, h) -> new_splitGT5(zzz16124, zzz1613, h) 130.57/78.26 new_splitGT5(Branch(Pos(Succ(zzz1612000)), zzz16121, zzz16122, zzz16123, zzz16124), zzz1613, h) -> new_splitGT29(zzz1612000, zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, zzz1613, zzz1612000, h) 130.57/78.26 new_splitGT29(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Succ(zzz34020), Zero, ba) -> new_splitGT5(zzz3400, zzz3401, ba) 130.57/78.26 new_splitGT5(Branch(Pos(Zero), zzz16121, zzz16122, zzz16123, zzz16124), zzz1613, h) -> new_splitGT5(zzz16124, zzz1613, h) 130.57/78.26 new_splitGT29(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Zero, Zero, ba) -> new_splitGT210(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, ba) 130.57/78.26 new_splitGT210(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, ba) -> new_splitGT10(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Succ(zzz3401), Succ(zzz3396), ba) 130.57/78.26 new_splitGT10(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, Succ(zzz44340), Succ(zzz44350), bb) -> new_splitGT10(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, zzz44340, zzz44350, bb) 130.57/78.26 new_splitGT10(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, Zero, Succ(zzz44350), bb) -> new_splitGT5(zzz4431, zzz4433, bb) 130.57/78.26 new_splitGT29(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Succ(zzz34020), Succ(zzz34030), ba) -> new_splitGT29(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, zzz34020, zzz34030, ba) 130.57/78.26 new_splitGT29(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Zero, Succ(zzz34030), ba) -> new_splitGT10(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Succ(zzz3401), Succ(zzz3396), ba) 130.57/78.26 130.57/78.26 R is empty. 130.57/78.26 Q is empty. 130.57/78.26 We have to consider all minimal (P,Q,R)-chains. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (78) QDPSizeChangeProof (EQUIVALENT) 130.57/78.26 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. 130.57/78.26 130.57/78.26 From the DPs we obtained the following set of size-change graphs: 130.57/78.26 *new_splitGT5(Branch(Pos(Succ(zzz1612000)), zzz16121, zzz16122, zzz16123, zzz16124), zzz1613, h) -> new_splitGT29(zzz1612000, zzz16121, zzz16122, zzz16123, zzz16124, zzz1613, zzz1613, zzz1612000, h) 130.57/78.26 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 >= 6, 2 >= 7, 1 > 8, 3 >= 9 130.57/78.26 130.57/78.26 130.57/78.26 *new_splitGT29(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Succ(zzz34020), Zero, ba) -> new_splitGT5(zzz3400, zzz3401, ba) 130.57/78.26 The graph contains the following edges 5 >= 1, 6 >= 2, 9 >= 3 130.57/78.26 130.57/78.26 130.57/78.26 *new_splitGT10(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, Zero, Succ(zzz44350), bb) -> new_splitGT5(zzz4431, zzz4433, bb) 130.57/78.26 The graph contains the following edges 4 >= 1, 6 >= 2, 9 >= 3 130.57/78.26 130.57/78.26 130.57/78.26 *new_splitGT29(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Succ(zzz34020), Succ(zzz34030), ba) -> new_splitGT29(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, zzz34020, zzz34030, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9 130.57/78.26 130.57/78.26 130.57/78.26 *new_splitGT210(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, ba) -> new_splitGT10(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Succ(zzz3401), Succ(zzz3396), ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 9 130.57/78.26 130.57/78.26 130.57/78.26 *new_splitGT10(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, Succ(zzz44340), Succ(zzz44350), bb) -> new_splitGT10(zzz4428, zzz4429, zzz4430, zzz4431, zzz4432, zzz4433, zzz44340, zzz44350, bb) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9 130.57/78.26 130.57/78.26 130.57/78.26 *new_splitGT29(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Zero, Zero, ba) -> new_splitGT210(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 7 130.57/78.26 130.57/78.26 130.57/78.26 *new_splitGT29(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Zero, Succ(zzz34030), ba) -> new_splitGT10(zzz3396, zzz3397, zzz3398, zzz3399, zzz3400, zzz3401, Succ(zzz3401), Succ(zzz3396), ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 9 130.57/78.26 130.57/78.26 130.57/78.26 *new_splitGT5(Branch(Neg(zzz161200), zzz16121, zzz16122, zzz16123, zzz16124), zzz1613, h) -> new_splitGT5(zzz16124, zzz1613, h) 130.57/78.26 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 130.57/78.26 130.57/78.26 130.57/78.26 *new_splitGT5(Branch(Pos(Zero), zzz16121, zzz16122, zzz16123, zzz16124), zzz1613, h) -> new_splitGT5(zzz16124, zzz1613, h) 130.57/78.26 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 130.57/78.26 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (79) 130.57/78.26 YES 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (80) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_addToFM_C21(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Succ(zzz31880), Succ(zzz31890), h) -> new_addToFM_C21(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, zzz31880, zzz31890, h) 130.57/78.26 new_addToFM_C0(Branch(Neg(zzz3400), zzz341, zzz342, zzz343, zzz344), Succ(zzz3000), zzz31, bb) -> new_addToFM_C0(zzz344, Succ(zzz3000), zzz31, bb) 130.57/78.26 new_addToFM_C0(Branch(Pos(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), Succ(zzz3000), zzz31, bb) -> new_addToFM_C21(zzz34000, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, zzz3000, zzz34000, bb) 130.57/78.26 new_addToFM_C21(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Zero, Succ(zzz31890), h) -> new_addToFM_C0(zzz3184, Succ(zzz3186), zzz3187, h) 130.57/78.26 new_addToFM_C10(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, Succ(zzz43100), Succ(zzz43110), ba) -> new_addToFM_C10(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, zzz43100, zzz43110, ba) 130.57/78.26 new_addToFM_C21(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Zero, Zero, h) -> new_addToFM_C22(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, h) 130.57/78.26 new_addToFM_C22(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, h) -> new_addToFM_C10(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Succ(zzz3186), Succ(zzz3181), h) 130.57/78.26 new_addToFM_C0(Branch(Neg(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), Zero, zzz31, bb) -> new_addToFM_C0(zzz344, Zero, zzz31, bb) 130.57/78.26 new_addToFM_C0(Branch(Pos(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), Zero, zzz31, bb) -> new_addToFM_C0(zzz343, Zero, zzz31, bb) 130.57/78.26 new_addToFM_C0(Branch(Pos(Zero), zzz341, zzz342, zzz343, zzz344), Succ(zzz3000), zzz31, bb) -> new_addToFM_C0(zzz344, Succ(zzz3000), zzz31, bb) 130.57/78.26 new_addToFM_C21(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Succ(zzz31880), Zero, h) -> new_addToFM_C10(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Succ(zzz3186), Succ(zzz3181), h) 130.57/78.26 new_addToFM_C10(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, Succ(zzz43100), Zero, ba) -> new_addToFM_C0(zzz4307, Succ(zzz4308), zzz4309, ba) 130.57/78.26 130.57/78.26 R is empty. 130.57/78.26 Q is empty. 130.57/78.26 We have to consider all minimal (P,Q,R)-chains. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (81) DependencyGraphProof (EQUIVALENT) 130.57/78.26 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (82) 130.57/78.26 Complex Obligation (AND) 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (83) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_addToFM_C0(Branch(Pos(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), Zero, zzz31, bb) -> new_addToFM_C0(zzz343, Zero, zzz31, bb) 130.57/78.26 new_addToFM_C0(Branch(Neg(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), Zero, zzz31, bb) -> new_addToFM_C0(zzz344, Zero, zzz31, bb) 130.57/78.26 130.57/78.26 R is empty. 130.57/78.26 Q is empty. 130.57/78.26 We have to consider all minimal (P,Q,R)-chains. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (84) QDPSizeChangeProof (EQUIVALENT) 130.57/78.26 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. 130.57/78.26 130.57/78.26 From the DPs we obtained the following set of size-change graphs: 130.57/78.26 *new_addToFM_C0(Branch(Pos(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), Zero, zzz31, bb) -> new_addToFM_C0(zzz343, Zero, zzz31, bb) 130.57/78.26 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C0(Branch(Neg(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), Zero, zzz31, bb) -> new_addToFM_C0(zzz344, Zero, zzz31, bb) 130.57/78.26 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4 130.57/78.26 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (85) 130.57/78.26 YES 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (86) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_addToFM_C21(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Zero, Succ(zzz31890), h) -> new_addToFM_C0(zzz3184, Succ(zzz3186), zzz3187, h) 130.57/78.26 new_addToFM_C0(Branch(Neg(zzz3400), zzz341, zzz342, zzz343, zzz344), Succ(zzz3000), zzz31, bb) -> new_addToFM_C0(zzz344, Succ(zzz3000), zzz31, bb) 130.57/78.26 new_addToFM_C0(Branch(Pos(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), Succ(zzz3000), zzz31, bb) -> new_addToFM_C21(zzz34000, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, zzz3000, zzz34000, bb) 130.57/78.26 new_addToFM_C21(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Succ(zzz31880), Succ(zzz31890), h) -> new_addToFM_C21(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, zzz31880, zzz31890, h) 130.57/78.26 new_addToFM_C21(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Zero, Zero, h) -> new_addToFM_C22(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, h) 130.57/78.26 new_addToFM_C22(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, h) -> new_addToFM_C10(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Succ(zzz3186), Succ(zzz3181), h) 130.57/78.26 new_addToFM_C10(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, Succ(zzz43100), Succ(zzz43110), ba) -> new_addToFM_C10(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, zzz43100, zzz43110, ba) 130.57/78.26 new_addToFM_C10(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, Succ(zzz43100), Zero, ba) -> new_addToFM_C0(zzz4307, Succ(zzz4308), zzz4309, ba) 130.57/78.26 new_addToFM_C0(Branch(Pos(Zero), zzz341, zzz342, zzz343, zzz344), Succ(zzz3000), zzz31, bb) -> new_addToFM_C0(zzz344, Succ(zzz3000), zzz31, bb) 130.57/78.26 new_addToFM_C21(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Succ(zzz31880), Zero, h) -> new_addToFM_C10(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Succ(zzz3186), Succ(zzz3181), h) 130.57/78.26 130.57/78.26 R is empty. 130.57/78.26 Q is empty. 130.57/78.26 We have to consider all minimal (P,Q,R)-chains. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (87) QDPSizeChangeProof (EQUIVALENT) 130.57/78.26 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. 130.57/78.26 130.57/78.26 From the DPs we obtained the following set of size-change graphs: 130.57/78.26 *new_addToFM_C0(Branch(Pos(Succ(zzz34000)), zzz341, zzz342, zzz343, zzz344), Succ(zzz3000), zzz31, bb) -> new_addToFM_C21(zzz34000, zzz341, zzz342, zzz343, zzz344, zzz3000, zzz31, zzz3000, zzz34000, bb) 130.57/78.26 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 > 6, 3 >= 7, 2 > 8, 1 > 9, 4 >= 10 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C21(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Succ(zzz31880), Succ(zzz31890), h) -> new_addToFM_C21(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, zzz31880, zzz31890, h) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 9 > 9, 10 >= 10 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C21(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Zero, Succ(zzz31890), h) -> new_addToFM_C0(zzz3184, Succ(zzz3186), zzz3187, h) 130.57/78.26 The graph contains the following edges 4 >= 1, 7 >= 3, 10 >= 4 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C10(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, Succ(zzz43100), Zero, ba) -> new_addToFM_C0(zzz4307, Succ(zzz4308), zzz4309, ba) 130.57/78.26 The graph contains the following edges 5 >= 1, 7 >= 3, 10 >= 4 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C22(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, h) -> new_addToFM_C10(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Succ(zzz3186), Succ(zzz3181), h) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 10 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C10(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, Succ(zzz43100), Succ(zzz43110), ba) -> new_addToFM_C10(zzz4303, zzz4304, zzz4305, zzz4306, zzz4307, zzz4308, zzz4309, zzz43100, zzz43110, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 9 > 9, 10 >= 10 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C21(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Zero, Zero, h) -> new_addToFM_C22(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, h) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 10 >= 8 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C21(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Succ(zzz31880), Zero, h) -> new_addToFM_C10(zzz3181, zzz3182, zzz3183, zzz3184, zzz3185, zzz3186, zzz3187, Succ(zzz3186), Succ(zzz3181), h) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 10 >= 10 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C0(Branch(Neg(zzz3400), zzz341, zzz342, zzz343, zzz344), Succ(zzz3000), zzz31, bb) -> new_addToFM_C0(zzz344, Succ(zzz3000), zzz31, bb) 130.57/78.26 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4 130.57/78.26 130.57/78.26 130.57/78.26 *new_addToFM_C0(Branch(Pos(Zero), zzz341, zzz342, zzz343, zzz344), Succ(zzz3000), zzz31, bb) -> new_addToFM_C0(zzz344, Succ(zzz3000), zzz31, bb) 130.57/78.26 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4 130.57/78.26 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (88) 130.57/78.26 YES 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (89) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_glueVBal3GlueVBal11(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Pos(Succ(zzz634300)), h, ba) -> new_glueVBal3GlueVBal15(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, zzz634300, h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(Zero), Pos(Succ(Succ(zzz6319000))), h, ba) -> new_glueVBal3GlueVBal24(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal11(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(Succ(zzz634900)), Pos(Succ(Succ(zzz6343000))), h, ba) -> new_glueVBal3GlueVBal13(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz634900, zzz6343000, h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63380), Pos(Zero), h, ba) -> new_glueVBal3GlueVBal23(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Neg(Zero), h, ba) -> new_glueVBal3GlueVBal25(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal15(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz634300), zzz63500, h, ba) -> new_glueVBal3GlueVBal13(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz634300, zzz63500, h, ba) 130.57/78.26 new_glueVBal3GlueVBal2(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Neg(zzz63370), zzz6319, h, ba) -> new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_primMulNat(zzz63370), zzz6319, h, ba) 130.57/78.26 new_glueVBal3GlueVBal14(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, Branch(zzz474640, zzz474641, zzz474642, zzz474643, zzz474644), h, ba) -> new_glueVBal3(zzz474640, zzz474641, zzz474642, zzz474643, zzz474644, zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, h, ba) 130.57/78.26 new_glueVBal3GlueVBal12(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63500), Neg(Zero), h, ba) -> new_glueVBal3GlueVBal14(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal12(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63500), Neg(Succ(zzz634300)), h, ba) -> new_glueVBal3GlueVBal13(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz634300, zzz63500, h, ba) 130.57/78.26 new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Pos(Succ(zzz631900)), h, ba) -> new_glueVBal3GlueVBal24(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal25(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) -> new_glueVBal3GlueVBal27(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal26(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz631900), zzz63400, h, ba) -> new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz631900, zzz63400, h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(Succ(zzz633800)), Pos(Succ(Zero)), h, ba) -> new_glueVBal3GlueVBal23(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63400), Neg(Zero), h, ba) -> new_glueVBal3GlueVBal24(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Pos(Succ(zzz631900)), h, ba) -> new_glueVBal3GlueVBal26(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, zzz631900, h, ba) 130.57/78.26 new_glueVBal3GlueVBal26(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, zzz63400, h, ba) -> new_glueVBal3GlueVBal24(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal15(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, zzz63500, h, ba) -> new_glueVBal3GlueVBal14(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Pos(Zero), h, ba) -> new_glueVBal3GlueVBal27(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Neg(Succ(zzz631900)), h, ba) -> new_glueVBal3GlueVBal23(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal28(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz633800), Succ(Succ(zzz6319000)), h, ba) -> new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz633800, zzz6319000, h, ba) 130.57/78.26 new_glueVBal3GlueVBal28(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz63380, Zero, h, ba) -> new_glueVBal3GlueVBal23(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal13(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz634900), Succ(zzz6343000), h, ba) -> new_glueVBal3GlueVBal13(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz634900, zzz6343000, h, ba) 130.57/78.26 new_glueVBal3GlueVBal28(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Succ(Zero), h, ba) -> new_glueVBal3GlueVBal25(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal13(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Succ(zzz6343000), h, ba) -> new_glueVBal3GlueVBal14(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal28(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Succ(Succ(zzz6319000)), h, ba) -> new_glueVBal3GlueVBal24(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal11(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(Zero), Pos(Succ(Succ(zzz6343000))), h, ba) -> new_glueVBal3GlueVBal14(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63380), Neg(zzz63190), h, ba) -> new_glueVBal3GlueVBal1(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_l(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), h, ba) 130.57/78.26 new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz633800), Succ(zzz6319000), h, ba) -> new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz633800, zzz6319000, h, ba) 130.57/78.26 new_glueVBal3GlueVBal2(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Pos(zzz63370), zzz6319, h, ba) -> new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_primMulNat(zzz63370), zzz6319, h, ba) 130.57/78.26 new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz633800), Zero, h, ba) -> new_glueVBal3GlueVBal23(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal16(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz634900), Succ(Succ(zzz6343000)), h, ba) -> new_glueVBal3GlueVBal13(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz634900, zzz6343000, h, ba) 130.57/78.26 new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Pos(Zero), h, ba) -> new_glueVBal3GlueVBal25(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Neg(Succ(zzz631900)), h, ba) -> new_glueVBal3GlueVBal28(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz631900, Zero, h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(Succ(zzz633800)), Pos(Succ(Succ(zzz6319000))), h, ba) -> new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz633800, zzz6319000, h, ba) 130.57/78.26 new_glueVBal3GlueVBal10(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Neg(zzz63480), zzz6343, h, ba) -> new_glueVBal3GlueVBal12(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_primMulNat(zzz63480), zzz6343, h, ba) 130.57/78.26 new_glueVBal3GlueVBal24(zzz474030, zzz474031, zzz474032, Branch(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334), zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) -> new_glueVBal3GlueVBal29(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_r(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), h, ba) 130.57/78.26 new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63400), Neg(Succ(zzz631900)), h, ba) -> new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz631900, zzz63400, h, ba) 130.57/78.26 new_glueVBal3GlueVBal12(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, Branch(zzz474640, zzz474641, zzz474642, zzz474643, zzz474644), Succ(zzz63500), Pos(zzz63430), h, ba) -> new_glueVBal3(zzz474640, zzz474641, zzz474642, zzz474643, zzz474644, zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, h, ba) 130.57/78.26 new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, Branch(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334), zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63400), Pos(zzz63190), h, ba) -> new_glueVBal3GlueVBal29(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_r(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), h, ba) 130.57/78.26 new_glueVBal3GlueVBal16(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Succ(Succ(zzz6343000)), h, ba) -> new_glueVBal3GlueVBal14(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Neg(Zero), h, ba) -> new_glueVBal3GlueVBal25(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Zero, h, ba) -> new_glueVBal3GlueVBal25(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal12(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Neg(Succ(zzz634300)), h, ba) -> new_glueVBal3GlueVBal16(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz634300, Zero, h, ba) 130.57/78.26 new_glueVBal3GlueVBal23(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) -> new_glueVBal3GlueVBal1(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_l(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), h, ba) 130.57/78.26 new_glueVBal3GlueVBal10(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Pos(zzz63480), zzz6343, h, ba) -> new_glueVBal3GlueVBal11(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_primMulNat(zzz63480), zzz6343, h, ba) 130.57/78.26 new_glueVBal3GlueVBal1(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz6343, h, ba) -> new_glueVBal3GlueVBal10(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_r(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), zzz6343, h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(Zero), Pos(Succ(Zero)), h, ba) -> new_glueVBal3GlueVBal25(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal12(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Pos(Succ(zzz634300)), h, ba) -> new_glueVBal3GlueVBal14(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal28(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz633800), Succ(Zero), h, ba) -> new_glueVBal3GlueVBal23(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal27(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) -> new_glueVBal3GlueVBal1(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_l(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), h, ba) 130.57/78.26 new_glueVBal3GlueVBal29(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz6319, h, ba) -> new_glueVBal3GlueVBal2(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_l(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), zzz6319, h, ba) 130.57/78.26 new_glueVBal3(zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, h, ba) -> new_glueVBal3GlueVBal29(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_r(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), h, ba) 130.57/78.26 new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Succ(zzz6319000), h, ba) -> new_glueVBal3GlueVBal24(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 130.57/78.26 The TRS R consists of the following rules: 130.57/78.26 130.57/78.26 new_primMulNat(Succ(zzz633700)) -> new_primPlusNat0(new_primMulNat0(zzz633700), Succ(zzz633700)) 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.26 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.26 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.26 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.26 new_primMulNat2(zzz4739) -> Zero 130.57/78.26 new_glueVBal3Size_l(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) -> new_sizeFM(Branch(zzz47460, zzz47461, zzz47462, zzz47463, zzz47464), h, ba) 130.57/78.26 new_primMulNat(Zero) -> Zero 130.57/78.26 new_sizeFM(Branch(zzz34900, zzz34901, zzz34902, zzz34903, zzz34904), bb, bc) -> zzz34902 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.26 new_sizeFM(EmptyFM, bb, bc) -> Pos(Zero) 130.57/78.26 new_glueVBal3Size_r(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) -> new_sizeFM(Branch(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034), h, ba) 130.57/78.26 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.26 130.57/78.26 The set Q consists of the following terms: 130.57/78.26 130.57/78.26 new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.26 new_primMulNat2(x0) 130.57/78.26 new_primPlusNat0(Succ(x0), Zero) 130.57/78.26 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.26 new_primMulNat0(x0) 130.57/78.26 new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.26 new_primMulNat(Succ(x0)) 130.57/78.26 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.26 new_primMulNat(Zero) 130.57/78.26 new_sizeFM(EmptyFM, x0, x1) 130.57/78.26 new_primMulNat1(x0) 130.57/78.26 new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6) 130.57/78.26 new_primPlusNat0(Zero, Zero) 130.57/78.26 130.57/78.26 We have to consider all minimal (P,Q,R)-chains. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (90) DependencyGraphProof (EQUIVALENT) 130.57/78.26 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 9 less nodes. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (91) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_glueVBal3GlueVBal15(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, zzz63500, h, ba) -> new_glueVBal3GlueVBal14(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal14(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, Branch(zzz474640, zzz474641, zzz474642, zzz474643, zzz474644), h, ba) -> new_glueVBal3(zzz474640, zzz474641, zzz474642, zzz474643, zzz474644, zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, h, ba) 130.57/78.26 new_glueVBal3(zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, h, ba) -> new_glueVBal3GlueVBal29(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_r(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), h, ba) 130.57/78.26 new_glueVBal3GlueVBal29(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz6319, h, ba) -> new_glueVBal3GlueVBal2(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_l(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), zzz6319, h, ba) 130.57/78.26 new_glueVBal3GlueVBal2(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Neg(zzz63370), zzz6319, h, ba) -> new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_primMulNat(zzz63370), zzz6319, h, ba) 130.57/78.26 new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Neg(Zero), h, ba) -> new_glueVBal3GlueVBal25(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal25(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) -> new_glueVBal3GlueVBal27(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal27(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) -> new_glueVBal3GlueVBal1(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_l(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), h, ba) 130.57/78.26 new_glueVBal3GlueVBal1(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz6343, h, ba) -> new_glueVBal3GlueVBal10(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_r(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), zzz6343, h, ba) 130.57/78.26 new_glueVBal3GlueVBal10(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Neg(zzz63480), zzz6343, h, ba) -> new_glueVBal3GlueVBal12(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_primMulNat(zzz63480), zzz6343, h, ba) 130.57/78.26 new_glueVBal3GlueVBal12(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63500), Neg(Zero), h, ba) -> new_glueVBal3GlueVBal14(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal12(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63500), Neg(Succ(zzz634300)), h, ba) -> new_glueVBal3GlueVBal13(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz634300, zzz63500, h, ba) 130.57/78.26 new_glueVBal3GlueVBal13(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz634900), Succ(zzz6343000), h, ba) -> new_glueVBal3GlueVBal13(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz634900, zzz6343000, h, ba) 130.57/78.26 new_glueVBal3GlueVBal13(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Succ(zzz6343000), h, ba) -> new_glueVBal3GlueVBal14(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal12(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, Branch(zzz474640, zzz474641, zzz474642, zzz474643, zzz474644), Succ(zzz63500), Pos(zzz63430), h, ba) -> new_glueVBal3(zzz474640, zzz474641, zzz474642, zzz474643, zzz474644, zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, h, ba) 130.57/78.26 new_glueVBal3GlueVBal12(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Pos(Succ(zzz634300)), h, ba) -> new_glueVBal3GlueVBal14(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal10(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Pos(zzz63480), zzz6343, h, ba) -> new_glueVBal3GlueVBal11(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_primMulNat(zzz63480), zzz6343, h, ba) 130.57/78.26 new_glueVBal3GlueVBal11(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Pos(Succ(zzz634300)), h, ba) -> new_glueVBal3GlueVBal15(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, zzz634300, h, ba) 130.57/78.26 new_glueVBal3GlueVBal11(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(Succ(zzz634900)), Pos(Succ(Succ(zzz6343000))), h, ba) -> new_glueVBal3GlueVBal13(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz634900, zzz6343000, h, ba) 130.57/78.26 new_glueVBal3GlueVBal11(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(Zero), Pos(Succ(Succ(zzz6343000))), h, ba) -> new_glueVBal3GlueVBal14(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Pos(Succ(zzz631900)), h, ba) -> new_glueVBal3GlueVBal24(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal24(zzz474030, zzz474031, zzz474032, Branch(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334), zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) -> new_glueVBal3GlueVBal29(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_r(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), h, ba) 130.57/78.26 new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63400), Neg(Zero), h, ba) -> new_glueVBal3GlueVBal24(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Pos(Zero), h, ba) -> new_glueVBal3GlueVBal25(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Neg(Succ(zzz631900)), h, ba) -> new_glueVBal3GlueVBal28(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz631900, Zero, h, ba) 130.57/78.26 new_glueVBal3GlueVBal28(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz63380, Zero, h, ba) -> new_glueVBal3GlueVBal23(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal23(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) -> new_glueVBal3GlueVBal1(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_l(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), h, ba) 130.57/78.26 new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63400), Neg(Succ(zzz631900)), h, ba) -> new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz631900, zzz63400, h, ba) 130.57/78.26 new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz633800), Succ(zzz6319000), h, ba) -> new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz633800, zzz6319000, h, ba) 130.57/78.26 new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz633800), Zero, h, ba) -> new_glueVBal3GlueVBal23(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Zero, h, ba) -> new_glueVBal3GlueVBal25(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Succ(zzz6319000), h, ba) -> new_glueVBal3GlueVBal24(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, Branch(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334), zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63400), Pos(zzz63190), h, ba) -> new_glueVBal3GlueVBal29(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_r(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), h, ba) 130.57/78.26 new_glueVBal3GlueVBal2(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Pos(zzz63370), zzz6319, h, ba) -> new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_primMulNat(zzz63370), zzz6319, h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(Zero), Pos(Succ(Succ(zzz6319000))), h, ba) -> new_glueVBal3GlueVBal24(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63380), Pos(Zero), h, ba) -> new_glueVBal3GlueVBal23(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(Succ(zzz633800)), Pos(Succ(Zero)), h, ba) -> new_glueVBal3GlueVBal23(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Pos(Succ(zzz631900)), h, ba) -> new_glueVBal3GlueVBal26(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, zzz631900, h, ba) 130.57/78.26 new_glueVBal3GlueVBal26(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, zzz63400, h, ba) -> new_glueVBal3GlueVBal24(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Pos(Zero), h, ba) -> new_glueVBal3GlueVBal27(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Neg(Succ(zzz631900)), h, ba) -> new_glueVBal3GlueVBal23(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63380), Neg(zzz63190), h, ba) -> new_glueVBal3GlueVBal1(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_l(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(Succ(zzz633800)), Pos(Succ(Succ(zzz6319000))), h, ba) -> new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz633800, zzz6319000, h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Neg(Zero), h, ba) -> new_glueVBal3GlueVBal25(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(Zero), Pos(Succ(Zero)), h, ba) -> new_glueVBal3GlueVBal25(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 130.57/78.26 The TRS R consists of the following rules: 130.57/78.26 130.57/78.26 new_primMulNat(Succ(zzz633700)) -> new_primPlusNat0(new_primMulNat0(zzz633700), Succ(zzz633700)) 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.26 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.26 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.26 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.26 new_primMulNat2(zzz4739) -> Zero 130.57/78.26 new_glueVBal3Size_l(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) -> new_sizeFM(Branch(zzz47460, zzz47461, zzz47462, zzz47463, zzz47464), h, ba) 130.57/78.26 new_primMulNat(Zero) -> Zero 130.57/78.26 new_sizeFM(Branch(zzz34900, zzz34901, zzz34902, zzz34903, zzz34904), bb, bc) -> zzz34902 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.26 new_sizeFM(EmptyFM, bb, bc) -> Pos(Zero) 130.57/78.26 new_glueVBal3Size_r(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) -> new_sizeFM(Branch(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034), h, ba) 130.57/78.26 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.26 130.57/78.26 The set Q consists of the following terms: 130.57/78.26 130.57/78.26 new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.26 new_primMulNat2(x0) 130.57/78.26 new_primPlusNat0(Succ(x0), Zero) 130.57/78.26 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.26 new_primMulNat0(x0) 130.57/78.26 new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 130.57/78.26 new_primMulNat(Succ(x0)) 130.57/78.26 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.26 new_primMulNat(Zero) 130.57/78.26 new_sizeFM(EmptyFM, x0, x1) 130.57/78.26 new_primMulNat1(x0) 130.57/78.26 new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6) 130.57/78.26 new_primPlusNat0(Zero, Zero) 130.57/78.26 130.57/78.26 We have to consider all minimal (P,Q,R)-chains. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (92) QDPSizeChangeProof (EQUIVALENT) 130.57/78.26 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. 130.57/78.26 130.57/78.26 From the DPs we obtained the following set of size-change graphs: 130.57/78.26 *new_glueVBal3GlueVBal14(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, Branch(zzz474640, zzz474641, zzz474642, zzz474643, zzz474644), h, ba) -> new_glueVBal3(zzz474640, zzz474641, zzz474642, zzz474643, zzz474644, zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, h, ba) 130.57/78.26 The graph contains the following edges 10 > 1, 10 > 2, 10 > 3, 10 > 4, 10 > 5, 1 >= 6, 2 >= 7, 3 >= 8, 4 >= 9, 5 >= 10, 11 >= 11, 12 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal11(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Pos(Succ(zzz634300)), h, ba) -> new_glueVBal3GlueVBal15(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, zzz634300, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 > 12, 13 >= 13, 14 >= 14 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3(zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, h, ba) -> new_glueVBal3GlueVBal29(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_r(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), h, ba) 130.57/78.26 The graph contains the following edges 6 >= 1, 7 >= 2, 8 >= 3, 9 >= 4, 10 >= 5, 1 >= 6, 2 >= 7, 3 >= 8, 4 >= 9, 5 >= 10, 11 >= 12, 12 >= 13 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal29(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz6319, h, ba) -> new_glueVBal3GlueVBal2(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_l(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), zzz6319, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 12, 12 >= 13, 13 >= 14 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal12(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, Branch(zzz474640, zzz474641, zzz474642, zzz474643, zzz474644), Succ(zzz63500), Pos(zzz63430), h, ba) -> new_glueVBal3(zzz474640, zzz474641, zzz474642, zzz474643, zzz474644, zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, h, ba) 130.57/78.26 The graph contains the following edges 10 > 1, 10 > 2, 10 > 3, 10 > 4, 10 > 5, 1 >= 6, 2 >= 7, 3 >= 8, 4 >= 9, 5 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, Branch(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334), zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63400), Pos(zzz63190), h, ba) -> new_glueVBal3GlueVBal29(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_r(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), h, ba) 130.57/78.26 The graph contains the following edges 4 > 1, 4 > 2, 4 > 3, 4 > 4, 4 > 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 12, 14 >= 13 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal24(zzz474030, zzz474031, zzz474032, Branch(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334), zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) -> new_glueVBal3GlueVBal29(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_r(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), h, ba) 130.57/78.26 The graph contains the following edges 4 > 1, 4 > 2, 4 > 3, 4 > 4, 4 > 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 12, 12 >= 13 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal2(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Neg(zzz63370), zzz6319, h, ba) -> new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_primMulNat(zzz63370), zzz6319, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 12 >= 12, 13 >= 13, 14 >= 14 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal2(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Pos(zzz63370), zzz6319, h, ba) -> new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_primMulNat(zzz63370), zzz6319, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 12 >= 12, 13 >= 13, 14 >= 14 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal25(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) -> new_glueVBal3GlueVBal27(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal27(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) -> new_glueVBal3GlueVBal1(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_l(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 12, 12 >= 13 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal1(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz6343, h, ba) -> new_glueVBal3GlueVBal10(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_r(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), zzz6343, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 12, 12 >= 13, 13 >= 14 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Pos(Zero), h, ba) -> new_glueVBal3GlueVBal27(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal12(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63500), Neg(Succ(zzz634300)), h, ba) -> new_glueVBal3GlueVBal13(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz634300, zzz63500, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 12 > 11, 11 > 12, 13 >= 13, 14 >= 14 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal10(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Neg(zzz63480), zzz6343, h, ba) -> new_glueVBal3GlueVBal12(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_primMulNat(zzz63480), zzz6343, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 12 >= 12, 13 >= 13, 14 >= 14 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal10(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Pos(zzz63480), zzz6343, h, ba) -> new_glueVBal3GlueVBal11(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_primMulNat(zzz63480), zzz6343, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 12 >= 12, 13 >= 13, 14 >= 14 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal13(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Succ(zzz6343000), h, ba) -> new_glueVBal3GlueVBal14(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal13(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz634900), Succ(zzz6343000), h, ba) -> new_glueVBal3GlueVBal13(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz634900, zzz6343000, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 > 11, 12 > 12, 13 >= 13, 14 >= 14 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal11(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(Succ(zzz634900)), Pos(Succ(Succ(zzz6343000))), h, ba) -> new_glueVBal3GlueVBal13(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz634900, zzz6343000, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 > 11, 12 > 12, 13 >= 13, 14 >= 14 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal11(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(Zero), Pos(Succ(Succ(zzz6343000))), h, ba) -> new_glueVBal3GlueVBal14(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal15(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, zzz63500, h, ba) -> new_glueVBal3GlueVBal14(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal28(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz63380, Zero, h, ba) -> new_glueVBal3GlueVBal23(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Neg(Succ(zzz631900)), h, ba) -> new_glueVBal3GlueVBal28(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz631900, Zero, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 12 > 11, 11 >= 12, 13 >= 13, 14 >= 14 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63400), Neg(Succ(zzz631900)), h, ba) -> new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz631900, zzz63400, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 12 > 11, 11 > 12, 13 >= 13, 14 >= 14 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal23(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) -> new_glueVBal3GlueVBal1(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_l(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 12, 12 >= 13 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63380), Neg(zzz63190), h, ba) -> new_glueVBal3GlueVBal1(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, new_glueVBal3Size_l(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba), h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 12, 14 >= 13 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Zero, h, ba) -> new_glueVBal3GlueVBal25(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Succ(zzz6319000), h, ba) -> new_glueVBal3GlueVBal24(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz633800), Zero, h, ba) -> new_glueVBal3GlueVBal23(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz633800), Succ(zzz6319000), h, ba) -> new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz633800, zzz6319000, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 > 11, 12 > 12, 13 >= 13, 14 >= 14 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(Succ(zzz633800)), Pos(Succ(Succ(zzz6319000))), h, ba) -> new_glueVBal3GlueVBal22(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, zzz633800, zzz6319000, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 > 11, 12 > 12, 13 >= 13, 14 >= 14 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Pos(Succ(zzz631900)), h, ba) -> new_glueVBal3GlueVBal26(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, zzz631900, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 > 12, 13 >= 13, 14 >= 14 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(Zero), Pos(Succ(Succ(zzz6319000))), h, ba) -> new_glueVBal3GlueVBal24(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal26(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, zzz63400, h, ba) -> new_glueVBal3GlueVBal24(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal12(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63500), Neg(Zero), h, ba) -> new_glueVBal3GlueVBal14(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal12(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Pos(Succ(zzz634300)), h, ba) -> new_glueVBal3GlueVBal14(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Neg(Zero), h, ba) -> new_glueVBal3GlueVBal25(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Pos(Zero), h, ba) -> new_glueVBal3GlueVBal25(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Pos(Succ(zzz631900)), h, ba) -> new_glueVBal3GlueVBal24(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal21(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63400), Neg(Zero), h, ba) -> new_glueVBal3GlueVBal24(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Neg(Zero), h, ba) -> new_glueVBal3GlueVBal25(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(Zero), Pos(Succ(Zero)), h, ba) -> new_glueVBal3GlueVBal25(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(zzz63380), Pos(Zero), h, ba) -> new_glueVBal3GlueVBal23(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Succ(Succ(zzz633800)), Pos(Succ(Zero)), h, ba) -> new_glueVBal3GlueVBal23(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 *new_glueVBal3GlueVBal20(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, Zero, Neg(Succ(zzz631900)), h, ba) -> new_glueVBal3GlueVBal23(zzz474030, zzz474031, zzz474032, zzz474033, zzz474034, zzz47460, zzz47461, zzz47462, zzz47463, zzz47464, h, ba) 130.57/78.26 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 13 >= 11, 14 >= 12 130.57/78.26 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (93) 130.57/78.26 YES 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (94) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_splitLT25(zzz618, zzz619, zzz620, Branch(Neg(Succ(zzz621000)), zzz6211, zzz6212, zzz6213, zzz6214), zzz622, h) -> new_splitLT3(zzz6214, h) 130.57/78.26 new_splitLT3(Branch(Pos(Succ(zzz621000)), zzz6211, zzz6212, zzz6213, zzz6214), h) -> new_splitLT25(zzz621000, zzz6211, zzz6212, zzz6213, zzz6214, h) 130.57/78.26 new_splitLT25(zzz618, zzz619, zzz620, Branch(Pos(Succ(zzz621000)), zzz6211, zzz6212, zzz6213, zzz6214), zzz622, h) -> new_splitLT25(zzz621000, zzz6211, zzz6212, zzz6213, zzz6214, h) 130.57/78.26 new_splitLT3(Branch(Neg(Succ(zzz621000)), zzz6211, zzz6212, zzz6213, zzz6214), h) -> new_splitLT3(zzz6214, h) 130.57/78.26 130.57/78.26 R is empty. 130.57/78.26 Q is empty. 130.57/78.26 We have to consider all minimal (P,Q,R)-chains. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (95) QDPSizeChangeProof (EQUIVALENT) 130.57/78.26 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. 130.57/78.26 130.57/78.26 From the DPs we obtained the following set of size-change graphs: 130.57/78.26 *new_splitLT3(Branch(Pos(Succ(zzz621000)), zzz6211, zzz6212, zzz6213, zzz6214), h) -> new_splitLT25(zzz621000, zzz6211, zzz6212, zzz6213, zzz6214, h) 130.57/78.26 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 >= 6 130.57/78.26 130.57/78.26 130.57/78.26 *new_splitLT3(Branch(Neg(Succ(zzz621000)), zzz6211, zzz6212, zzz6213, zzz6214), h) -> new_splitLT3(zzz6214, h) 130.57/78.26 The graph contains the following edges 1 > 1, 2 >= 2 130.57/78.26 130.57/78.26 130.57/78.26 *new_splitLT25(zzz618, zzz619, zzz620, Branch(Pos(Succ(zzz621000)), zzz6211, zzz6212, zzz6213, zzz6214), zzz622, h) -> new_splitLT25(zzz621000, zzz6211, zzz6212, zzz6213, zzz6214, h) 130.57/78.26 The graph contains the following edges 4 > 1, 4 > 2, 4 > 3, 4 > 4, 4 > 5, 6 >= 6 130.57/78.26 130.57/78.26 130.57/78.26 *new_splitLT25(zzz618, zzz619, zzz620, Branch(Neg(Succ(zzz621000)), zzz6211, zzz6212, zzz6213, zzz6214), zzz622, h) -> new_splitLT3(zzz6214, h) 130.57/78.26 The graph contains the following edges 4 > 1, 6 >= 2 130.57/78.26 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (96) 130.57/78.26 YES 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (97) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.57/78.26 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000)))), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.26 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Zero)))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.57/78.26 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat6, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, zzz4455, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.57/78.26 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primMulNat3(zzz3745), bh) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000)))), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.57/78.26 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.57/78.26 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.57/78.26 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.57/78.26 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.57/78.26 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.57/78.26 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat7, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.57/78.26 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.57/78.26 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.57/78.26 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat4, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.57/78.26 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Zero, be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.57/78.26 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.57/78.26 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Zero, bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Zero, bh) 130.57/78.26 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Zero, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 130.57/78.26 The TRS R consists of the following rules: 130.57/78.26 130.57/78.26 new_primPlusNat3(Zero) -> Succ(Zero) 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.26 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.26 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.57/78.26 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.26 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.57/78.26 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.57/78.26 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.57/78.26 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.26 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.57/78.26 new_primMulNat6 -> new_primPlusNat5(new_primMulNat4) 130.57/78.26 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.57/78.26 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.26 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.57/78.26 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.57/78.26 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.57/78.26 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.26 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.57/78.26 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.57/78.26 new_primMulNat2(zzz4739) -> Zero 130.57/78.26 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.57/78.26 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.57/78.26 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.57/78.26 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.26 new_primPlusNat2(Zero) -> Zero 130.57/78.26 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.57/78.26 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.26 130.57/78.26 The set Q consists of the following terms: 130.57/78.26 130.57/78.26 new_primPlusNat1(Succ(x0)) 130.57/78.26 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.26 new_primMulNat6 130.57/78.26 new_primMulNat0(x0) 130.57/78.26 new_primPlusNat1(Zero) 130.57/78.26 new_primPlusNat2(Zero) 130.57/78.26 new_primPlusNat3(Succ(x0)) 130.57/78.26 new_primMulNat7 130.57/78.26 new_primPlusNat8(Succ(x0), x1) 130.57/78.26 new_primMulNat3(x0) 130.57/78.26 new_primMulNat2(x0) 130.57/78.26 new_primPlusNat6(x0, Succ(x1)) 130.57/78.26 new_primPlusNat0(Succ(x0), Zero) 130.57/78.26 new_primPlusNat6(x0, Zero) 130.57/78.26 new_primPlusNat5(Succ(x0)) 130.57/78.26 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.26 new_primMulNat4 130.57/78.26 new_primPlusNat4(Succ(x0)) 130.57/78.26 new_primPlusNat8(Zero, x0) 130.57/78.26 new_primPlusNat3(Zero) 130.57/78.26 new_primPlusNat7(x0, Zero) 130.57/78.26 new_primPlusNat5(Zero) 130.57/78.26 new_primMulNat5 130.57/78.26 new_primMulNat1(x0) 130.57/78.26 new_primPlusNat7(x0, Succ(x1)) 130.57/78.26 new_primPlusNat4(Zero) 130.57/78.26 new_primPlusNat2(Succ(x0)) 130.57/78.26 new_primPlusNat0(Zero, Zero) 130.57/78.26 130.57/78.26 We have to consider all minimal (P,Q,R)-chains. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (98) DependencyGraphProof (EQUIVALENT) 130.57/78.26 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 6 SCCs with 7 less nodes. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (99) 130.57/78.26 Complex Obligation (AND) 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (100) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.26 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000)))), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, zzz4455, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000)))), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primMulNat3(zzz3745), bh) 130.57/78.26 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 130.57/78.26 The TRS R consists of the following rules: 130.57/78.26 130.57/78.26 new_primPlusNat3(Zero) -> Succ(Zero) 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.26 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.26 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.57/78.26 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.26 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.57/78.26 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.57/78.26 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.57/78.26 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.26 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.57/78.26 new_primMulNat6 -> new_primPlusNat5(new_primMulNat4) 130.57/78.26 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.57/78.26 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.26 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.57/78.26 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.57/78.26 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.57/78.26 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.26 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.57/78.26 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.57/78.26 new_primMulNat2(zzz4739) -> Zero 130.57/78.26 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.57/78.26 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.57/78.26 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.57/78.26 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.26 new_primPlusNat2(Zero) -> Zero 130.57/78.26 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.57/78.26 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.26 130.57/78.26 The set Q consists of the following terms: 130.57/78.26 130.57/78.26 new_primPlusNat1(Succ(x0)) 130.57/78.26 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.26 new_primMulNat6 130.57/78.26 new_primMulNat0(x0) 130.57/78.26 new_primPlusNat1(Zero) 130.57/78.26 new_primPlusNat2(Zero) 130.57/78.26 new_primPlusNat3(Succ(x0)) 130.57/78.26 new_primMulNat7 130.57/78.26 new_primPlusNat8(Succ(x0), x1) 130.57/78.26 new_primMulNat3(x0) 130.57/78.26 new_primMulNat2(x0) 130.57/78.26 new_primPlusNat6(x0, Succ(x1)) 130.57/78.26 new_primPlusNat0(Succ(x0), Zero) 130.57/78.26 new_primPlusNat6(x0, Zero) 130.57/78.26 new_primPlusNat5(Succ(x0)) 130.57/78.26 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.26 new_primMulNat4 130.57/78.26 new_primPlusNat4(Succ(x0)) 130.57/78.26 new_primPlusNat8(Zero, x0) 130.57/78.26 new_primPlusNat3(Zero) 130.57/78.26 new_primPlusNat7(x0, Zero) 130.57/78.26 new_primPlusNat5(Zero) 130.57/78.26 new_primMulNat5 130.57/78.26 new_primMulNat1(x0) 130.57/78.26 new_primPlusNat7(x0, Succ(x1)) 130.57/78.26 new_primPlusNat4(Zero) 130.57/78.26 new_primPlusNat2(Succ(x0)) 130.57/78.26 new_primPlusNat0(Zero, Zero) 130.57/78.26 130.57/78.26 We have to consider all minimal (P,Q,R)-chains. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (101) TransformationProof (EQUIVALENT) 130.57/78.26 By instantiating [LPAR04] the rule new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, zzz4455, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) we obtained the following new rules [LPAR04]: 130.57/78.26 130.57/78.26 (new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10),new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10)) 130.57/78.26 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (102) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.26 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000)))), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000)))), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primMulNat3(zzz3745), bh) 130.57/78.26 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.26 130.57/78.26 The TRS R consists of the following rules: 130.57/78.26 130.57/78.26 new_primPlusNat3(Zero) -> Succ(Zero) 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.26 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.26 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.57/78.26 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.26 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.57/78.26 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.57/78.26 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.57/78.26 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.26 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.57/78.26 new_primMulNat6 -> new_primPlusNat5(new_primMulNat4) 130.57/78.26 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.57/78.26 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.26 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.57/78.26 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.57/78.26 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.57/78.26 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.26 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.57/78.26 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.57/78.26 new_primMulNat2(zzz4739) -> Zero 130.57/78.26 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.57/78.26 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.57/78.26 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.57/78.26 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.26 new_primPlusNat2(Zero) -> Zero 130.57/78.26 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.57/78.26 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.26 130.57/78.26 The set Q consists of the following terms: 130.57/78.26 130.57/78.26 new_primPlusNat1(Succ(x0)) 130.57/78.26 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.26 new_primMulNat6 130.57/78.26 new_primMulNat0(x0) 130.57/78.26 new_primPlusNat1(Zero) 130.57/78.26 new_primPlusNat2(Zero) 130.57/78.26 new_primPlusNat3(Succ(x0)) 130.57/78.26 new_primMulNat7 130.57/78.26 new_primPlusNat8(Succ(x0), x1) 130.57/78.26 new_primMulNat3(x0) 130.57/78.26 new_primMulNat2(x0) 130.57/78.26 new_primPlusNat6(x0, Succ(x1)) 130.57/78.26 new_primPlusNat0(Succ(x0), Zero) 130.57/78.26 new_primPlusNat6(x0, Zero) 130.57/78.26 new_primPlusNat5(Succ(x0)) 130.57/78.26 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.26 new_primMulNat4 130.57/78.26 new_primPlusNat4(Succ(x0)) 130.57/78.26 new_primPlusNat8(Zero, x0) 130.57/78.26 new_primPlusNat3(Zero) 130.57/78.26 new_primPlusNat7(x0, Zero) 130.57/78.26 new_primPlusNat5(Zero) 130.57/78.26 new_primMulNat5 130.57/78.26 new_primMulNat1(x0) 130.57/78.26 new_primPlusNat7(x0, Succ(x1)) 130.57/78.26 new_primPlusNat4(Zero) 130.57/78.26 new_primPlusNat2(Succ(x0)) 130.57/78.26 new_primPlusNat0(Zero, Zero) 130.57/78.26 130.57/78.26 We have to consider all minimal (P,Q,R)-chains. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (103) UsableRulesProof (EQUIVALENT) 130.57/78.26 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (104) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.26 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000)))), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000)))), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primMulNat3(zzz3745), bh) 130.57/78.26 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.26 130.57/78.26 The TRS R consists of the following rules: 130.57/78.26 130.57/78.26 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.57/78.26 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.26 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.26 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.26 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.26 new_primMulNat2(zzz4739) -> Zero 130.57/78.26 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.26 new_primPlusNat2(Zero) -> Zero 130.57/78.26 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.26 130.57/78.26 The set Q consists of the following terms: 130.57/78.26 130.57/78.26 new_primPlusNat1(Succ(x0)) 130.57/78.26 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.26 new_primMulNat6 130.57/78.26 new_primMulNat0(x0) 130.57/78.26 new_primPlusNat1(Zero) 130.57/78.26 new_primPlusNat2(Zero) 130.57/78.26 new_primPlusNat3(Succ(x0)) 130.57/78.26 new_primMulNat7 130.57/78.26 new_primPlusNat8(Succ(x0), x1) 130.57/78.26 new_primMulNat3(x0) 130.57/78.26 new_primMulNat2(x0) 130.57/78.26 new_primPlusNat6(x0, Succ(x1)) 130.57/78.26 new_primPlusNat0(Succ(x0), Zero) 130.57/78.26 new_primPlusNat6(x0, Zero) 130.57/78.26 new_primPlusNat5(Succ(x0)) 130.57/78.26 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.26 new_primMulNat4 130.57/78.26 new_primPlusNat4(Succ(x0)) 130.57/78.26 new_primPlusNat8(Zero, x0) 130.57/78.26 new_primPlusNat3(Zero) 130.57/78.26 new_primPlusNat7(x0, Zero) 130.57/78.26 new_primPlusNat5(Zero) 130.57/78.26 new_primMulNat5 130.57/78.26 new_primMulNat1(x0) 130.57/78.26 new_primPlusNat7(x0, Succ(x1)) 130.57/78.26 new_primPlusNat4(Zero) 130.57/78.26 new_primPlusNat2(Succ(x0)) 130.57/78.26 new_primPlusNat0(Zero, Zero) 130.57/78.26 130.57/78.26 We have to consider all minimal (P,Q,R)-chains. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (105) QReductionProof (EQUIVALENT) 130.57/78.26 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.57/78.26 130.57/78.26 new_primPlusNat1(Succ(x0)) 130.57/78.26 new_primMulNat6 130.57/78.26 new_primPlusNat1(Zero) 130.57/78.26 new_primMulNat7 130.57/78.26 new_primPlusNat8(Succ(x0), x1) 130.57/78.26 new_primPlusNat6(x0, Succ(x1)) 130.57/78.26 new_primPlusNat6(x0, Zero) 130.57/78.26 new_primPlusNat5(Succ(x0)) 130.57/78.26 new_primMulNat4 130.57/78.26 new_primPlusNat4(Succ(x0)) 130.57/78.26 new_primPlusNat8(Zero, x0) 130.57/78.26 new_primPlusNat7(x0, Zero) 130.57/78.26 new_primPlusNat5(Zero) 130.57/78.26 new_primMulNat5 130.57/78.26 new_primPlusNat7(x0, Succ(x1)) 130.57/78.26 new_primPlusNat4(Zero) 130.57/78.26 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (106) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.26 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000)))), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000)))), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primMulNat3(zzz3745), bh) 130.57/78.26 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.26 130.57/78.26 The TRS R consists of the following rules: 130.57/78.26 130.57/78.26 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.57/78.26 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.26 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.26 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.26 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.26 new_primMulNat2(zzz4739) -> Zero 130.57/78.26 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.26 new_primPlusNat2(Zero) -> Zero 130.57/78.26 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.26 130.57/78.26 The set Q consists of the following terms: 130.57/78.26 130.57/78.26 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.26 new_primMulNat0(x0) 130.57/78.26 new_primPlusNat2(Zero) 130.57/78.26 new_primPlusNat3(Succ(x0)) 130.57/78.26 new_primMulNat3(x0) 130.57/78.26 new_primMulNat2(x0) 130.57/78.26 new_primPlusNat0(Succ(x0), Zero) 130.57/78.26 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.26 new_primPlusNat3(Zero) 130.57/78.26 new_primMulNat1(x0) 130.57/78.26 new_primPlusNat2(Succ(x0)) 130.57/78.26 new_primPlusNat0(Zero, Zero) 130.57/78.26 130.57/78.26 We have to consider all minimal (P,Q,R)-chains. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (107) TransformationProof (EQUIVALENT) 130.57/78.26 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000)))), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000))), bb) at position [13,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.57/78.26 130.57/78.26 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb)) 130.57/78.26 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (108) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.26 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000)))), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primMulNat3(zzz3745), bh) 130.57/78.26 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.26 130.57/78.26 The TRS R consists of the following rules: 130.57/78.26 130.57/78.26 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.57/78.26 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.26 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.26 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.26 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.26 new_primMulNat2(zzz4739) -> Zero 130.57/78.26 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.26 new_primPlusNat2(Zero) -> Zero 130.57/78.26 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.26 130.57/78.26 The set Q consists of the following terms: 130.57/78.26 130.57/78.26 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.26 new_primMulNat0(x0) 130.57/78.26 new_primPlusNat2(Zero) 130.57/78.26 new_primPlusNat3(Succ(x0)) 130.57/78.26 new_primMulNat3(x0) 130.57/78.26 new_primMulNat2(x0) 130.57/78.26 new_primPlusNat0(Succ(x0), Zero) 130.57/78.26 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.26 new_primPlusNat3(Zero) 130.57/78.26 new_primMulNat1(x0) 130.57/78.26 new_primPlusNat2(Succ(x0)) 130.57/78.26 new_primPlusNat0(Zero, Zero) 130.57/78.26 130.57/78.26 We have to consider all minimal (P,Q,R)-chains. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (109) TransformationProof (EQUIVALENT) 130.57/78.26 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), bb) at position [12,0,0] we obtained the following new rules [LPAR04]: 130.57/78.26 130.57/78.26 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb)) 130.57/78.26 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (110) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.26 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000)))), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primMulNat3(zzz3745), bh) 130.57/78.26 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.26 130.57/78.26 The TRS R consists of the following rules: 130.57/78.26 130.57/78.26 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.57/78.26 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.26 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.26 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.26 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.26 new_primMulNat2(zzz4739) -> Zero 130.57/78.26 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.26 new_primPlusNat2(Zero) -> Zero 130.57/78.26 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.26 130.57/78.26 The set Q consists of the following terms: 130.57/78.26 130.57/78.26 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.26 new_primMulNat0(x0) 130.57/78.26 new_primPlusNat2(Zero) 130.57/78.26 new_primPlusNat3(Succ(x0)) 130.57/78.26 new_primMulNat3(x0) 130.57/78.26 new_primMulNat2(x0) 130.57/78.26 new_primPlusNat0(Succ(x0), Zero) 130.57/78.26 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.26 new_primPlusNat3(Zero) 130.57/78.26 new_primMulNat1(x0) 130.57/78.26 new_primPlusNat2(Succ(x0)) 130.57/78.26 new_primPlusNat0(Zero, Zero) 130.57/78.26 130.57/78.26 We have to consider all minimal (P,Q,R)-chains. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (111) TransformationProof (EQUIVALENT) 130.57/78.26 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), bb) at position [12,0,0] we obtained the following new rules [LPAR04]: 130.57/78.26 130.57/78.26 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb)) 130.57/78.26 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (112) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.26 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000)))), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primMulNat3(zzz3745), bh) 130.57/78.26 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.26 130.57/78.26 The TRS R consists of the following rules: 130.57/78.26 130.57/78.26 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.57/78.26 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.26 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.26 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.26 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.26 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.26 new_primMulNat2(zzz4739) -> Zero 130.57/78.26 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.26 new_primPlusNat2(Zero) -> Zero 130.57/78.26 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.26 130.57/78.26 The set Q consists of the following terms: 130.57/78.26 130.57/78.26 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.26 new_primMulNat0(x0) 130.57/78.26 new_primPlusNat2(Zero) 130.57/78.26 new_primPlusNat3(Succ(x0)) 130.57/78.26 new_primMulNat3(x0) 130.57/78.26 new_primMulNat2(x0) 130.57/78.26 new_primPlusNat0(Succ(x0), Zero) 130.57/78.26 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.26 new_primPlusNat3(Zero) 130.57/78.26 new_primMulNat1(x0) 130.57/78.26 new_primPlusNat2(Succ(x0)) 130.57/78.26 new_primPlusNat0(Zero, Zero) 130.57/78.26 130.57/78.26 We have to consider all minimal (P,Q,R)-chains. 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (113) TransformationProof (EQUIVALENT) 130.57/78.26 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000)))), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000))), bb) at position [13,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.57/78.26 130.57/78.26 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb)) 130.57/78.26 130.57/78.26 130.57/78.26 ---------------------------------------- 130.57/78.26 130.57/78.26 (114) 130.57/78.26 Obligation: 130.57/78.26 Q DP problem: 130.57/78.26 The TRS P consists of the following rules: 130.57/78.26 130.57/78.26 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.26 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) 130.57/78.26 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primMulNat3(zzz3745), bh) 130.57/78.26 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.26 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.26 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat3(x0) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (115) TransformationProof (EQUIVALENT) 130.57/78.27 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) at position [12] we obtained the following new rules [LPAR04]: 130.57/78.27 130.57/78.27 (new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be),new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be)) 130.57/78.27 130.57/78.27 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (116) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primMulNat3(zzz3745), bh) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat3(x0) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (117) TransformationProof (EQUIVALENT) 130.57/78.27 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primMulNat3(zzz5119), be) at position [12] we obtained the following new rules [LPAR04]: 130.57/78.27 130.57/78.27 (new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be),new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be)) 130.57/78.27 130.57/78.27 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (118) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primMulNat3(zzz3745), bh) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat3(x0) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (119) TransformationProof (EQUIVALENT) 130.57/78.27 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primMulNat3(zzz3745), bh) at position [11] we obtained the following new rules [LPAR04]: 130.57/78.27 130.57/78.27 (new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primMulNat0(zzz3745), Succ(zzz3745)), bh),new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primMulNat0(zzz3745), Succ(zzz3745)), bh)) 130.57/78.27 130.57/78.27 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (120) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primMulNat0(zzz3745), Succ(zzz3745)), bh) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat3(x0) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (121) TransformationProof (EQUIVALENT) 130.57/78.27 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) at position [11] we obtained the following new rules [LPAR04]: 130.57/78.27 130.57/78.27 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb)) 130.57/78.27 130.57/78.27 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (122) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primMulNat0(zzz3745), Succ(zzz3745)), bh) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat3(x0) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (123) TransformationProof (EQUIVALENT) 130.57/78.27 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) at position [11] we obtained the following new rules [LPAR04]: 130.57/78.27 130.57/78.27 (new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg),new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg)) 130.57/78.27 130.57/78.27 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (124) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primMulNat0(zzz3745), Succ(zzz3745)), bh) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat3(x0) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (125) TransformationProof (EQUIVALENT) 130.57/78.27 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primMulNat3(zzz4109), bg) at position [11] we obtained the following new rules [LPAR04]: 130.57/78.27 130.57/78.27 (new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg),new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg)) 130.57/78.27 130.57/78.27 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (126) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primMulNat0(zzz3745), Succ(zzz3745)), bh) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat3(x0) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (127) UsableRulesProof (EQUIVALENT) 130.57/78.27 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (128) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primMulNat0(zzz3745), Succ(zzz3745)), bh) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat3(x0) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (129) QReductionProof (EQUIVALENT) 130.57/78.27 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.57/78.27 130.57/78.27 new_primMulNat3(x0) 130.57/78.27 130.57/78.27 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (130) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primMulNat0(zzz3745), Succ(zzz3745)), bh) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (131) TransformationProof (EQUIVALENT) 130.57/78.27 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) at position [13,0,0,0,0] we obtained the following new rules [LPAR04]: 130.57/78.27 130.57/78.27 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb)) 130.57/78.27 130.57/78.27 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (132) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primMulNat0(zzz3745), Succ(zzz3745)), bh) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (133) TransformationProof (EQUIVALENT) 130.57/78.27 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) at position [12,0] we obtained the following new rules [LPAR04]: 130.57/78.27 130.57/78.27 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb)) 130.57/78.27 130.57/78.27 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (134) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primMulNat0(zzz3745), Succ(zzz3745)), bh) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (135) TransformationProof (EQUIVALENT) 130.57/78.27 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), bb) at position [12,0] we obtained the following new rules [LPAR04]: 130.57/78.27 130.57/78.27 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb)) 130.57/78.27 130.57/78.27 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (136) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primMulNat0(zzz3745), Succ(zzz3745)), bh) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (137) TransformationProof (EQUIVALENT) 130.57/78.27 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000))), bb) at position [13,0,0,0,0] we obtained the following new rules [LPAR04]: 130.57/78.27 130.57/78.27 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb)) 130.57/78.27 130.57/78.27 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (138) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.27 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primMulNat0(zzz3745), Succ(zzz3745)), bh) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (139) TransformationProof (EQUIVALENT) 130.57/78.27 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) at position [12,0] we obtained the following new rules [LPAR04]: 130.57/78.27 130.57/78.27 (new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be),new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be)) 130.57/78.27 130.57/78.27 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (140) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primMulNat0(zzz3745), Succ(zzz3745)), bh) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (141) TransformationProof (EQUIVALENT) 130.57/78.27 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primMulNat0(zzz5119), Succ(zzz5119)), be) at position [12,0] we obtained the following new rules [LPAR04]: 130.57/78.27 130.57/78.27 (new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be),new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be)) 130.57/78.27 130.57/78.27 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (142) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.27 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primMulNat0(zzz3745), Succ(zzz3745)), bh) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (143) TransformationProof (EQUIVALENT) 130.57/78.27 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primMulNat0(zzz3745), Succ(zzz3745)), bh) at position [11,0] we obtained the following new rules [LPAR04]: 130.57/78.27 130.57/78.27 (new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh),new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh)) 130.57/78.27 130.57/78.27 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (144) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (145) TransformationProof (EQUIVALENT) 130.57/78.27 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) at position [11,0] we obtained the following new rules [LPAR04]: 130.57/78.27 130.57/78.27 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb)) 130.57/78.27 130.57/78.27 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (146) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (147) TransformationProof (EQUIVALENT) 130.57/78.27 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) at position [11,0] we obtained the following new rules [LPAR04]: 130.57/78.27 130.57/78.27 (new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg),new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg)) 130.57/78.27 130.57/78.27 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (148) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.27 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (149) TransformationProof (EQUIVALENT) 130.57/78.27 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primMulNat0(zzz4109), Succ(zzz4109)), bg) at position [11,0] we obtained the following new rules [LPAR04]: 130.57/78.27 130.57/78.27 (new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg),new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg)) 130.57/78.27 130.57/78.27 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (150) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (151) UsableRulesProof (EQUIVALENT) 130.57/78.27 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (152) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.57/78.27 130.57/78.27 The TRS R consists of the following rules: 130.57/78.27 130.57/78.27 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.27 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.27 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.27 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.27 new_primMulNat2(zzz4739) -> Zero 130.57/78.27 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.27 new_primPlusNat2(Zero) -> Zero 130.57/78.27 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.27 130.57/78.27 The set Q consists of the following terms: 130.57/78.27 130.57/78.27 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 new_primPlusNat2(Zero) 130.57/78.27 new_primPlusNat3(Succ(x0)) 130.57/78.27 new_primMulNat2(x0) 130.57/78.27 new_primPlusNat0(Succ(x0), Zero) 130.57/78.27 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.27 new_primPlusNat3(Zero) 130.57/78.27 new_primMulNat1(x0) 130.57/78.27 new_primPlusNat2(Succ(x0)) 130.57/78.27 new_primPlusNat0(Zero, Zero) 130.57/78.27 130.57/78.27 We have to consider all minimal (P,Q,R)-chains. 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (153) QReductionProof (EQUIVALENT) 130.57/78.27 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.57/78.27 130.57/78.27 new_primMulNat0(x0) 130.57/78.27 130.57/78.27 130.57/78.27 ---------------------------------------- 130.57/78.27 130.57/78.27 (154) 130.57/78.27 Obligation: 130.57/78.27 Q DP problem: 130.57/78.27 The TRS P consists of the following rules: 130.57/78.27 130.57/78.27 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.27 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.27 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.27 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.27 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.27 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.57/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.57/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.57/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.57/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.57/78.28 130.57/78.28 The TRS R consists of the following rules: 130.57/78.28 130.57/78.28 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.28 new_primMulNat2(zzz4739) -> Zero 130.57/78.28 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.28 new_primPlusNat2(Zero) -> Zero 130.57/78.28 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.28 130.57/78.28 The set Q consists of the following terms: 130.57/78.28 130.57/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.28 new_primPlusNat2(Zero) 130.57/78.28 new_primPlusNat3(Succ(x0)) 130.57/78.28 new_primMulNat2(x0) 130.57/78.28 new_primPlusNat0(Succ(x0), Zero) 130.57/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.28 new_primPlusNat3(Zero) 130.57/78.28 new_primMulNat1(x0) 130.57/78.28 new_primPlusNat2(Succ(x0)) 130.57/78.28 new_primPlusNat0(Zero, Zero) 130.57/78.28 130.57/78.28 We have to consider all minimal (P,Q,R)-chains. 130.57/78.28 ---------------------------------------- 130.57/78.28 130.57/78.28 (155) TransformationProof (EQUIVALENT) 130.57/78.28 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) at position [13,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.57/78.28 130.57/78.28 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb)) 130.57/78.28 130.57/78.28 130.57/78.28 ---------------------------------------- 130.57/78.28 130.57/78.28 (156) 130.57/78.28 Obligation: 130.57/78.28 Q DP problem: 130.57/78.28 The TRS P consists of the following rules: 130.57/78.28 130.57/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.57/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.57/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.57/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.57/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.57/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.57/78.28 130.57/78.28 The TRS R consists of the following rules: 130.57/78.28 130.57/78.28 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.57/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.57/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.57/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.57/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.57/78.28 new_primMulNat2(zzz4739) -> Zero 130.57/78.28 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.57/78.28 new_primPlusNat2(Zero) -> Zero 130.57/78.28 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.57/78.28 130.57/78.28 The set Q consists of the following terms: 130.57/78.28 130.57/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.57/78.28 new_primPlusNat2(Zero) 130.57/78.28 new_primPlusNat3(Succ(x0)) 130.57/78.28 new_primMulNat2(x0) 130.57/78.28 new_primPlusNat0(Succ(x0), Zero) 130.57/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.57/78.28 new_primPlusNat3(Zero) 130.57/78.28 new_primMulNat1(x0) 130.57/78.28 new_primPlusNat2(Succ(x0)) 130.57/78.28 new_primPlusNat0(Zero, Zero) 130.57/78.28 130.57/78.28 We have to consider all minimal (P,Q,R)-chains. 130.57/78.28 ---------------------------------------- 130.57/78.28 130.57/78.28 (157) TransformationProof (EQUIVALENT) 130.57/78.28 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.57/78.28 130.57/78.28 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb)) 130.57/78.28 130.57/78.28 130.57/78.28 ---------------------------------------- 130.57/78.28 130.57/78.28 (158) 130.57/78.28 Obligation: 130.57/78.28 Q DP problem: 130.57/78.28 The TRS P consists of the following rules: 130.57/78.28 130.57/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.57/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.57/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.57/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.57/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.57/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.57/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.57/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.57/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.57/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 130.72/78.28 The TRS R consists of the following rules: 130.72/78.28 130.72/78.28 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.28 new_primMulNat2(zzz4739) -> Zero 130.72/78.28 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.28 new_primPlusNat2(Zero) -> Zero 130.72/78.28 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.28 130.72/78.28 The set Q consists of the following terms: 130.72/78.28 130.72/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.28 new_primPlusNat2(Zero) 130.72/78.28 new_primPlusNat3(Succ(x0)) 130.72/78.28 new_primMulNat2(x0) 130.72/78.28 new_primPlusNat0(Succ(x0), Zero) 130.72/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.28 new_primPlusNat3(Zero) 130.72/78.28 new_primMulNat1(x0) 130.72/78.28 new_primPlusNat2(Succ(x0)) 130.72/78.28 new_primPlusNat0(Zero, Zero) 130.72/78.28 130.72/78.28 We have to consider all minimal (P,Q,R)-chains. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (159) TransformationProof (EQUIVALENT) 130.72/78.28 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), bb) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.28 130.72/78.28 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb)) 130.72/78.28 130.72/78.28 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (160) 130.72/78.28 Obligation: 130.72/78.28 Q DP problem: 130.72/78.28 The TRS P consists of the following rules: 130.72/78.28 130.72/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 130.72/78.28 The TRS R consists of the following rules: 130.72/78.28 130.72/78.28 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.28 new_primMulNat2(zzz4739) -> Zero 130.72/78.28 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.28 new_primPlusNat2(Zero) -> Zero 130.72/78.28 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.28 130.72/78.28 The set Q consists of the following terms: 130.72/78.28 130.72/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.28 new_primPlusNat2(Zero) 130.72/78.28 new_primPlusNat3(Succ(x0)) 130.72/78.28 new_primMulNat2(x0) 130.72/78.28 new_primPlusNat0(Succ(x0), Zero) 130.72/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.28 new_primPlusNat3(Zero) 130.72/78.28 new_primMulNat1(x0) 130.72/78.28 new_primPlusNat2(Succ(x0)) 130.72/78.28 new_primPlusNat0(Zero, Zero) 130.72/78.28 130.72/78.28 We have to consider all minimal (P,Q,R)-chains. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (161) UsableRulesProof (EQUIVALENT) 130.72/78.28 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (162) 130.72/78.28 Obligation: 130.72/78.28 Q DP problem: 130.72/78.28 The TRS P consists of the following rules: 130.72/78.28 130.72/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 130.72/78.28 The TRS R consists of the following rules: 130.72/78.28 130.72/78.28 new_primPlusNat2(Zero) -> Zero 130.72/78.28 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.28 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.28 new_primMulNat2(zzz4739) -> Zero 130.72/78.28 130.72/78.28 The set Q consists of the following terms: 130.72/78.28 130.72/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.28 new_primPlusNat2(Zero) 130.72/78.28 new_primPlusNat3(Succ(x0)) 130.72/78.28 new_primMulNat2(x0) 130.72/78.28 new_primPlusNat0(Succ(x0), Zero) 130.72/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.28 new_primPlusNat3(Zero) 130.72/78.28 new_primMulNat1(x0) 130.72/78.28 new_primPlusNat2(Succ(x0)) 130.72/78.28 new_primPlusNat0(Zero, Zero) 130.72/78.28 130.72/78.28 We have to consider all minimal (P,Q,R)-chains. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (163) QReductionProof (EQUIVALENT) 130.72/78.28 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.72/78.28 130.72/78.28 new_primPlusNat3(Succ(x0)) 130.72/78.28 new_primPlusNat3(Zero) 130.72/78.28 130.72/78.28 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (164) 130.72/78.28 Obligation: 130.72/78.28 Q DP problem: 130.72/78.28 The TRS P consists of the following rules: 130.72/78.28 130.72/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 130.72/78.28 The TRS R consists of the following rules: 130.72/78.28 130.72/78.28 new_primPlusNat2(Zero) -> Zero 130.72/78.28 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.28 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.28 new_primMulNat2(zzz4739) -> Zero 130.72/78.28 130.72/78.28 The set Q consists of the following terms: 130.72/78.28 130.72/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.28 new_primPlusNat2(Zero) 130.72/78.28 new_primMulNat2(x0) 130.72/78.28 new_primPlusNat0(Succ(x0), Zero) 130.72/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.28 new_primMulNat1(x0) 130.72/78.28 new_primPlusNat2(Succ(x0)) 130.72/78.28 new_primPlusNat0(Zero, Zero) 130.72/78.28 130.72/78.28 We have to consider all minimal (P,Q,R)-chains. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (165) TransformationProof (EQUIVALENT) 130.72/78.28 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(zzz25020000)), Succ(Succ(zzz25020000))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) at position [13,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.28 130.72/78.28 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb)) 130.72/78.28 130.72/78.28 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (166) 130.72/78.28 Obligation: 130.72/78.28 Q DP problem: 130.72/78.28 The TRS P consists of the following rules: 130.72/78.28 130.72/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 130.72/78.28 The TRS R consists of the following rules: 130.72/78.28 130.72/78.28 new_primPlusNat2(Zero) -> Zero 130.72/78.28 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.28 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.28 new_primMulNat2(zzz4739) -> Zero 130.72/78.28 130.72/78.28 The set Q consists of the following terms: 130.72/78.28 130.72/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.28 new_primPlusNat2(Zero) 130.72/78.28 new_primMulNat2(x0) 130.72/78.28 new_primPlusNat0(Succ(x0), Zero) 130.72/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.28 new_primMulNat1(x0) 130.72/78.28 new_primPlusNat2(Succ(x0)) 130.72/78.28 new_primPlusNat0(Zero, Zero) 130.72/78.28 130.72/78.28 We have to consider all minimal (P,Q,R)-chains. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (167) TransformationProof (EQUIVALENT) 130.72/78.28 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.28 130.72/78.28 (new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be),new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be)) 130.72/78.28 130.72/78.28 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (168) 130.72/78.28 Obligation: 130.72/78.28 Q DP problem: 130.72/78.28 The TRS P consists of the following rules: 130.72/78.28 130.72/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 130.72/78.28 The TRS R consists of the following rules: 130.72/78.28 130.72/78.28 new_primPlusNat2(Zero) -> Zero 130.72/78.28 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.28 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.28 new_primMulNat2(zzz4739) -> Zero 130.72/78.28 130.72/78.28 The set Q consists of the following terms: 130.72/78.28 130.72/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.28 new_primPlusNat2(Zero) 130.72/78.28 new_primMulNat2(x0) 130.72/78.28 new_primPlusNat0(Succ(x0), Zero) 130.72/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.28 new_primMulNat1(x0) 130.72/78.28 new_primPlusNat2(Succ(x0)) 130.72/78.28 new_primPlusNat0(Zero, Zero) 130.72/78.28 130.72/78.28 We have to consider all minimal (P,Q,R)-chains. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (169) TransformationProof (EQUIVALENT) 130.72/78.28 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.28 130.72/78.28 (new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be),new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be)) 130.72/78.28 130.72/78.28 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (170) 130.72/78.28 Obligation: 130.72/78.28 Q DP problem: 130.72/78.28 The TRS P consists of the following rules: 130.72/78.28 130.72/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 130.72/78.28 The TRS R consists of the following rules: 130.72/78.28 130.72/78.28 new_primPlusNat2(Zero) -> Zero 130.72/78.28 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.28 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.28 new_primMulNat2(zzz4739) -> Zero 130.72/78.28 130.72/78.28 The set Q consists of the following terms: 130.72/78.28 130.72/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.28 new_primPlusNat2(Zero) 130.72/78.28 new_primMulNat2(x0) 130.72/78.28 new_primPlusNat0(Succ(x0), Zero) 130.72/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.28 new_primMulNat1(x0) 130.72/78.28 new_primPlusNat2(Succ(x0)) 130.72/78.28 new_primPlusNat0(Zero, Zero) 130.72/78.28 130.72/78.28 We have to consider all minimal (P,Q,R)-chains. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (171) TransformationProof (EQUIVALENT) 130.72/78.28 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.28 130.72/78.28 (new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh),new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh)) 130.72/78.28 130.72/78.28 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (172) 130.72/78.28 Obligation: 130.72/78.28 Q DP problem: 130.72/78.28 The TRS P consists of the following rules: 130.72/78.28 130.72/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.28 130.72/78.28 The TRS R consists of the following rules: 130.72/78.28 130.72/78.28 new_primPlusNat2(Zero) -> Zero 130.72/78.28 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.28 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.28 new_primMulNat2(zzz4739) -> Zero 130.72/78.28 130.72/78.28 The set Q consists of the following terms: 130.72/78.28 130.72/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.28 new_primPlusNat2(Zero) 130.72/78.28 new_primMulNat2(x0) 130.72/78.28 new_primPlusNat0(Succ(x0), Zero) 130.72/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.28 new_primMulNat1(x0) 130.72/78.28 new_primPlusNat2(Succ(x0)) 130.72/78.28 new_primPlusNat0(Zero, Zero) 130.72/78.28 130.72/78.28 We have to consider all minimal (P,Q,R)-chains. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (173) TransformationProof (EQUIVALENT) 130.72/78.28 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.28 130.72/78.28 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb)) 130.72/78.28 130.72/78.28 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (174) 130.72/78.28 Obligation: 130.72/78.28 Q DP problem: 130.72/78.28 The TRS P consists of the following rules: 130.72/78.28 130.72/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.28 130.72/78.28 The TRS R consists of the following rules: 130.72/78.28 130.72/78.28 new_primPlusNat2(Zero) -> Zero 130.72/78.28 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.28 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.28 new_primMulNat2(zzz4739) -> Zero 130.72/78.28 130.72/78.28 The set Q consists of the following terms: 130.72/78.28 130.72/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.28 new_primPlusNat2(Zero) 130.72/78.28 new_primMulNat2(x0) 130.72/78.28 new_primPlusNat0(Succ(x0), Zero) 130.72/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.28 new_primMulNat1(x0) 130.72/78.28 new_primPlusNat2(Succ(x0)) 130.72/78.28 new_primPlusNat0(Zero, Zero) 130.72/78.28 130.72/78.28 We have to consider all minimal (P,Q,R)-chains. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (175) TransformationProof (EQUIVALENT) 130.72/78.28 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.28 130.72/78.28 (new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg),new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg)) 130.72/78.28 130.72/78.28 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (176) 130.72/78.28 Obligation: 130.72/78.28 Q DP problem: 130.72/78.28 The TRS P consists of the following rules: 130.72/78.28 130.72/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 130.72/78.28 The TRS R consists of the following rules: 130.72/78.28 130.72/78.28 new_primPlusNat2(Zero) -> Zero 130.72/78.28 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.28 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.28 new_primMulNat2(zzz4739) -> Zero 130.72/78.28 130.72/78.28 The set Q consists of the following terms: 130.72/78.28 130.72/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.28 new_primPlusNat2(Zero) 130.72/78.28 new_primMulNat2(x0) 130.72/78.28 new_primPlusNat0(Succ(x0), Zero) 130.72/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.28 new_primMulNat1(x0) 130.72/78.28 new_primPlusNat2(Succ(x0)) 130.72/78.28 new_primPlusNat0(Zero, Zero) 130.72/78.28 130.72/78.28 We have to consider all minimal (P,Q,R)-chains. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (177) TransformationProof (EQUIVALENT) 130.72/78.28 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.28 130.72/78.28 (new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg),new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg)) 130.72/78.28 130.72/78.28 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (178) 130.72/78.28 Obligation: 130.72/78.28 Q DP problem: 130.72/78.28 The TRS P consists of the following rules: 130.72/78.28 130.72/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 130.72/78.28 The TRS R consists of the following rules: 130.72/78.28 130.72/78.28 new_primPlusNat2(Zero) -> Zero 130.72/78.28 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.28 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.28 new_primMulNat2(zzz4739) -> Zero 130.72/78.28 130.72/78.28 The set Q consists of the following terms: 130.72/78.28 130.72/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.28 new_primPlusNat2(Zero) 130.72/78.28 new_primMulNat2(x0) 130.72/78.28 new_primPlusNat0(Succ(x0), Zero) 130.72/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.28 new_primMulNat1(x0) 130.72/78.28 new_primPlusNat2(Succ(x0)) 130.72/78.28 new_primPlusNat0(Zero, Zero) 130.72/78.28 130.72/78.28 We have to consider all minimal (P,Q,R)-chains. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (179) UsableRulesProof (EQUIVALENT) 130.72/78.28 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (180) 130.72/78.28 Obligation: 130.72/78.28 Q DP problem: 130.72/78.28 The TRS P consists of the following rules: 130.72/78.28 130.72/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 130.72/78.28 The TRS R consists of the following rules: 130.72/78.28 130.72/78.28 new_primMulNat2(zzz4739) -> Zero 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.28 new_primPlusNat2(Zero) -> Zero 130.72/78.28 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.28 130.72/78.28 The set Q consists of the following terms: 130.72/78.28 130.72/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.28 new_primPlusNat2(Zero) 130.72/78.28 new_primMulNat2(x0) 130.72/78.28 new_primPlusNat0(Succ(x0), Zero) 130.72/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.28 new_primMulNat1(x0) 130.72/78.28 new_primPlusNat2(Succ(x0)) 130.72/78.28 new_primPlusNat0(Zero, Zero) 130.72/78.28 130.72/78.28 We have to consider all minimal (P,Q,R)-chains. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (181) QReductionProof (EQUIVALENT) 130.72/78.28 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.72/78.28 130.72/78.28 new_primMulNat1(x0) 130.72/78.28 130.72/78.28 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (182) 130.72/78.28 Obligation: 130.72/78.28 Q DP problem: 130.72/78.28 The TRS P consists of the following rules: 130.72/78.28 130.72/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 130.72/78.28 The TRS R consists of the following rules: 130.72/78.28 130.72/78.28 new_primMulNat2(zzz4739) -> Zero 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.28 new_primPlusNat2(Zero) -> Zero 130.72/78.28 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.28 130.72/78.28 The set Q consists of the following terms: 130.72/78.28 130.72/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.28 new_primPlusNat2(Zero) 130.72/78.28 new_primMulNat2(x0) 130.72/78.28 new_primPlusNat0(Succ(x0), Zero) 130.72/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.28 new_primPlusNat2(Succ(x0)) 130.72/78.28 new_primPlusNat0(Zero, Zero) 130.72/78.28 130.72/78.28 We have to consider all minimal (P,Q,R)-chains. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (183) TransformationProof (EQUIVALENT) 130.72/78.28 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) at position [13,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.28 130.72/78.28 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb)) 130.72/78.28 130.72/78.28 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (184) 130.72/78.28 Obligation: 130.72/78.28 Q DP problem: 130.72/78.28 The TRS P consists of the following rules: 130.72/78.28 130.72/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 130.72/78.28 The TRS R consists of the following rules: 130.72/78.28 130.72/78.28 new_primMulNat2(zzz4739) -> Zero 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.28 new_primPlusNat2(Zero) -> Zero 130.72/78.28 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.28 130.72/78.28 The set Q consists of the following terms: 130.72/78.28 130.72/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.28 new_primPlusNat2(Zero) 130.72/78.28 new_primMulNat2(x0) 130.72/78.28 new_primPlusNat0(Succ(x0), Zero) 130.72/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.28 new_primPlusNat2(Succ(x0)) 130.72/78.28 new_primPlusNat0(Zero, Zero) 130.72/78.28 130.72/78.28 We have to consider all minimal (P,Q,R)-chains. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (185) TransformationProof (EQUIVALENT) 130.72/78.28 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) at position [12,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.28 130.72/78.28 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb)) 130.72/78.28 130.72/78.28 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (186) 130.72/78.28 Obligation: 130.72/78.28 Q DP problem: 130.72/78.28 The TRS P consists of the following rules: 130.72/78.28 130.72/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.28 130.72/78.28 The TRS R consists of the following rules: 130.72/78.28 130.72/78.28 new_primMulNat2(zzz4739) -> Zero 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.28 new_primPlusNat2(Zero) -> Zero 130.72/78.28 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.28 130.72/78.28 The set Q consists of the following terms: 130.72/78.28 130.72/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.28 new_primPlusNat2(Zero) 130.72/78.28 new_primMulNat2(x0) 130.72/78.28 new_primPlusNat0(Succ(x0), Zero) 130.72/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.28 new_primPlusNat2(Succ(x0)) 130.72/78.28 new_primPlusNat0(Zero, Zero) 130.72/78.28 130.72/78.28 We have to consider all minimal (P,Q,R)-chains. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (187) TransformationProof (EQUIVALENT) 130.72/78.28 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), bb) at position [12,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.28 130.72/78.28 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb)) 130.72/78.28 130.72/78.28 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (188) 130.72/78.28 Obligation: 130.72/78.28 Q DP problem: 130.72/78.28 The TRS P consists of the following rules: 130.72/78.28 130.72/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.28 130.72/78.28 The TRS R consists of the following rules: 130.72/78.28 130.72/78.28 new_primMulNat2(zzz4739) -> Zero 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.28 new_primPlusNat2(Zero) -> Zero 130.72/78.28 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.28 130.72/78.28 The set Q consists of the following terms: 130.72/78.28 130.72/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.28 new_primPlusNat2(Zero) 130.72/78.28 new_primMulNat2(x0) 130.72/78.28 new_primPlusNat0(Succ(x0), Zero) 130.72/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.28 new_primPlusNat2(Succ(x0)) 130.72/78.28 new_primPlusNat0(Zero, Zero) 130.72/78.28 130.72/78.28 We have to consider all minimal (P,Q,R)-chains. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (189) UsableRulesProof (EQUIVALENT) 130.72/78.28 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (190) 130.72/78.28 Obligation: 130.72/78.28 Q DP problem: 130.72/78.28 The TRS P consists of the following rules: 130.72/78.28 130.72/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.28 130.72/78.28 The TRS R consists of the following rules: 130.72/78.28 130.72/78.28 new_primPlusNat2(Zero) -> Zero 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.28 new_primMulNat2(zzz4739) -> Zero 130.72/78.28 130.72/78.28 The set Q consists of the following terms: 130.72/78.28 130.72/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.28 new_primPlusNat2(Zero) 130.72/78.28 new_primMulNat2(x0) 130.72/78.28 new_primPlusNat0(Succ(x0), Zero) 130.72/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.28 new_primPlusNat2(Succ(x0)) 130.72/78.28 new_primPlusNat0(Zero, Zero) 130.72/78.28 130.72/78.28 We have to consider all minimal (P,Q,R)-chains. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (191) TransformationProof (EQUIVALENT) 130.72/78.28 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000)))), Succ(zzz25020000))), zzz25020000)))), zzz25020000))), bb) at position [13,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.28 130.72/78.28 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb)) 130.72/78.28 130.72/78.28 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (192) 130.72/78.28 Obligation: 130.72/78.28 Q DP problem: 130.72/78.28 The TRS P consists of the following rules: 130.72/78.28 130.72/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 130.72/78.28 The TRS R consists of the following rules: 130.72/78.28 130.72/78.28 new_primPlusNat2(Zero) -> Zero 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.28 new_primMulNat2(zzz4739) -> Zero 130.72/78.28 130.72/78.28 The set Q consists of the following terms: 130.72/78.28 130.72/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.28 new_primPlusNat2(Zero) 130.72/78.28 new_primMulNat2(x0) 130.72/78.28 new_primPlusNat0(Succ(x0), Zero) 130.72/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.28 new_primPlusNat2(Succ(x0)) 130.72/78.28 new_primPlusNat0(Zero, Zero) 130.72/78.28 130.72/78.28 We have to consider all minimal (P,Q,R)-chains. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (193) TransformationProof (EQUIVALENT) 130.72/78.28 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) at position [12,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.28 130.72/78.28 (new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be),new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be)) 130.72/78.28 130.72/78.28 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (194) 130.72/78.28 Obligation: 130.72/78.28 Q DP problem: 130.72/78.28 The TRS P consists of the following rules: 130.72/78.28 130.72/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.28 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.28 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.28 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.28 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.28 130.72/78.28 The TRS R consists of the following rules: 130.72/78.28 130.72/78.28 new_primPlusNat2(Zero) -> Zero 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.28 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.28 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.28 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.28 new_primMulNat2(zzz4739) -> Zero 130.72/78.28 130.72/78.28 The set Q consists of the following terms: 130.72/78.28 130.72/78.28 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.28 new_primPlusNat2(Zero) 130.72/78.28 new_primMulNat2(x0) 130.72/78.28 new_primPlusNat0(Succ(x0), Zero) 130.72/78.28 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.28 new_primPlusNat2(Succ(x0)) 130.72/78.28 new_primPlusNat0(Zero, Zero) 130.72/78.28 130.72/78.28 We have to consider all minimal (P,Q,R)-chains. 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (195) TransformationProof (EQUIVALENT) 130.72/78.28 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) at position [12,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.28 130.72/78.28 (new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be),new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be)) 130.72/78.28 130.72/78.28 130.72/78.28 ---------------------------------------- 130.72/78.28 130.72/78.28 (196) 130.72/78.28 Obligation: 130.72/78.28 Q DP problem: 130.72/78.28 The TRS P consists of the following rules: 130.72/78.28 130.72/78.28 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.28 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat2(Zero) -> Zero 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primMulNat2(zzz4739) -> Zero 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat2(Zero) 130.72/78.29 new_primMulNat2(x0) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat2(Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (197) TransformationProof (EQUIVALENT) 130.72/78.29 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.29 130.72/78.29 (new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh),new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh)) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (198) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat2(Zero) -> Zero 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primMulNat2(zzz4739) -> Zero 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat2(Zero) 130.72/78.29 new_primMulNat2(x0) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat2(Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (199) TransformationProof (EQUIVALENT) 130.72/78.29 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.29 130.72/78.29 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb)) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (200) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat2(Zero) -> Zero 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primMulNat2(zzz4739) -> Zero 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat2(Zero) 130.72/78.29 new_primMulNat2(x0) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat2(Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (201) TransformationProof (EQUIVALENT) 130.72/78.29 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.29 130.72/78.29 (new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg),new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg)) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (202) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat2(Zero) -> Zero 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primMulNat2(zzz4739) -> Zero 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat2(Zero) 130.72/78.29 new_primMulNat2(x0) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat2(Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (203) TransformationProof (EQUIVALENT) 130.72/78.29 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.29 130.72/78.29 (new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg),new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg)) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (204) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat2(Zero) -> Zero 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primMulNat2(zzz4739) -> Zero 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat2(Zero) 130.72/78.29 new_primMulNat2(x0) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat2(Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (205) UsableRulesProof (EQUIVALENT) 130.72/78.29 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (206) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primPlusNat2(Zero) -> Zero 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat2(Zero) 130.72/78.29 new_primMulNat2(x0) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat2(Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (207) QReductionProof (EQUIVALENT) 130.72/78.29 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.72/78.29 130.72/78.29 new_primMulNat2(x0) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (208) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primPlusNat2(Zero) -> Zero 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat2(Zero) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat2(Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (209) TransformationProof (EQUIVALENT) 130.72/78.29 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) at position [13,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.29 130.72/78.29 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb)) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (210) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primPlusNat2(Zero) -> Zero 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat2(Zero) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat2(Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (211) TransformationProof (EQUIVALENT) 130.72/78.29 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) at position [12,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.29 130.72/78.29 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb)) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (212) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primPlusNat2(Zero) -> Zero 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat2(Zero) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat2(Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (213) TransformationProof (EQUIVALENT) 130.72/78.29 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) at position [12,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.29 130.72/78.29 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb)) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (214) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primPlusNat2(Zero) -> Zero 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat2(Zero) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat2(Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (215) UsableRulesProof (EQUIVALENT) 130.72/78.29 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (216) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat2(Zero) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat2(Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (217) QReductionProof (EQUIVALENT) 130.72/78.29 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.72/78.29 130.72/78.29 new_primPlusNat2(Zero) 130.72/78.29 new_primPlusNat2(Succ(x0)) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (218) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (219) TransformationProof (EQUIVALENT) 130.72/78.29 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz25020000), Succ(zzz25020000))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) at position [13,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.29 130.72/78.29 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb)) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (220) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (221) TransformationProof (EQUIVALENT) 130.72/78.29 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.29 130.72/78.29 (new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be),new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be)) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (222) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (223) TransformationProof (EQUIVALENT) 130.72/78.29 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.29 130.72/78.29 (new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be),new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be)) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (224) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (225) TransformationProof (EQUIVALENT) 130.72/78.29 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.29 130.72/78.29 (new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh),new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh)) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (226) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (227) TransformationProof (EQUIVALENT) 130.72/78.29 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.29 130.72/78.29 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb)) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (228) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (229) TransformationProof (EQUIVALENT) 130.72/78.29 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.29 130.72/78.29 (new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg),new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg)) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (230) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (231) TransformationProof (EQUIVALENT) 130.72/78.29 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.29 130.72/78.29 (new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg),new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg)) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (232) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (233) TransformationProof (EQUIVALENT) 130.72/78.29 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) at position [12,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.29 130.72/78.29 (new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5119, zzz5119))), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be),new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5119, zzz5119))), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be)) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (234) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5119, zzz5119))), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (235) TransformationProof (EQUIVALENT) 130.72/78.29 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5119), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) at position [12,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.29 130.72/78.29 (new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5119, zzz5119))), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be),new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5119, zzz5119))), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be)) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (236) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5119, zzz5119))), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5119, zzz5119))), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (237) TransformationProof (EQUIVALENT) 130.72/78.29 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3745), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.29 130.72/78.29 (new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3745, zzz3745))), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh),new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3745, zzz3745))), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh)) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (238) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.29 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.29 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.29 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.29 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5119, zzz5119))), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5119, zzz5119))), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3745, zzz3745))), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.29 130.72/78.29 The TRS R consists of the following rules: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.29 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.29 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.29 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.29 130.72/78.29 The set Q consists of the following terms: 130.72/78.29 130.72/78.29 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.29 new_primPlusNat0(Succ(x0), Zero) 130.72/78.29 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.29 new_primPlusNat0(Zero, Zero) 130.72/78.29 130.72/78.29 We have to consider all minimal (P,Q,R)-chains. 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (239) TransformationProof (EQUIVALENT) 130.72/78.29 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.29 130.72/78.29 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb)) 130.72/78.29 130.72/78.29 130.72/78.29 ---------------------------------------- 130.72/78.29 130.72/78.29 (240) 130.72/78.29 Obligation: 130.72/78.29 Q DP problem: 130.72/78.29 The TRS P consists of the following rules: 130.72/78.29 130.72/78.29 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.29 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5119, zzz5119))), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5119, zzz5119))), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3745, zzz3745))), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (241) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4109, zzz4109))), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg),new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4109, zzz4109))), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (242) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5119, zzz5119))), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5119, zzz5119))), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3745, zzz3745))), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4109, zzz4109))), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (243) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4109), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4109, zzz4109))), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg),new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4109, zzz4109))), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (244) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5119, zzz5119))), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5119, zzz5119))), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3745, zzz3745))), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4109, zzz4109))), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4109, zzz4109))), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (245) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5119, zzz5119))), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) at position [12,0,0] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119))), Succ(zzz5119)), Succ(zzz5119)), be),new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119))), Succ(zzz5119)), Succ(zzz5119)), be)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (246) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5119, zzz5119))), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3745, zzz3745))), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4109, zzz4109))), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4109, zzz4109))), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119))), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (247) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5119, zzz5119))), Succ(zzz5119)), Succ(zzz5119)), Succ(zzz5119)), be) at position [12,0,0] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119))), Succ(zzz5119)), Succ(zzz5119)), be),new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119))), Succ(zzz5119)), Succ(zzz5119)), be)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (248) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3745, zzz3745))), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4109, zzz4109))), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4109, zzz4109))), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119))), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119))), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (249) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3745, zzz3745))), Succ(zzz3745)), Succ(zzz3745)), Succ(zzz3745)), bh) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745))), Succ(zzz3745)), Succ(zzz3745)), bh),new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745))), Succ(zzz3745)), Succ(zzz3745)), bh)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (250) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4109, zzz4109))), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4109, zzz4109))), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119))), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119))), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745))), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (251) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (252) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4109, zzz4109))), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4109, zzz4109))), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119))), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119))), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745))), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (253) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4109, zzz4109))), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109))), Succ(zzz4109)), Succ(zzz4109)), bg),new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109))), Succ(zzz4109)), Succ(zzz4109)), bg)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (254) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4109, zzz4109))), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119))), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119))), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745))), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109))), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (255) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4109, zzz4109))), Succ(zzz4109)), Succ(zzz4109)), Succ(zzz4109)), bg) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109))), Succ(zzz4109)), Succ(zzz4109)), bg),new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109))), Succ(zzz4109)), Succ(zzz4109)), bg)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (256) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119))), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119))), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745))), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109))), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109))), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (257) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119))), Succ(zzz5119)), Succ(zzz5119)), be) at position [12,0] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119))), Succ(zzz5119)), be),new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119))), Succ(zzz5119)), be)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (258) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119))), Succ(zzz5119)), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745))), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109))), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109))), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119))), Succ(zzz5119)), be) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (259) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119))), Succ(zzz5119)), Succ(zzz5119)), be) at position [12,0] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119))), Succ(zzz5119)), be),new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119))), Succ(zzz5119)), be)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (260) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745))), Succ(zzz3745)), Succ(zzz3745)), bh) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109))), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109))), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119))), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119))), Succ(zzz5119)), be) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (261) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745))), Succ(zzz3745)), Succ(zzz3745)), bh) at position [11,0] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745))), Succ(zzz3745)), bh),new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745))), Succ(zzz3745)), bh)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (262) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109))), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109))), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119))), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119))), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745))), Succ(zzz3745)), bh) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (263) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) at position [11,0] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (264) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109))), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109))), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119))), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119))), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745))), Succ(zzz3745)), bh) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (265) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109))), Succ(zzz4109)), Succ(zzz4109)), bg) at position [11,0] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109))), Succ(zzz4109)), bg),new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109))), Succ(zzz4109)), bg)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (266) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109))), Succ(zzz4109)), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119))), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119))), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745))), Succ(zzz3745)), bh) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109))), Succ(zzz4109)), bg) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (267) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109))), Succ(zzz4109)), Succ(zzz4109)), bg) at position [11,0] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109))), Succ(zzz4109)), bg),new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109))), Succ(zzz4109)), bg)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (268) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119))), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119))), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745))), Succ(zzz3745)), bh) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109))), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109))), Succ(zzz4109)), bg) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (269) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119))), Succ(zzz5119)), be) at position [12] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be),new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (270) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119))), Succ(zzz5119)), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745))), Succ(zzz3745)), bh) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109))), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109))), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (271) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119))), Succ(zzz5119)), be) at position [12] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be),new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (272) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745))), Succ(zzz3745)), bh) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109))), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109))), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (273) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745))), Succ(zzz3745)), bh) at position [11] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh),new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (274) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109))), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109))), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (275) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) at position [11] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (276) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109))), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109))), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (277) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109))), Succ(zzz4109)), bg) at position [11] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg),new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (278) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109))), Succ(zzz4109)), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (279) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109))), Succ(zzz4109)), bg) at position [11] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg),new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (280) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (281) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))))), bb)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (282) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))))), bb) 130.72/78.30 130.72/78.30 The TRS R consists of the following rules: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.30 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.30 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.30 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.30 130.72/78.30 The set Q consists of the following terms: 130.72/78.30 130.72/78.30 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.30 new_primPlusNat0(Succ(x0), Zero) 130.72/78.30 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.30 new_primPlusNat0(Zero, Zero) 130.72/78.30 130.72/78.30 We have to consider all minimal (P,Q,R)-chains. 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (283) TransformationProof (EQUIVALENT) 130.72/78.30 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))))), bb) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.30 130.72/78.30 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))))))), bb)) 130.72/78.30 130.72/78.30 130.72/78.30 ---------------------------------------- 130.72/78.30 130.72/78.30 (284) 130.72/78.30 Obligation: 130.72/78.30 Q DP problem: 130.72/78.30 The TRS P consists of the following rules: 130.72/78.30 130.72/78.30 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.30 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.30 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.30 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.30 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.30 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))))))), bb) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (285) TransformationProof (EQUIVALENT) 130.72/78.31 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))))))), bb) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))), bb)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (286) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))), bb) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (287) TransformationProof (EQUIVALENT) 130.72/78.31 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))), bb) at position [11,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (288) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (289) TransformationProof (EQUIVALENT) 130.72/78.31 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (290) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (291) TransformationProof (EQUIVALENT) 130.72/78.31 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))), Succ(Zero)))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))), Succ(Zero)))))))))), bb)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (292) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))), Succ(Zero)))))))))), bb) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (293) TransformationProof (EQUIVALENT) 130.72/78.31 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))), Succ(Zero)))))))))), bb) at position [11,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))), Zero))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))), Zero))))))))))), bb)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (294) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))), Zero))))))))))), bb) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (295) TransformationProof (EQUIVALENT) 130.72/78.31 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))), Zero))))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))))))))))))), bb)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (296) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))))))))))))), bb) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (297) TransformationProof (EQUIVALENT) 130.72/78.31 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))))))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (298) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (299) TransformationProof (EQUIVALENT) 130.72/78.31 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (300) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (301) TransformationProof (EQUIVALENT) 130.72/78.31 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))), Succ(Zero))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))), Succ(Zero))))))))))))))), bb)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (302) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))), Succ(Zero))))))))))))))), bb) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (303) TransformationProof (EQUIVALENT) 130.72/78.31 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))), Succ(Zero))))))))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))), Zero)))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))), Zero)))))))))))))))), bb)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (304) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))), Zero)))))))))))))))), bb) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (305) TransformationProof (EQUIVALENT) 130.72/78.31 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))), Zero)))))))))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))))))))))))), bb)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (306) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))))))))))))), bb) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (307) TransformationProof (EQUIVALENT) 130.72/78.31 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))))))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))))))))))))), bb)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (308) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))))))))))))), bb) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (309) TransformationProof (EQUIVALENT) 130.72/78.31 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))))))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))), Succ(Zero)))))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))), Succ(Zero)))))))))))))))))))), bb)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (310) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))), Succ(Zero)))))))))))))))))))), bb) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (311) TransformationProof (EQUIVALENT) 130.72/78.31 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))), Succ(Zero)))))))))))))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Zero))))))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Zero))))))))))))))))))))), bb)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (312) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Zero))))))))))))))))))))), bb) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (313) TransformationProof (EQUIVALENT) 130.72/78.31 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Zero))))))))))))))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))))))))))))), bb)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (314) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))))))))))))), bb) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (315) TransformationProof (EQUIVALENT) 130.72/78.31 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))))))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))))))))))))), bb)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (316) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (317) TransformationProof (EQUIVALENT) 130.72/78.31 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))))))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))))))))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))))))))))))))))))))))), bb)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (318) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))))))))))))))))))))))), bb) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (319) TransformationProof (EQUIVALENT) 130.72/78.31 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))))))))))))))))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (320) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (321) TransformationProof (EQUIVALENT) 130.72/78.31 By instantiating [LPAR04] the rule new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(zzz411400)), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11),new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (322) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (323) TransformationProof (EQUIVALENT) 130.72/78.31 By instantiating [LPAR04] the rule new_mkVBalBranch3MkVBalBranch212(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Zero), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11),new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (324) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (325) TransformationProof (EQUIVALENT) 130.72/78.31 By instantiating [LPAR04] the rule new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(y_2), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10),new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (326) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (327) TransformationProof (EQUIVALENT) 130.72/78.31 By instantiating [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, zzz3750, bh) -> new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3745, zzz3745)), zzz3745)), zzz3745)), zzz3745))), bh) we obtained the following new rules [LPAR04]: 130.72/78.31 130.72/78.31 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))))), z11)) 130.72/78.31 130.72/78.31 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (328) 130.72/78.31 Obligation: 130.72/78.31 Q DP problem: 130.72/78.31 The TRS P consists of the following rules: 130.72/78.31 130.72/78.31 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.31 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.31 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.31 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.31 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.31 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))))), z11) 130.72/78.31 130.72/78.31 The TRS R consists of the following rules: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.31 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.31 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.31 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.31 130.72/78.31 The set Q consists of the following terms: 130.72/78.31 130.72/78.31 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.31 new_primPlusNat0(Succ(x0), Zero) 130.72/78.31 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.31 new_primPlusNat0(Zero, Zero) 130.72/78.31 130.72/78.31 We have to consider all minimal (P,Q,R)-chains. 130.72/78.31 ---------------------------------------- 130.72/78.31 130.72/78.31 (329) TransformationProof (EQUIVALENT) 130.72/78.31 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))))), z11) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (330) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (331) TransformationProof (EQUIVALENT) 130.72/78.32 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))))))), z11) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(z8))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(z8))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (332) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(z8))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (333) TransformationProof (EQUIVALENT) 130.72/78.32 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(z8))))))))), z11) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (334) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (335) TransformationProof (EQUIVALENT) 130.72/78.32 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))))))))), z11) at position [11,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (336) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (337) TransformationProof (EQUIVALENT) 130.72/78.32 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (338) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (339) TransformationProof (EQUIVALENT) 130.72/78.32 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))))), Succ(Succ(z8))))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))))), Succ(Succ(z8))))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (340) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))))), Succ(Succ(z8))))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (341) TransformationProof (EQUIVALENT) 130.72/78.32 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))))), Succ(Succ(z8))))))))))), z11) at position [11,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8))))), Succ(z8)))))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8))))), Succ(z8)))))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (342) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8))))), Succ(z8)))))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (343) TransformationProof (EQUIVALENT) 130.72/78.32 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8))))), Succ(z8)))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))), z8))))))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))), z8))))))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (344) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))), z8))))))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (345) TransformationProof (EQUIVALENT) 130.72/78.32 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))), z8))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))), z8))))))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))), z8))))))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (346) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))), z8))))))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (347) TransformationProof (EQUIVALENT) 130.72/78.32 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(z8))))), Succ(Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))), z8))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))), z8))))))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))), z8))))))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (348) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))), z8))))))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (349) TransformationProof (EQUIVALENT) 130.72/78.32 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8))))))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))), z8))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))))), Succ(Succ(z8))))), z8))))))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))))), Succ(Succ(z8))))), z8))))))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (350) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))))), Succ(Succ(z8))))), z8))))))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (351) TransformationProof (EQUIVALENT) 130.72/78.32 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))))), Succ(Succ(z8))))), z8))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8))))), Succ(z8)))))), z8))))))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8))))), Succ(z8)))))), z8))))))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (352) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8))))), Succ(z8)))))), z8))))))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (353) TransformationProof (EQUIVALENT) 130.72/78.32 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8))))), Succ(z8)))))), z8))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))), z8))))))), z8))))))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))), z8))))))), z8))))))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (354) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))), z8))))))), z8))))))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (355) TransformationProof (EQUIVALENT) 130.72/78.32 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8)))))), Succ(Succ(Succ(z8)))), z8))))))), z8))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))), z8))))))), z8))))))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))), z8))))))), z8))))))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (356) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))), z8))))))), z8))))))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (357) TransformationProof (EQUIVALENT) 130.72/78.32 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(z8)))), Succ(Succ(Succ(Succ(z8))))), Succ(Succ(z8))))), z8))))))), z8))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(z8))), Succ(Succ(Succ(z8)))))), Succ(Succ(z8))))), z8))))))), z8))))))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(z8))), Succ(Succ(Succ(z8)))))), Succ(Succ(z8))))), z8))))))), z8))))))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (358) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(z8))), Succ(Succ(Succ(z8)))))), Succ(Succ(z8))))), z8))))))), z8))))))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (359) TransformationProof (EQUIVALENT) 130.72/78.32 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(z8))), Succ(Succ(Succ(z8)))))), Succ(Succ(z8))))), z8))))))), z8))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(z8))), Succ(Succ(Succ(z8))))), Succ(z8)))))), z8))))))), z8))))))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(z8))), Succ(Succ(Succ(z8))))), Succ(z8)))))), z8))))))), z8))))))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (360) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(z8))), Succ(Succ(Succ(z8))))), Succ(z8)))))), z8))))))), z8))))))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (361) TransformationProof (EQUIVALENT) 130.72/78.32 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(z8))), Succ(Succ(Succ(z8))))), Succ(z8)))))), z8))))))), z8))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(z8))), Succ(Succ(Succ(z8)))), z8))))))), z8))))))), z8))))))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(z8))), Succ(Succ(Succ(z8)))), z8))))))), z8))))))), z8))))))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (362) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(z8))), Succ(Succ(Succ(z8)))), z8))))))), z8))))))), z8))))))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (363) TransformationProof (EQUIVALENT) 130.72/78.32 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(z8))), Succ(Succ(Succ(z8)))), z8))))))), z8))))))), z8))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(z8)), Succ(Succ(z8))))), z8))))))), z8))))))), z8))))))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(z8)), Succ(Succ(z8))))), z8))))))), z8))))))), z8))))))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (364) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(z8)), Succ(Succ(z8))))), z8))))))), z8))))))), z8))))))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (365) TransformationProof (EQUIVALENT) 130.72/78.32 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(z8)), Succ(Succ(z8))))), z8))))))), z8))))))), z8))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(z8), Succ(z8)))))), z8))))))), z8))))))), z8))))))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(z8), Succ(z8)))))), z8))))))), z8))))))), z8))))))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (366) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(z8), Succ(z8)))))), z8))))))), z8))))))), z8))))))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (367) TransformationProof (EQUIVALENT) 130.72/78.32 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(z8), Succ(z8)))))), z8))))))), z8))))))), z8))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.32 130.72/78.32 (new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(z8, z8))))))), z8))))))), z8))))))), z8))))))))))))), z11),new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(z8, z8))))))), z8))))))), z8))))))), z8))))))))))))), z11)) 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (368) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(z8, z8))))))), z8))))))), z8))))))), z8))))))))))))), z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (369) QDPOrderProof (EQUIVALENT) 130.72/78.32 We use the reduction pair processor [LPAR04,JAR06]. 130.72/78.32 130.72/78.32 130.72/78.32 The following pairs can be oriented strictly and are deleted. 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz52450), be) -> new_mkVBalBranch3MkVBalBranch123(zzz5112, zzz5113, Succ(Succ(zzz5114)), zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(Succ(zzz5114))), Succ(zzz52450), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Zero, bg) -> new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Zero, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch119(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch213(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, z8, z11) -> new_mkVBalBranch3MkVBalBranch119(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(z8))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(z8, z8))))))), z8))))))), z8))))))), z8))))))))))))), z11) 130.72/78.32 The remaining pairs can at least be oriented weakly. 130.72/78.32 Used ordering: Polynomial interpretation [POLO]: 130.72/78.32 130.72/78.32 POL(Branch(x_1, x_2, x_3, x_4, x_5)) = x_1 + x_2 + x_3 + x_4 + x_5 130.72/78.32 POL(Neg(x_1)) = 1 130.72/78.32 POL(Pos(x_1)) = x_1 130.72/78.32 POL(Succ(x_1)) = 0 130.72/78.32 POL(Zero) = 0 130.72/78.32 POL(new_mkVBalBranch3MkVBalBranch119(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13)) = x_2 + x_3 + x_4 130.72/78.32 POL(new_mkVBalBranch3MkVBalBranch122(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13, x_14)) = 1 + x_1 + x_2 + x_4 + x_5 130.72/78.32 POL(new_mkVBalBranch3MkVBalBranch123(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13, x_14, x_15)) = x_2 + x_4 + x_5 130.72/78.32 POL(new_mkVBalBranch3MkVBalBranch124(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13)) = x_1 + x_2 + x_3 + x_4 130.72/78.32 POL(new_mkVBalBranch3MkVBalBranch211(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13, x_14, x_15)) = 1 + x_1 + x_2 + x_4 + x_5 130.72/78.32 POL(new_mkVBalBranch3MkVBalBranch212(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13, x_14)) = 1 + x_1 + x_2 + x_3 + x_4 130.72/78.32 POL(new_mkVBalBranch3MkVBalBranch213(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13)) = 1 + x_2 + x_3 + x_4 130.72/78.32 POL(new_mkVBalBranch3MkVBalBranch217(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13)) = 1 + x_1 + x_2 + x_4 + x_5 130.72/78.32 POL(new_mkVBalBranch3MkVBalBranch218(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13, x_14)) = 1 + x_1 + x_2 + x_3 + x_4 130.72/78.32 POL(new_mkVBalBranch3MkVBalBranch219(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12)) = 1 + x_1 + x_2 + x_3 + x_4 130.72/78.32 POL(new_mkVBalBranch3MkVBalBranch220(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12)) = x_1 + x_2 + x_3 + x_4 130.72/78.32 POL(new_mkVBalBranch4(x_1, x_2, x_3, x_4, x_5)) = x_3 130.72/78.32 POL(new_primPlusNat0(x_1, x_2)) = 0 130.72/78.32 130.72/78.32 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 130.72/78.32 none 130.72/78.32 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (370) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Zero, Succ(zzz63360), bf) -> new_mkVBalBranch4(zzz6333, zzz6334, zzz6327, Branch(zzz6328, zzz6329, Neg(Succ(zzz6330)), zzz6331, zzz6332), bf) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Zero, be) -> new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch213(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, zzz3420000000, bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch119(zzz3739, zzz3740, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(zzz49680), bh) -> new_mkVBalBranch3MkVBalBranch123(zzz3739, zzz3740, Zero, zzz3741, zzz3742, zzz3743, zzz3744, zzz3745, zzz3746, zzz3747, zzz3748, zzz3749, Succ(Zero), Succ(zzz49680), bh) 130.72/78.32 new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz52420), bg) -> new_mkVBalBranch3MkVBalBranch123(zzz4103, zzz4104, Succ(Zero), zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(Zero)), Succ(zzz52420), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch217(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Zero, be) -> new_mkVBalBranch3MkVBalBranch122(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5119, zzz5119)), zzz5119)), zzz5119)), zzz5119))), be) 130.72/78.32 new_mkVBalBranch3MkVBalBranch220(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch3MkVBalBranch124(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4109, zzz4109)), zzz4109)), zzz4109)), zzz4109))), bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (371) DependencyGraphProof (EQUIVALENT) 130.72/78.32 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs with 8 less nodes. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (372) 130.72/78.32 Complex Obligation (AND) 130.72/78.32 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (373) 130.72/78.32 Obligation: 130.72/78.32 Q DP problem: 130.72/78.32 The TRS P consists of the following rules: 130.72/78.32 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.32 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.32 new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.32 130.72/78.32 The TRS R consists of the following rules: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.32 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.32 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.32 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.32 130.72/78.32 The set Q consists of the following terms: 130.72/78.32 130.72/78.32 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.32 new_primPlusNat0(Succ(x0), Zero) 130.72/78.32 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.32 new_primPlusNat0(Zero, Zero) 130.72/78.32 130.72/78.32 We have to consider all minimal (P,Q,R)-chains. 130.72/78.32 ---------------------------------------- 130.72/78.32 130.72/78.32 (374) QDPSizeChangeProof (EQUIVALENT) 130.72/78.32 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. 130.72/78.32 130.72/78.32 From the DPs we obtained the following set of size-change graphs: 130.72/78.32 *new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Zero, Succ(zzz51250), be) -> new_mkVBalBranch4(zzz5122, zzz5123, Branch(zzz5112, zzz5113, Neg(Succ(Succ(Succ(zzz5114)))), zzz5115, zzz5116), zzz5120, be) 130.72/78.32 The graph contains the following edges 11 >= 1, 12 >= 2, 9 >= 4, 15 >= 5 130.72/78.32 130.72/78.32 130.72/78.32 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 The graph contains the following edges 3 > 1, 3 > 2, 3 > 3, 3 > 4, 3 > 5, 4 > 6, 4 > 7, 4 > 8, 4 > 9, 4 > 10, 1 >= 11, 2 >= 12, 4 > 13, 5 >= 15 130.72/78.32 130.72/78.32 130.72/78.32 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch211(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(new_primPlusNat0(zzz25020000, zzz25020000)))), zzz25020000)))), zzz25020000)))), zzz25020000))), bb) 130.72/78.32 The graph contains the following edges 3 > 1, 3 > 2, 3 > 3, 3 > 4, 3 > 5, 4 > 6, 4 > 7, 4 > 8, 4 > 9, 4 > 10, 1 >= 11, 2 >= 12, 4 > 13, 5 >= 15 130.72/78.32 130.72/78.32 130.72/78.32 *new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, Succ(zzz51240), Succ(zzz51250), be) -> new_mkVBalBranch3MkVBalBranch211(zzz5112, zzz5113, zzz5114, zzz5115, zzz5116, zzz5117, zzz5118, zzz5119, zzz5120, zzz5121, zzz5122, zzz5123, zzz51240, zzz51250, be) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 > 13, 14 > 14, 15 >= 15 130.72/78.33 130.72/78.33 130.72/78.33 *new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), z10) -> new_mkVBalBranch4(z0, z1, Branch(z2, z3, Neg(Succ(Succ(Zero))), z4, z5), z8, z10) 130.72/78.33 The graph contains the following edges 10 >= 1, 11 >= 2, 8 >= 4, 14 >= 5 130.72/78.33 130.72/78.33 130.72/78.33 *new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) -> new_mkVBalBranch4(zzz4112, zzz4113, Branch(zzz4103, zzz4104, Neg(Succ(Succ(Zero))), zzz4105, zzz4106), zzz4110, bg) 130.72/78.33 The graph contains the following edges 10 >= 1, 11 >= 2, 8 >= 4, 12 >= 5 130.72/78.33 130.72/78.33 130.72/78.33 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.33 The graph contains the following edges 3 > 1, 3 > 2, 3 > 3, 3 > 4, 4 > 5, 4 > 6, 4 > 7, 4 > 8, 4 > 9, 1 >= 10, 2 >= 11, 3 > 12, 4 > 12, 5 >= 14 130.72/78.33 130.72/78.33 130.72/78.33 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Succ(zzz342000000)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch212(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(zzz342000000)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz342000000), Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.33 The graph contains the following edges 3 > 1, 3 > 2, 3 > 3, 3 > 4, 4 > 5, 4 > 6, 4 > 7, 4 > 8, 4 > 9, 1 >= 10, 2 >= 11, 4 > 12, 5 >= 14 130.72/78.33 130.72/78.33 130.72/78.33 *new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, Succ(Succ(x11)), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch218(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x11))))), z9, z10, z0, z1, x11, Succ(Succ(Succ(Succ(Zero)))), z11) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 7 > 12, 12 > 12, 13 > 13, 14 >= 14 130.72/78.33 130.72/78.33 130.72/78.33 *new_mkVBalBranch3MkVBalBranch212(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch219(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 13 > 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 14 >= 12 130.72/78.33 130.72/78.33 130.72/78.33 *new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Succ(zzz411400), Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, zzz411400, zzz44550, bg) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 > 12, 13 > 13, 14 >= 14 130.72/78.33 130.72/78.33 130.72/78.33 *new_mkVBalBranch3MkVBalBranch218(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, Zero, Succ(zzz44550), bg) -> new_mkVBalBranch3MkVBalBranch219(zzz4103, zzz4104, zzz4105, zzz4106, zzz4107, zzz4108, zzz4109, zzz4110, zzz4111, zzz4112, zzz4113, bg) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 14 >= 12 130.72/78.33 130.72/78.33 130.72/78.33 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5 130.72/78.33 130.72/78.33 130.72/78.33 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5 130.72/78.33 130.72/78.33 130.72/78.33 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(zzz250200)), zzz2503, zzz2504), zzz343, bb) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5 130.72/78.33 130.72/78.33 130.72/78.33 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5 130.72/78.33 130.72/78.33 130.72/78.33 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5 130.72/78.33 130.72/78.33 130.72/78.33 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Zero)), zzz2503, zzz2504), zzz343, bb) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5 130.72/78.33 130.72/78.33 130.72/78.33 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5 130.72/78.33 130.72/78.33 130.72/78.33 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Succ(Succ(zzz2502000))), zzz2503, zzz2504), zzz343, bb) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5 130.72/78.33 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (375) 130.72/78.33 YES 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (376) 130.72/78.33 Obligation: 130.72/78.33 Q DP problem: 130.72/78.33 The TRS P consists of the following rules: 130.72/78.33 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.33 130.72/78.33 The TRS R consists of the following rules: 130.72/78.33 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.33 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.33 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.33 130.72/78.33 The set Q consists of the following terms: 130.72/78.33 130.72/78.33 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.33 new_primPlusNat0(Succ(x0), Zero) 130.72/78.33 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Zero) 130.72/78.33 130.72/78.33 We have to consider all minimal (P,Q,R)-chains. 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (377) QDPSizeChangeProof (EQUIVALENT) 130.72/78.33 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. 130.72/78.33 130.72/78.33 From the DPs we obtained the following set of size-change graphs: 130.72/78.33 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5 130.72/78.33 130.72/78.33 130.72/78.33 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), bb) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5 130.72/78.33 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (378) 130.72/78.33 YES 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (379) 130.72/78.33 Obligation: 130.72/78.33 Q DP problem: 130.72/78.33 The TRS P consists of the following rules: 130.72/78.33 130.72/78.33 new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.33 130.72/78.33 The TRS R consists of the following rules: 130.72/78.33 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.33 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.33 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.33 130.72/78.33 The set Q consists of the following terms: 130.72/78.33 130.72/78.33 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.33 new_primPlusNat0(Succ(x0), Zero) 130.72/78.33 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Zero) 130.72/78.33 130.72/78.33 We have to consider all minimal (P,Q,R)-chains. 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (380) QDPSizeChangeProof (EQUIVALENT) 130.72/78.33 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. 130.72/78.33 130.72/78.33 From the DPs we obtained the following set of size-change graphs: 130.72/78.33 *new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, Succ(zzz63350), Succ(zzz63360), bf) -> new_mkVBalBranch3MkVBalBranch123(zzz6323, zzz6324, zzz6325, zzz6326, zzz6327, zzz6328, zzz6329, zzz6330, zzz6331, zzz6332, zzz6333, zzz6334, zzz63350, zzz63360, bf) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 > 13, 14 > 14, 15 >= 15 130.72/78.33 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (381) 130.72/78.33 YES 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (382) 130.72/78.33 Obligation: 130.72/78.33 Q DP problem: 130.72/78.33 The TRS P consists of the following rules: 130.72/78.33 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) 130.72/78.33 130.72/78.33 The TRS R consists of the following rules: 130.72/78.33 130.72/78.33 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.33 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.33 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.33 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.33 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.33 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.33 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.33 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.33 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.33 new_primMulNat6 -> new_primPlusNat5(new_primMulNat4) 130.72/78.33 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.33 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.33 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.72/78.33 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.33 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.33 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.33 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.33 new_primMulNat2(zzz4739) -> Zero 130.72/78.33 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.33 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.33 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.33 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.33 new_primPlusNat2(Zero) -> Zero 130.72/78.33 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.33 130.72/78.33 The set Q consists of the following terms: 130.72/78.33 130.72/78.33 new_primPlusNat1(Succ(x0)) 130.72/78.33 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.33 new_primMulNat6 130.72/78.33 new_primMulNat0(x0) 130.72/78.33 new_primPlusNat1(Zero) 130.72/78.33 new_primPlusNat2(Zero) 130.72/78.33 new_primPlusNat3(Succ(x0)) 130.72/78.33 new_primMulNat7 130.72/78.33 new_primPlusNat8(Succ(x0), x1) 130.72/78.33 new_primMulNat3(x0) 130.72/78.33 new_primMulNat2(x0) 130.72/78.33 new_primPlusNat6(x0, Succ(x1)) 130.72/78.33 new_primPlusNat0(Succ(x0), Zero) 130.72/78.33 new_primPlusNat6(x0, Zero) 130.72/78.33 new_primPlusNat5(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.33 new_primMulNat4 130.72/78.33 new_primPlusNat4(Succ(x0)) 130.72/78.33 new_primPlusNat8(Zero, x0) 130.72/78.33 new_primPlusNat3(Zero) 130.72/78.33 new_primPlusNat7(x0, Zero) 130.72/78.33 new_primPlusNat5(Zero) 130.72/78.33 new_primMulNat5 130.72/78.33 new_primMulNat1(x0) 130.72/78.33 new_primPlusNat7(x0, Succ(x1)) 130.72/78.33 new_primPlusNat4(Zero) 130.72/78.33 new_primPlusNat2(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Zero) 130.72/78.33 130.72/78.33 We have to consider all minimal (P,Q,R)-chains. 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (383) QDPSizeChangeProof (EQUIVALENT) 130.72/78.33 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. 130.72/78.33 130.72/78.33 From the DPs we obtained the following set of size-change graphs: 130.72/78.33 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), bb) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5 130.72/78.33 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (384) 130.72/78.33 YES 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (385) 130.72/78.33 Obligation: 130.72/78.33 Q DP problem: 130.72/78.33 The TRS P consists of the following rules: 130.72/78.33 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bb) 130.72/78.33 130.72/78.33 The TRS R consists of the following rules: 130.72/78.33 130.72/78.33 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.33 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.33 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.33 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.33 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.33 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.33 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.33 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.33 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.33 new_primMulNat6 -> new_primPlusNat5(new_primMulNat4) 130.72/78.33 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.33 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.33 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.72/78.33 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.33 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.33 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.33 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.33 new_primMulNat2(zzz4739) -> Zero 130.72/78.33 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.33 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.33 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.33 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.33 new_primPlusNat2(Zero) -> Zero 130.72/78.33 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.33 130.72/78.33 The set Q consists of the following terms: 130.72/78.33 130.72/78.33 new_primPlusNat1(Succ(x0)) 130.72/78.33 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.33 new_primMulNat6 130.72/78.33 new_primMulNat0(x0) 130.72/78.33 new_primPlusNat1(Zero) 130.72/78.33 new_primPlusNat2(Zero) 130.72/78.33 new_primPlusNat3(Succ(x0)) 130.72/78.33 new_primMulNat7 130.72/78.33 new_primPlusNat8(Succ(x0), x1) 130.72/78.33 new_primMulNat3(x0) 130.72/78.33 new_primMulNat2(x0) 130.72/78.33 new_primPlusNat6(x0, Succ(x1)) 130.72/78.33 new_primPlusNat0(Succ(x0), Zero) 130.72/78.33 new_primPlusNat6(x0, Zero) 130.72/78.33 new_primPlusNat5(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.33 new_primMulNat4 130.72/78.33 new_primPlusNat4(Succ(x0)) 130.72/78.33 new_primPlusNat8(Zero, x0) 130.72/78.33 new_primPlusNat3(Zero) 130.72/78.33 new_primPlusNat7(x0, Zero) 130.72/78.33 new_primPlusNat5(Zero) 130.72/78.33 new_primMulNat5 130.72/78.33 new_primMulNat1(x0) 130.72/78.33 new_primPlusNat7(x0, Succ(x1)) 130.72/78.33 new_primPlusNat4(Zero) 130.72/78.33 new_primPlusNat2(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Zero) 130.72/78.33 130.72/78.33 We have to consider all minimal (P,Q,R)-chains. 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (386) QDPSizeChangeProof (EQUIVALENT) 130.72/78.33 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. 130.72/78.33 130.72/78.33 From the DPs we obtained the following set of size-change graphs: 130.72/78.33 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, zzz2504, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), bb) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5 130.72/78.33 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (387) 130.72/78.33 YES 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (388) 130.72/78.33 Obligation: 130.72/78.33 Q DP problem: 130.72/78.33 The TRS P consists of the following rules: 130.72/78.33 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), zzz343, bb) 130.72/78.33 130.72/78.33 The TRS R consists of the following rules: 130.72/78.33 130.72/78.33 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.33 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.33 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.33 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.33 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.33 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.33 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.33 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.33 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.33 new_primMulNat6 -> new_primPlusNat5(new_primMulNat4) 130.72/78.33 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.33 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.33 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.72/78.33 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.33 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.33 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.33 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.33 new_primMulNat2(zzz4739) -> Zero 130.72/78.33 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.33 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.33 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.33 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.33 new_primPlusNat2(Zero) -> Zero 130.72/78.33 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.33 130.72/78.33 The set Q consists of the following terms: 130.72/78.33 130.72/78.33 new_primPlusNat1(Succ(x0)) 130.72/78.33 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.33 new_primMulNat6 130.72/78.33 new_primMulNat0(x0) 130.72/78.33 new_primPlusNat1(Zero) 130.72/78.33 new_primPlusNat2(Zero) 130.72/78.33 new_primPlusNat3(Succ(x0)) 130.72/78.33 new_primMulNat7 130.72/78.33 new_primPlusNat8(Succ(x0), x1) 130.72/78.33 new_primMulNat3(x0) 130.72/78.33 new_primMulNat2(x0) 130.72/78.33 new_primPlusNat6(x0, Succ(x1)) 130.72/78.33 new_primPlusNat0(Succ(x0), Zero) 130.72/78.33 new_primPlusNat6(x0, Zero) 130.72/78.33 new_primPlusNat5(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.33 new_primMulNat4 130.72/78.33 new_primPlusNat4(Succ(x0)) 130.72/78.33 new_primPlusNat8(Zero, x0) 130.72/78.33 new_primPlusNat3(Zero) 130.72/78.33 new_primPlusNat7(x0, Zero) 130.72/78.33 new_primPlusNat5(Zero) 130.72/78.33 new_primMulNat5 130.72/78.33 new_primMulNat1(x0) 130.72/78.33 new_primPlusNat7(x0, Succ(x1)) 130.72/78.33 new_primPlusNat4(Zero) 130.72/78.33 new_primPlusNat2(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Zero) 130.72/78.33 130.72/78.33 We have to consider all minimal (P,Q,R)-chains. 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (389) QDPSizeChangeProof (EQUIVALENT) 130.72/78.33 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. 130.72/78.33 130.72/78.33 From the DPs we obtained the following set of size-change graphs: 130.72/78.33 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Neg(Zero), zzz2503, zzz2504), zzz343, bb) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5 130.72/78.33 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (390) 130.72/78.33 YES 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (391) 130.72/78.33 Obligation: 130.72/78.33 Q DP problem: 130.72/78.33 The TRS P consists of the following rules: 130.72/78.33 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), zzz343, bb) 130.72/78.33 130.72/78.33 The TRS R consists of the following rules: 130.72/78.33 130.72/78.33 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.33 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.33 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.33 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.33 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.33 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.33 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.33 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.33 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.33 new_primMulNat6 -> new_primPlusNat5(new_primMulNat4) 130.72/78.33 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.33 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.33 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.72/78.33 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.33 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.33 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.33 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.33 new_primMulNat2(zzz4739) -> Zero 130.72/78.33 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.33 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.33 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.33 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.33 new_primPlusNat2(Zero) -> Zero 130.72/78.33 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.33 130.72/78.33 The set Q consists of the following terms: 130.72/78.33 130.72/78.33 new_primPlusNat1(Succ(x0)) 130.72/78.33 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.33 new_primMulNat6 130.72/78.33 new_primMulNat0(x0) 130.72/78.33 new_primPlusNat1(Zero) 130.72/78.33 new_primPlusNat2(Zero) 130.72/78.33 new_primPlusNat3(Succ(x0)) 130.72/78.33 new_primMulNat7 130.72/78.33 new_primPlusNat8(Succ(x0), x1) 130.72/78.33 new_primMulNat3(x0) 130.72/78.33 new_primMulNat2(x0) 130.72/78.33 new_primPlusNat6(x0, Succ(x1)) 130.72/78.33 new_primPlusNat0(Succ(x0), Zero) 130.72/78.33 new_primPlusNat6(x0, Zero) 130.72/78.33 new_primPlusNat5(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.33 new_primMulNat4 130.72/78.33 new_primPlusNat4(Succ(x0)) 130.72/78.33 new_primPlusNat8(Zero, x0) 130.72/78.33 new_primPlusNat3(Zero) 130.72/78.33 new_primPlusNat7(x0, Zero) 130.72/78.33 new_primPlusNat5(Zero) 130.72/78.33 new_primMulNat5 130.72/78.33 new_primMulNat1(x0) 130.72/78.33 new_primPlusNat7(x0, Succ(x1)) 130.72/78.33 new_primPlusNat4(Zero) 130.72/78.33 new_primPlusNat2(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Zero) 130.72/78.33 130.72/78.33 We have to consider all minimal (P,Q,R)-chains. 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (392) QDPSizeChangeProof (EQUIVALENT) 130.72/78.33 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. 130.72/78.33 130.72/78.33 From the DPs we obtained the following set of size-change graphs: 130.72/78.33 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), bb) -> new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Zero), zzz2503, zzz2504), zzz343, bb) 130.72/78.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5 130.72/78.33 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (393) 130.72/78.33 YES 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (394) 130.72/78.33 Obligation: 130.72/78.33 Q DP problem: 130.72/78.33 The TRS P consists of the following rules: 130.72/78.33 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Zero)))), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat6, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat7, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat4, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 130.72/78.33 The TRS R consists of the following rules: 130.72/78.33 130.72/78.33 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.33 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.33 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.33 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.33 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.33 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.33 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.33 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.33 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.33 new_primMulNat6 -> new_primPlusNat5(new_primMulNat4) 130.72/78.33 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.33 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.33 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.72/78.33 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.33 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.33 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.33 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.33 new_primMulNat2(zzz4739) -> Zero 130.72/78.33 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.33 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.33 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.33 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.33 new_primPlusNat2(Zero) -> Zero 130.72/78.33 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.33 130.72/78.33 The set Q consists of the following terms: 130.72/78.33 130.72/78.33 new_primPlusNat1(Succ(x0)) 130.72/78.33 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.33 new_primMulNat6 130.72/78.33 new_primMulNat0(x0) 130.72/78.33 new_primPlusNat1(Zero) 130.72/78.33 new_primPlusNat2(Zero) 130.72/78.33 new_primPlusNat3(Succ(x0)) 130.72/78.33 new_primMulNat7 130.72/78.33 new_primPlusNat8(Succ(x0), x1) 130.72/78.33 new_primMulNat3(x0) 130.72/78.33 new_primMulNat2(x0) 130.72/78.33 new_primPlusNat6(x0, Succ(x1)) 130.72/78.33 new_primPlusNat0(Succ(x0), Zero) 130.72/78.33 new_primPlusNat6(x0, Zero) 130.72/78.33 new_primPlusNat5(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.33 new_primMulNat4 130.72/78.33 new_primPlusNat4(Succ(x0)) 130.72/78.33 new_primPlusNat8(Zero, x0) 130.72/78.33 new_primPlusNat3(Zero) 130.72/78.33 new_primPlusNat7(x0, Zero) 130.72/78.33 new_primPlusNat5(Zero) 130.72/78.33 new_primMulNat5 130.72/78.33 new_primMulNat1(x0) 130.72/78.33 new_primPlusNat7(x0, Succ(x1)) 130.72/78.33 new_primPlusNat4(Zero) 130.72/78.33 new_primPlusNat2(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Zero) 130.72/78.33 130.72/78.33 We have to consider all minimal (P,Q,R)-chains. 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (395) TransformationProof (EQUIVALENT) 130.72/78.33 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Zero)))), bb) at position [10] we obtained the following new rules [LPAR04]: 130.72/78.33 130.72/78.33 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb)) 130.72/78.33 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (396) 130.72/78.33 Obligation: 130.72/78.33 Q DP problem: 130.72/78.33 The TRS P consists of the following rules: 130.72/78.33 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat6, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat7, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat4, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.33 130.72/78.33 The TRS R consists of the following rules: 130.72/78.33 130.72/78.33 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.33 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.33 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.33 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.33 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.33 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.33 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.33 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.33 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.33 new_primMulNat6 -> new_primPlusNat5(new_primMulNat4) 130.72/78.33 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.33 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.33 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.72/78.33 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.33 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.33 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.33 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.33 new_primMulNat2(zzz4739) -> Zero 130.72/78.33 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.33 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.33 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.33 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.33 new_primPlusNat2(Zero) -> Zero 130.72/78.33 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.33 130.72/78.33 The set Q consists of the following terms: 130.72/78.33 130.72/78.33 new_primPlusNat1(Succ(x0)) 130.72/78.33 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.33 new_primMulNat6 130.72/78.33 new_primMulNat0(x0) 130.72/78.33 new_primPlusNat1(Zero) 130.72/78.33 new_primPlusNat2(Zero) 130.72/78.33 new_primPlusNat3(Succ(x0)) 130.72/78.33 new_primMulNat7 130.72/78.33 new_primPlusNat8(Succ(x0), x1) 130.72/78.33 new_primMulNat3(x0) 130.72/78.33 new_primMulNat2(x0) 130.72/78.33 new_primPlusNat6(x0, Succ(x1)) 130.72/78.33 new_primPlusNat0(Succ(x0), Zero) 130.72/78.33 new_primPlusNat6(x0, Zero) 130.72/78.33 new_primPlusNat5(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.33 new_primMulNat4 130.72/78.33 new_primPlusNat4(Succ(x0)) 130.72/78.33 new_primPlusNat8(Zero, x0) 130.72/78.33 new_primPlusNat3(Zero) 130.72/78.33 new_primPlusNat7(x0, Zero) 130.72/78.33 new_primPlusNat5(Zero) 130.72/78.33 new_primMulNat5 130.72/78.33 new_primMulNat1(x0) 130.72/78.33 new_primPlusNat7(x0, Succ(x1)) 130.72/78.33 new_primPlusNat4(Zero) 130.72/78.33 new_primPlusNat2(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Zero) 130.72/78.33 130.72/78.33 We have to consider all minimal (P,Q,R)-chains. 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (397) TransformationProof (EQUIVALENT) 130.72/78.33 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat6, bb) at position [10] we obtained the following new rules [LPAR04]: 130.72/78.33 130.72/78.33 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb)) 130.72/78.33 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (398) 130.72/78.33 Obligation: 130.72/78.33 Q DP problem: 130.72/78.33 The TRS P consists of the following rules: 130.72/78.33 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat7, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat4, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.33 130.72/78.33 The TRS R consists of the following rules: 130.72/78.33 130.72/78.33 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.33 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.33 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.33 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.33 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.33 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.33 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.33 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.33 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.33 new_primMulNat6 -> new_primPlusNat5(new_primMulNat4) 130.72/78.33 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.33 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.33 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.72/78.33 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.33 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.33 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.33 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.33 new_primMulNat2(zzz4739) -> Zero 130.72/78.33 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.33 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.33 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.33 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.33 new_primPlusNat2(Zero) -> Zero 130.72/78.33 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.33 130.72/78.33 The set Q consists of the following terms: 130.72/78.33 130.72/78.33 new_primPlusNat1(Succ(x0)) 130.72/78.33 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.33 new_primMulNat6 130.72/78.33 new_primMulNat0(x0) 130.72/78.33 new_primPlusNat1(Zero) 130.72/78.33 new_primPlusNat2(Zero) 130.72/78.33 new_primPlusNat3(Succ(x0)) 130.72/78.33 new_primMulNat7 130.72/78.33 new_primPlusNat8(Succ(x0), x1) 130.72/78.33 new_primMulNat3(x0) 130.72/78.33 new_primMulNat2(x0) 130.72/78.33 new_primPlusNat6(x0, Succ(x1)) 130.72/78.33 new_primPlusNat0(Succ(x0), Zero) 130.72/78.33 new_primPlusNat6(x0, Zero) 130.72/78.33 new_primPlusNat5(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.33 new_primMulNat4 130.72/78.33 new_primPlusNat4(Succ(x0)) 130.72/78.33 new_primPlusNat8(Zero, x0) 130.72/78.33 new_primPlusNat3(Zero) 130.72/78.33 new_primPlusNat7(x0, Zero) 130.72/78.33 new_primPlusNat5(Zero) 130.72/78.33 new_primMulNat5 130.72/78.33 new_primMulNat1(x0) 130.72/78.33 new_primPlusNat7(x0, Succ(x1)) 130.72/78.33 new_primPlusNat4(Zero) 130.72/78.33 new_primPlusNat2(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Zero) 130.72/78.33 130.72/78.33 We have to consider all minimal (P,Q,R)-chains. 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (399) UsableRulesProof (EQUIVALENT) 130.72/78.33 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (400) 130.72/78.33 Obligation: 130.72/78.33 Q DP problem: 130.72/78.33 The TRS P consists of the following rules: 130.72/78.33 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat7, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat4, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.33 130.72/78.33 The TRS R consists of the following rules: 130.72/78.33 130.72/78.33 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.33 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.33 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.33 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.33 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.33 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.33 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.33 new_primPlusNat2(Zero) -> Zero 130.72/78.33 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.33 new_primMulNat2(zzz4739) -> Zero 130.72/78.33 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.33 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.33 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.33 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.33 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.33 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.33 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.33 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.33 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.33 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.33 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.33 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.33 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.72/78.33 130.72/78.33 The set Q consists of the following terms: 130.72/78.33 130.72/78.33 new_primPlusNat1(Succ(x0)) 130.72/78.33 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.33 new_primMulNat6 130.72/78.33 new_primMulNat0(x0) 130.72/78.33 new_primPlusNat1(Zero) 130.72/78.33 new_primPlusNat2(Zero) 130.72/78.33 new_primPlusNat3(Succ(x0)) 130.72/78.33 new_primMulNat7 130.72/78.33 new_primPlusNat8(Succ(x0), x1) 130.72/78.33 new_primMulNat3(x0) 130.72/78.33 new_primMulNat2(x0) 130.72/78.33 new_primPlusNat6(x0, Succ(x1)) 130.72/78.33 new_primPlusNat0(Succ(x0), Zero) 130.72/78.33 new_primPlusNat6(x0, Zero) 130.72/78.33 new_primPlusNat5(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.33 new_primMulNat4 130.72/78.33 new_primPlusNat4(Succ(x0)) 130.72/78.33 new_primPlusNat8(Zero, x0) 130.72/78.33 new_primPlusNat3(Zero) 130.72/78.33 new_primPlusNat7(x0, Zero) 130.72/78.33 new_primPlusNat5(Zero) 130.72/78.33 new_primMulNat5 130.72/78.33 new_primMulNat1(x0) 130.72/78.33 new_primPlusNat7(x0, Succ(x1)) 130.72/78.33 new_primPlusNat4(Zero) 130.72/78.33 new_primPlusNat2(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Zero) 130.72/78.33 130.72/78.33 We have to consider all minimal (P,Q,R)-chains. 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (401) QReductionProof (EQUIVALENT) 130.72/78.33 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.72/78.33 130.72/78.33 new_primMulNat6 130.72/78.33 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (402) 130.72/78.33 Obligation: 130.72/78.33 Q DP problem: 130.72/78.33 The TRS P consists of the following rules: 130.72/78.33 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat7, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat4, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.33 130.72/78.33 The TRS R consists of the following rules: 130.72/78.33 130.72/78.33 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.33 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.33 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.33 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.33 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.33 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.33 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.33 new_primPlusNat2(Zero) -> Zero 130.72/78.33 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.33 new_primMulNat2(zzz4739) -> Zero 130.72/78.33 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.33 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.33 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.33 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.33 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.33 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.33 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.33 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.33 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.33 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.33 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.33 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.33 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.72/78.33 130.72/78.33 The set Q consists of the following terms: 130.72/78.33 130.72/78.33 new_primPlusNat1(Succ(x0)) 130.72/78.33 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.33 new_primMulNat0(x0) 130.72/78.33 new_primPlusNat1(Zero) 130.72/78.33 new_primPlusNat2(Zero) 130.72/78.33 new_primPlusNat3(Succ(x0)) 130.72/78.33 new_primMulNat7 130.72/78.33 new_primPlusNat8(Succ(x0), x1) 130.72/78.33 new_primMulNat3(x0) 130.72/78.33 new_primMulNat2(x0) 130.72/78.33 new_primPlusNat6(x0, Succ(x1)) 130.72/78.33 new_primPlusNat0(Succ(x0), Zero) 130.72/78.33 new_primPlusNat6(x0, Zero) 130.72/78.33 new_primPlusNat5(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.33 new_primMulNat4 130.72/78.33 new_primPlusNat4(Succ(x0)) 130.72/78.33 new_primPlusNat8(Zero, x0) 130.72/78.33 new_primPlusNat3(Zero) 130.72/78.33 new_primPlusNat7(x0, Zero) 130.72/78.33 new_primPlusNat5(Zero) 130.72/78.33 new_primMulNat5 130.72/78.33 new_primMulNat1(x0) 130.72/78.33 new_primPlusNat7(x0, Succ(x1)) 130.72/78.33 new_primPlusNat4(Zero) 130.72/78.33 new_primPlusNat2(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Zero) 130.72/78.33 130.72/78.33 We have to consider all minimal (P,Q,R)-chains. 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (403) TransformationProof (EQUIVALENT) 130.72/78.33 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat3(Succ(Succ(Succ(Succ(Zero))))), bb) at position [10] we obtained the following new rules [LPAR04]: 130.72/78.33 130.72/78.33 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb)) 130.72/78.33 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (404) 130.72/78.33 Obligation: 130.72/78.33 Q DP problem: 130.72/78.33 The TRS P consists of the following rules: 130.72/78.33 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat7, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat4, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.33 130.72/78.33 The TRS R consists of the following rules: 130.72/78.33 130.72/78.33 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.33 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.33 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.33 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.33 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.33 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.33 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.33 new_primPlusNat2(Zero) -> Zero 130.72/78.33 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.33 new_primMulNat2(zzz4739) -> Zero 130.72/78.33 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.33 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.33 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.33 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.33 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.33 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.33 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.33 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.33 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.33 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.33 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.33 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.33 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.72/78.33 130.72/78.33 The set Q consists of the following terms: 130.72/78.33 130.72/78.33 new_primPlusNat1(Succ(x0)) 130.72/78.33 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.33 new_primMulNat0(x0) 130.72/78.33 new_primPlusNat1(Zero) 130.72/78.33 new_primPlusNat2(Zero) 130.72/78.33 new_primPlusNat3(Succ(x0)) 130.72/78.33 new_primMulNat7 130.72/78.33 new_primPlusNat8(Succ(x0), x1) 130.72/78.33 new_primMulNat3(x0) 130.72/78.33 new_primMulNat2(x0) 130.72/78.33 new_primPlusNat6(x0, Succ(x1)) 130.72/78.33 new_primPlusNat0(Succ(x0), Zero) 130.72/78.33 new_primPlusNat6(x0, Zero) 130.72/78.33 new_primPlusNat5(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.33 new_primMulNat4 130.72/78.33 new_primPlusNat4(Succ(x0)) 130.72/78.33 new_primPlusNat8(Zero, x0) 130.72/78.33 new_primPlusNat3(Zero) 130.72/78.33 new_primPlusNat7(x0, Zero) 130.72/78.33 new_primPlusNat5(Zero) 130.72/78.33 new_primMulNat5 130.72/78.33 new_primMulNat1(x0) 130.72/78.33 new_primPlusNat7(x0, Succ(x1)) 130.72/78.33 new_primPlusNat4(Zero) 130.72/78.33 new_primPlusNat2(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Zero) 130.72/78.33 130.72/78.33 We have to consider all minimal (P,Q,R)-chains. 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (405) TransformationProof (EQUIVALENT) 130.72/78.33 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.72/78.33 130.72/78.33 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb)) 130.72/78.33 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (406) 130.72/78.33 Obligation: 130.72/78.33 Q DP problem: 130.72/78.33 The TRS P consists of the following rules: 130.72/78.33 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat7, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat4, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.33 130.72/78.33 The TRS R consists of the following rules: 130.72/78.33 130.72/78.33 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.33 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.33 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.33 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.33 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.33 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.33 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.33 new_primPlusNat2(Zero) -> Zero 130.72/78.33 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.33 new_primMulNat2(zzz4739) -> Zero 130.72/78.33 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.33 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.33 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.33 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.33 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.33 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.33 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.33 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.33 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.33 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.33 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.33 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.33 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.72/78.33 130.72/78.33 The set Q consists of the following terms: 130.72/78.33 130.72/78.33 new_primPlusNat1(Succ(x0)) 130.72/78.33 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.33 new_primMulNat0(x0) 130.72/78.33 new_primPlusNat1(Zero) 130.72/78.33 new_primPlusNat2(Zero) 130.72/78.33 new_primPlusNat3(Succ(x0)) 130.72/78.33 new_primMulNat7 130.72/78.33 new_primPlusNat8(Succ(x0), x1) 130.72/78.33 new_primMulNat3(x0) 130.72/78.33 new_primMulNat2(x0) 130.72/78.33 new_primPlusNat6(x0, Succ(x1)) 130.72/78.33 new_primPlusNat0(Succ(x0), Zero) 130.72/78.33 new_primPlusNat6(x0, Zero) 130.72/78.33 new_primPlusNat5(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.33 new_primMulNat4 130.72/78.33 new_primPlusNat4(Succ(x0)) 130.72/78.33 new_primPlusNat8(Zero, x0) 130.72/78.33 new_primPlusNat3(Zero) 130.72/78.33 new_primPlusNat7(x0, Zero) 130.72/78.33 new_primPlusNat5(Zero) 130.72/78.33 new_primMulNat5 130.72/78.33 new_primMulNat1(x0) 130.72/78.33 new_primPlusNat7(x0, Succ(x1)) 130.72/78.33 new_primPlusNat4(Zero) 130.72/78.33 new_primPlusNat2(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Zero) 130.72/78.33 130.72/78.33 We have to consider all minimal (P,Q,R)-chains. 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (407) TransformationProof (EQUIVALENT) 130.72/78.33 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) at position [11] we obtained the following new rules [LPAR04]: 130.72/78.33 130.72/78.33 (new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc)) 130.72/78.33 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (408) 130.72/78.33 Obligation: 130.72/78.33 Q DP problem: 130.72/78.33 The TRS P consists of the following rules: 130.72/78.33 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat7, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat4, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.33 130.72/78.33 The TRS R consists of the following rules: 130.72/78.33 130.72/78.33 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.33 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.33 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.33 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.33 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.33 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.33 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.33 new_primPlusNat2(Zero) -> Zero 130.72/78.33 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.33 new_primMulNat2(zzz4739) -> Zero 130.72/78.33 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.33 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.33 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.33 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.33 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.33 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.33 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.33 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.33 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.33 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.33 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.33 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.33 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.72/78.33 130.72/78.33 The set Q consists of the following terms: 130.72/78.33 130.72/78.33 new_primPlusNat1(Succ(x0)) 130.72/78.33 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.33 new_primMulNat0(x0) 130.72/78.33 new_primPlusNat1(Zero) 130.72/78.33 new_primPlusNat2(Zero) 130.72/78.33 new_primPlusNat3(Succ(x0)) 130.72/78.33 new_primMulNat7 130.72/78.33 new_primPlusNat8(Succ(x0), x1) 130.72/78.33 new_primMulNat3(x0) 130.72/78.33 new_primMulNat2(x0) 130.72/78.33 new_primPlusNat6(x0, Succ(x1)) 130.72/78.33 new_primPlusNat0(Succ(x0), Zero) 130.72/78.33 new_primPlusNat6(x0, Zero) 130.72/78.33 new_primPlusNat5(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.33 new_primMulNat4 130.72/78.33 new_primPlusNat4(Succ(x0)) 130.72/78.33 new_primPlusNat8(Zero, x0) 130.72/78.33 new_primPlusNat3(Zero) 130.72/78.33 new_primPlusNat7(x0, Zero) 130.72/78.33 new_primPlusNat5(Zero) 130.72/78.33 new_primMulNat5 130.72/78.33 new_primMulNat1(x0) 130.72/78.33 new_primPlusNat7(x0, Succ(x1)) 130.72/78.33 new_primPlusNat4(Zero) 130.72/78.33 new_primPlusNat2(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Zero) 130.72/78.33 130.72/78.33 We have to consider all minimal (P,Q,R)-chains. 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (409) TransformationProof (EQUIVALENT) 130.72/78.33 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) at position [11] we obtained the following new rules [LPAR04]: 130.72/78.33 130.72/78.33 (new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc)) 130.72/78.33 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (410) 130.72/78.33 Obligation: 130.72/78.33 Q DP problem: 130.72/78.33 The TRS P consists of the following rules: 130.72/78.33 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat7, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat4, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.33 130.72/78.33 The TRS R consists of the following rules: 130.72/78.33 130.72/78.33 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.33 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.33 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.33 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.33 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.33 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.33 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.33 new_primPlusNat2(Zero) -> Zero 130.72/78.33 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.33 new_primMulNat2(zzz4739) -> Zero 130.72/78.33 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.33 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.33 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.33 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.33 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.33 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.33 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.33 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.33 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.33 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.33 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.33 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.33 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.72/78.33 130.72/78.33 The set Q consists of the following terms: 130.72/78.33 130.72/78.33 new_primPlusNat1(Succ(x0)) 130.72/78.33 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.33 new_primMulNat0(x0) 130.72/78.33 new_primPlusNat1(Zero) 130.72/78.33 new_primPlusNat2(Zero) 130.72/78.33 new_primPlusNat3(Succ(x0)) 130.72/78.33 new_primMulNat7 130.72/78.33 new_primPlusNat8(Succ(x0), x1) 130.72/78.33 new_primMulNat3(x0) 130.72/78.33 new_primMulNat2(x0) 130.72/78.33 new_primPlusNat6(x0, Succ(x1)) 130.72/78.33 new_primPlusNat0(Succ(x0), Zero) 130.72/78.33 new_primPlusNat6(x0, Zero) 130.72/78.33 new_primPlusNat5(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.33 new_primMulNat4 130.72/78.33 new_primPlusNat4(Succ(x0)) 130.72/78.33 new_primPlusNat8(Zero, x0) 130.72/78.33 new_primPlusNat3(Zero) 130.72/78.33 new_primPlusNat7(x0, Zero) 130.72/78.33 new_primPlusNat5(Zero) 130.72/78.33 new_primMulNat5 130.72/78.33 new_primMulNat1(x0) 130.72/78.33 new_primPlusNat7(x0, Succ(x1)) 130.72/78.33 new_primPlusNat4(Zero) 130.72/78.33 new_primPlusNat2(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Zero) 130.72/78.33 130.72/78.33 We have to consider all minimal (P,Q,R)-chains. 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (411) TransformationProof (EQUIVALENT) 130.72/78.33 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primMulNat3(zzz3882), bc) at position [11] we obtained the following new rules [LPAR04]: 130.72/78.33 130.72/78.33 (new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc)) 130.72/78.33 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (412) 130.72/78.33 Obligation: 130.72/78.33 Q DP problem: 130.72/78.33 The TRS P consists of the following rules: 130.72/78.33 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat7, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat4, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.33 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.33 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.33 130.72/78.33 The TRS R consists of the following rules: 130.72/78.33 130.72/78.33 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.33 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.33 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.33 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.33 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.33 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.33 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.33 new_primPlusNat2(Zero) -> Zero 130.72/78.33 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.33 new_primMulNat2(zzz4739) -> Zero 130.72/78.33 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.33 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.33 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.33 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.33 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.33 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.33 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.33 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.33 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.33 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.33 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.33 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.33 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.33 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.33 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.72/78.33 130.72/78.33 The set Q consists of the following terms: 130.72/78.33 130.72/78.33 new_primPlusNat1(Succ(x0)) 130.72/78.33 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.33 new_primMulNat0(x0) 130.72/78.33 new_primPlusNat1(Zero) 130.72/78.33 new_primPlusNat2(Zero) 130.72/78.33 new_primPlusNat3(Succ(x0)) 130.72/78.33 new_primMulNat7 130.72/78.33 new_primPlusNat8(Succ(x0), x1) 130.72/78.33 new_primMulNat3(x0) 130.72/78.33 new_primMulNat2(x0) 130.72/78.33 new_primPlusNat6(x0, Succ(x1)) 130.72/78.33 new_primPlusNat0(Succ(x0), Zero) 130.72/78.33 new_primPlusNat6(x0, Zero) 130.72/78.33 new_primPlusNat5(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.33 new_primMulNat4 130.72/78.33 new_primPlusNat4(Succ(x0)) 130.72/78.33 new_primPlusNat8(Zero, x0) 130.72/78.33 new_primPlusNat3(Zero) 130.72/78.33 new_primPlusNat7(x0, Zero) 130.72/78.33 new_primPlusNat5(Zero) 130.72/78.33 new_primMulNat5 130.72/78.33 new_primMulNat1(x0) 130.72/78.33 new_primPlusNat7(x0, Succ(x1)) 130.72/78.33 new_primPlusNat4(Zero) 130.72/78.33 new_primPlusNat2(Succ(x0)) 130.72/78.33 new_primPlusNat0(Zero, Zero) 130.72/78.33 130.72/78.33 We have to consider all minimal (P,Q,R)-chains. 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (413) TransformationProof (EQUIVALENT) 130.72/78.33 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) at position [11] we obtained the following new rules [LPAR04]: 130.72/78.33 130.72/78.33 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb)) 130.72/78.33 130.72/78.33 130.72/78.33 ---------------------------------------- 130.72/78.33 130.72/78.33 (414) 130.72/78.33 Obligation: 130.72/78.33 Q DP problem: 130.72/78.33 The TRS P consists of the following rules: 130.72/78.33 130.72/78.33 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.33 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat7, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat4, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 130.72/78.34 The TRS R consists of the following rules: 130.72/78.34 130.72/78.34 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.34 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.34 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.34 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.34 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.34 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.34 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.34 new_primPlusNat2(Zero) -> Zero 130.72/78.34 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.34 new_primMulNat2(zzz4739) -> Zero 130.72/78.34 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.34 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.34 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.34 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.34 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.34 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.34 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.34 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.34 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.34 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.34 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.34 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.34 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.72/78.34 130.72/78.34 The set Q consists of the following terms: 130.72/78.34 130.72/78.34 new_primPlusNat1(Succ(x0)) 130.72/78.34 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.34 new_primMulNat0(x0) 130.72/78.34 new_primPlusNat1(Zero) 130.72/78.34 new_primPlusNat2(Zero) 130.72/78.34 new_primPlusNat3(Succ(x0)) 130.72/78.34 new_primMulNat7 130.72/78.34 new_primPlusNat8(Succ(x0), x1) 130.72/78.34 new_primMulNat3(x0) 130.72/78.34 new_primMulNat2(x0) 130.72/78.34 new_primPlusNat6(x0, Succ(x1)) 130.72/78.34 new_primPlusNat0(Succ(x0), Zero) 130.72/78.34 new_primPlusNat6(x0, Zero) 130.72/78.34 new_primPlusNat5(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.34 new_primMulNat4 130.72/78.34 new_primPlusNat4(Succ(x0)) 130.72/78.34 new_primPlusNat8(Zero, x0) 130.72/78.34 new_primPlusNat3(Zero) 130.72/78.34 new_primPlusNat7(x0, Zero) 130.72/78.34 new_primPlusNat5(Zero) 130.72/78.34 new_primMulNat5 130.72/78.34 new_primMulNat1(x0) 130.72/78.34 new_primPlusNat7(x0, Succ(x1)) 130.72/78.34 new_primPlusNat4(Zero) 130.72/78.34 new_primPlusNat2(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Zero) 130.72/78.34 130.72/78.34 We have to consider all minimal (P,Q,R)-chains. 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (415) TransformationProof (EQUIVALENT) 130.72/78.34 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat7, bb) at position [11] we obtained the following new rules [LPAR04]: 130.72/78.34 130.72/78.34 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb)) 130.72/78.34 130.72/78.34 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (416) 130.72/78.34 Obligation: 130.72/78.34 Q DP problem: 130.72/78.34 The TRS P consists of the following rules: 130.72/78.34 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat4, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.34 130.72/78.34 The TRS R consists of the following rules: 130.72/78.34 130.72/78.34 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.34 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.34 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.34 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.34 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.34 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.34 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.34 new_primPlusNat2(Zero) -> Zero 130.72/78.34 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.34 new_primMulNat2(zzz4739) -> Zero 130.72/78.34 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.34 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.34 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.34 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.34 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.34 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.34 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.34 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.34 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.34 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.34 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.34 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.34 new_primMulNat7 -> new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))) 130.72/78.34 130.72/78.34 The set Q consists of the following terms: 130.72/78.34 130.72/78.34 new_primPlusNat1(Succ(x0)) 130.72/78.34 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.34 new_primMulNat0(x0) 130.72/78.34 new_primPlusNat1(Zero) 130.72/78.34 new_primPlusNat2(Zero) 130.72/78.34 new_primPlusNat3(Succ(x0)) 130.72/78.34 new_primMulNat7 130.72/78.34 new_primPlusNat8(Succ(x0), x1) 130.72/78.34 new_primMulNat3(x0) 130.72/78.34 new_primMulNat2(x0) 130.72/78.34 new_primPlusNat6(x0, Succ(x1)) 130.72/78.34 new_primPlusNat0(Succ(x0), Zero) 130.72/78.34 new_primPlusNat6(x0, Zero) 130.72/78.34 new_primPlusNat5(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.34 new_primMulNat4 130.72/78.34 new_primPlusNat4(Succ(x0)) 130.72/78.34 new_primPlusNat8(Zero, x0) 130.72/78.34 new_primPlusNat3(Zero) 130.72/78.34 new_primPlusNat7(x0, Zero) 130.72/78.34 new_primPlusNat5(Zero) 130.72/78.34 new_primMulNat5 130.72/78.34 new_primMulNat1(x0) 130.72/78.34 new_primPlusNat7(x0, Succ(x1)) 130.72/78.34 new_primPlusNat4(Zero) 130.72/78.34 new_primPlusNat2(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Zero) 130.72/78.34 130.72/78.34 We have to consider all minimal (P,Q,R)-chains. 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (417) UsableRulesProof (EQUIVALENT) 130.72/78.34 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (418) 130.72/78.34 Obligation: 130.72/78.34 Q DP problem: 130.72/78.34 The TRS P consists of the following rules: 130.72/78.34 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat4, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.34 130.72/78.34 The TRS R consists of the following rules: 130.72/78.34 130.72/78.34 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.34 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.34 new_primPlusNat2(Zero) -> Zero 130.72/78.34 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.34 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.34 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.34 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.34 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.34 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.34 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primMulNat2(zzz4739) -> Zero 130.72/78.34 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.34 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.34 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.34 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.34 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.34 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.34 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.34 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.34 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.34 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.34 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.34 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.34 130.72/78.34 The set Q consists of the following terms: 130.72/78.34 130.72/78.34 new_primPlusNat1(Succ(x0)) 130.72/78.34 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.34 new_primMulNat0(x0) 130.72/78.34 new_primPlusNat1(Zero) 130.72/78.34 new_primPlusNat2(Zero) 130.72/78.34 new_primPlusNat3(Succ(x0)) 130.72/78.34 new_primMulNat7 130.72/78.34 new_primPlusNat8(Succ(x0), x1) 130.72/78.34 new_primMulNat3(x0) 130.72/78.34 new_primMulNat2(x0) 130.72/78.34 new_primPlusNat6(x0, Succ(x1)) 130.72/78.34 new_primPlusNat0(Succ(x0), Zero) 130.72/78.34 new_primPlusNat6(x0, Zero) 130.72/78.34 new_primPlusNat5(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.34 new_primMulNat4 130.72/78.34 new_primPlusNat4(Succ(x0)) 130.72/78.34 new_primPlusNat8(Zero, x0) 130.72/78.34 new_primPlusNat3(Zero) 130.72/78.34 new_primPlusNat7(x0, Zero) 130.72/78.34 new_primPlusNat5(Zero) 130.72/78.34 new_primMulNat5 130.72/78.34 new_primMulNat1(x0) 130.72/78.34 new_primPlusNat7(x0, Succ(x1)) 130.72/78.34 new_primPlusNat4(Zero) 130.72/78.34 new_primPlusNat2(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Zero) 130.72/78.34 130.72/78.34 We have to consider all minimal (P,Q,R)-chains. 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (419) QReductionProof (EQUIVALENT) 130.72/78.34 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.72/78.34 130.72/78.34 new_primMulNat7 130.72/78.34 130.72/78.34 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (420) 130.72/78.34 Obligation: 130.72/78.34 Q DP problem: 130.72/78.34 The TRS P consists of the following rules: 130.72/78.34 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat4, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.34 130.72/78.34 The TRS R consists of the following rules: 130.72/78.34 130.72/78.34 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.34 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.34 new_primPlusNat2(Zero) -> Zero 130.72/78.34 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.34 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.34 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.34 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.34 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.34 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.34 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primMulNat2(zzz4739) -> Zero 130.72/78.34 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.34 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.34 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.34 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.34 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.34 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.34 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.34 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.34 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.34 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.34 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.34 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.34 130.72/78.34 The set Q consists of the following terms: 130.72/78.34 130.72/78.34 new_primPlusNat1(Succ(x0)) 130.72/78.34 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.34 new_primMulNat0(x0) 130.72/78.34 new_primPlusNat1(Zero) 130.72/78.34 new_primPlusNat2(Zero) 130.72/78.34 new_primPlusNat3(Succ(x0)) 130.72/78.34 new_primPlusNat8(Succ(x0), x1) 130.72/78.34 new_primMulNat3(x0) 130.72/78.34 new_primMulNat2(x0) 130.72/78.34 new_primPlusNat6(x0, Succ(x1)) 130.72/78.34 new_primPlusNat0(Succ(x0), Zero) 130.72/78.34 new_primPlusNat6(x0, Zero) 130.72/78.34 new_primPlusNat5(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.34 new_primMulNat4 130.72/78.34 new_primPlusNat4(Succ(x0)) 130.72/78.34 new_primPlusNat8(Zero, x0) 130.72/78.34 new_primPlusNat3(Zero) 130.72/78.34 new_primPlusNat7(x0, Zero) 130.72/78.34 new_primPlusNat5(Zero) 130.72/78.34 new_primMulNat5 130.72/78.34 new_primMulNat1(x0) 130.72/78.34 new_primPlusNat7(x0, Succ(x1)) 130.72/78.34 new_primPlusNat4(Zero) 130.72/78.34 new_primPlusNat2(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Zero) 130.72/78.34 130.72/78.34 We have to consider all minimal (P,Q,R)-chains. 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (421) TransformationProof (EQUIVALENT) 130.72/78.34 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat4, bb) at position [11] we obtained the following new rules [LPAR04]: 130.72/78.34 130.72/78.34 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb)) 130.72/78.34 130.72/78.34 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (422) 130.72/78.34 Obligation: 130.72/78.34 Q DP problem: 130.72/78.34 The TRS P consists of the following rules: 130.72/78.34 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 130.72/78.34 The TRS R consists of the following rules: 130.72/78.34 130.72/78.34 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.34 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.34 new_primPlusNat2(Zero) -> Zero 130.72/78.34 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.34 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.34 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.34 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.34 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.34 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.34 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primMulNat2(zzz4739) -> Zero 130.72/78.34 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.34 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.34 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.34 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.34 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.34 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.34 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.34 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.34 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.34 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.34 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.34 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.34 130.72/78.34 The set Q consists of the following terms: 130.72/78.34 130.72/78.34 new_primPlusNat1(Succ(x0)) 130.72/78.34 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.34 new_primMulNat0(x0) 130.72/78.34 new_primPlusNat1(Zero) 130.72/78.34 new_primPlusNat2(Zero) 130.72/78.34 new_primPlusNat3(Succ(x0)) 130.72/78.34 new_primPlusNat8(Succ(x0), x1) 130.72/78.34 new_primMulNat3(x0) 130.72/78.34 new_primMulNat2(x0) 130.72/78.34 new_primPlusNat6(x0, Succ(x1)) 130.72/78.34 new_primPlusNat0(Succ(x0), Zero) 130.72/78.34 new_primPlusNat6(x0, Zero) 130.72/78.34 new_primPlusNat5(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.34 new_primMulNat4 130.72/78.34 new_primPlusNat4(Succ(x0)) 130.72/78.34 new_primPlusNat8(Zero, x0) 130.72/78.34 new_primPlusNat3(Zero) 130.72/78.34 new_primPlusNat7(x0, Zero) 130.72/78.34 new_primPlusNat5(Zero) 130.72/78.34 new_primMulNat5 130.72/78.34 new_primMulNat1(x0) 130.72/78.34 new_primPlusNat7(x0, Succ(x1)) 130.72/78.34 new_primPlusNat4(Zero) 130.72/78.34 new_primPlusNat2(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Zero) 130.72/78.34 130.72/78.34 We have to consider all minimal (P,Q,R)-chains. 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (423) TransformationProof (EQUIVALENT) 130.72/78.34 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primMulNat5, bb) at position [10] we obtained the following new rules [LPAR04]: 130.72/78.34 130.72/78.34 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb)) 130.72/78.34 130.72/78.34 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (424) 130.72/78.34 Obligation: 130.72/78.34 Q DP problem: 130.72/78.34 The TRS P consists of the following rules: 130.72/78.34 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 130.72/78.34 The TRS R consists of the following rules: 130.72/78.34 130.72/78.34 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.34 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.34 new_primPlusNat2(Zero) -> Zero 130.72/78.34 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.34 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.34 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.34 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.34 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.34 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.34 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primMulNat2(zzz4739) -> Zero 130.72/78.34 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.34 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.34 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.34 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.34 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.34 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.34 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.34 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.34 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.34 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.34 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.34 new_primMulNat5 -> new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))) 130.72/78.34 130.72/78.34 The set Q consists of the following terms: 130.72/78.34 130.72/78.34 new_primPlusNat1(Succ(x0)) 130.72/78.34 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.34 new_primMulNat0(x0) 130.72/78.34 new_primPlusNat1(Zero) 130.72/78.34 new_primPlusNat2(Zero) 130.72/78.34 new_primPlusNat3(Succ(x0)) 130.72/78.34 new_primPlusNat8(Succ(x0), x1) 130.72/78.34 new_primMulNat3(x0) 130.72/78.34 new_primMulNat2(x0) 130.72/78.34 new_primPlusNat6(x0, Succ(x1)) 130.72/78.34 new_primPlusNat0(Succ(x0), Zero) 130.72/78.34 new_primPlusNat6(x0, Zero) 130.72/78.34 new_primPlusNat5(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.34 new_primMulNat4 130.72/78.34 new_primPlusNat4(Succ(x0)) 130.72/78.34 new_primPlusNat8(Zero, x0) 130.72/78.34 new_primPlusNat3(Zero) 130.72/78.34 new_primPlusNat7(x0, Zero) 130.72/78.34 new_primPlusNat5(Zero) 130.72/78.34 new_primMulNat5 130.72/78.34 new_primMulNat1(x0) 130.72/78.34 new_primPlusNat7(x0, Succ(x1)) 130.72/78.34 new_primPlusNat4(Zero) 130.72/78.34 new_primPlusNat2(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Zero) 130.72/78.34 130.72/78.34 We have to consider all minimal (P,Q,R)-chains. 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (425) UsableRulesProof (EQUIVALENT) 130.72/78.34 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (426) 130.72/78.34 Obligation: 130.72/78.34 Q DP problem: 130.72/78.34 The TRS P consists of the following rules: 130.72/78.34 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 130.72/78.34 The TRS R consists of the following rules: 130.72/78.34 130.72/78.34 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.34 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.34 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.34 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.34 new_primPlusNat2(Zero) -> Zero 130.72/78.34 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.34 new_primMulNat2(zzz4739) -> Zero 130.72/78.34 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.34 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.34 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.34 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.34 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.34 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.34 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.34 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.34 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.34 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.34 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.34 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.34 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.34 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.34 130.72/78.34 The set Q consists of the following terms: 130.72/78.34 130.72/78.34 new_primPlusNat1(Succ(x0)) 130.72/78.34 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.34 new_primMulNat0(x0) 130.72/78.34 new_primPlusNat1(Zero) 130.72/78.34 new_primPlusNat2(Zero) 130.72/78.34 new_primPlusNat3(Succ(x0)) 130.72/78.34 new_primPlusNat8(Succ(x0), x1) 130.72/78.34 new_primMulNat3(x0) 130.72/78.34 new_primMulNat2(x0) 130.72/78.34 new_primPlusNat6(x0, Succ(x1)) 130.72/78.34 new_primPlusNat0(Succ(x0), Zero) 130.72/78.34 new_primPlusNat6(x0, Zero) 130.72/78.34 new_primPlusNat5(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.34 new_primMulNat4 130.72/78.34 new_primPlusNat4(Succ(x0)) 130.72/78.34 new_primPlusNat8(Zero, x0) 130.72/78.34 new_primPlusNat3(Zero) 130.72/78.34 new_primPlusNat7(x0, Zero) 130.72/78.34 new_primPlusNat5(Zero) 130.72/78.34 new_primMulNat5 130.72/78.34 new_primMulNat1(x0) 130.72/78.34 new_primPlusNat7(x0, Succ(x1)) 130.72/78.34 new_primPlusNat4(Zero) 130.72/78.34 new_primPlusNat2(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Zero) 130.72/78.34 130.72/78.34 We have to consider all minimal (P,Q,R)-chains. 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (427) QReductionProof (EQUIVALENT) 130.72/78.34 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.72/78.34 130.72/78.34 new_primMulNat5 130.72/78.34 130.72/78.34 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (428) 130.72/78.34 Obligation: 130.72/78.34 Q DP problem: 130.72/78.34 The TRS P consists of the following rules: 130.72/78.34 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 130.72/78.34 The TRS R consists of the following rules: 130.72/78.34 130.72/78.34 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.34 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.34 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.34 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.34 new_primPlusNat2(Zero) -> Zero 130.72/78.34 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.34 new_primMulNat2(zzz4739) -> Zero 130.72/78.34 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.34 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.34 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.34 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.34 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.34 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.34 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.34 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.34 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.34 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.34 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.34 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.34 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.34 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.34 130.72/78.34 The set Q consists of the following terms: 130.72/78.34 130.72/78.34 new_primPlusNat1(Succ(x0)) 130.72/78.34 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.34 new_primMulNat0(x0) 130.72/78.34 new_primPlusNat1(Zero) 130.72/78.34 new_primPlusNat2(Zero) 130.72/78.34 new_primPlusNat3(Succ(x0)) 130.72/78.34 new_primPlusNat8(Succ(x0), x1) 130.72/78.34 new_primMulNat3(x0) 130.72/78.34 new_primMulNat2(x0) 130.72/78.34 new_primPlusNat6(x0, Succ(x1)) 130.72/78.34 new_primPlusNat0(Succ(x0), Zero) 130.72/78.34 new_primPlusNat6(x0, Zero) 130.72/78.34 new_primPlusNat5(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.34 new_primMulNat4 130.72/78.34 new_primPlusNat4(Succ(x0)) 130.72/78.34 new_primPlusNat8(Zero, x0) 130.72/78.34 new_primPlusNat3(Zero) 130.72/78.34 new_primPlusNat7(x0, Zero) 130.72/78.34 new_primPlusNat5(Zero) 130.72/78.34 new_primMulNat1(x0) 130.72/78.34 new_primPlusNat7(x0, Succ(x1)) 130.72/78.34 new_primPlusNat4(Zero) 130.72/78.34 new_primPlusNat2(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Zero) 130.72/78.34 130.72/78.34 We have to consider all minimal (P,Q,R)-chains. 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (429) TransformationProof (EQUIVALENT) 130.72/78.34 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) at position [12] we obtained the following new rules [LPAR04]: 130.72/78.34 130.72/78.34 (new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h),new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h)) 130.72/78.34 130.72/78.34 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (430) 130.72/78.34 Obligation: 130.72/78.34 Q DP problem: 130.72/78.34 The TRS P consists of the following rules: 130.72/78.34 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.34 130.72/78.34 The TRS R consists of the following rules: 130.72/78.34 130.72/78.34 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.34 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.34 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.34 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.34 new_primPlusNat2(Zero) -> Zero 130.72/78.34 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.34 new_primMulNat2(zzz4739) -> Zero 130.72/78.34 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.34 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.34 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.34 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.34 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.34 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.34 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.34 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.34 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.34 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.34 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.34 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.34 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.34 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.34 130.72/78.34 The set Q consists of the following terms: 130.72/78.34 130.72/78.34 new_primPlusNat1(Succ(x0)) 130.72/78.34 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.34 new_primMulNat0(x0) 130.72/78.34 new_primPlusNat1(Zero) 130.72/78.34 new_primPlusNat2(Zero) 130.72/78.34 new_primPlusNat3(Succ(x0)) 130.72/78.34 new_primPlusNat8(Succ(x0), x1) 130.72/78.34 new_primMulNat3(x0) 130.72/78.34 new_primMulNat2(x0) 130.72/78.34 new_primPlusNat6(x0, Succ(x1)) 130.72/78.34 new_primPlusNat0(Succ(x0), Zero) 130.72/78.34 new_primPlusNat6(x0, Zero) 130.72/78.34 new_primPlusNat5(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.34 new_primMulNat4 130.72/78.34 new_primPlusNat4(Succ(x0)) 130.72/78.34 new_primPlusNat8(Zero, x0) 130.72/78.34 new_primPlusNat3(Zero) 130.72/78.34 new_primPlusNat7(x0, Zero) 130.72/78.34 new_primPlusNat5(Zero) 130.72/78.34 new_primMulNat1(x0) 130.72/78.34 new_primPlusNat7(x0, Succ(x1)) 130.72/78.34 new_primPlusNat4(Zero) 130.72/78.34 new_primPlusNat2(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Zero) 130.72/78.34 130.72/78.34 We have to consider all minimal (P,Q,R)-chains. 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (431) TransformationProof (EQUIVALENT) 130.72/78.34 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primMulNat3(zzz4708), h) at position [12] we obtained the following new rules [LPAR04]: 130.72/78.34 130.72/78.34 (new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h),new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h)) 130.72/78.34 130.72/78.34 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (432) 130.72/78.34 Obligation: 130.72/78.34 Q DP problem: 130.72/78.34 The TRS P consists of the following rules: 130.72/78.34 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.34 130.72/78.34 The TRS R consists of the following rules: 130.72/78.34 130.72/78.34 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.34 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.34 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.34 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.34 new_primPlusNat2(Zero) -> Zero 130.72/78.34 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.34 new_primMulNat2(zzz4739) -> Zero 130.72/78.34 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.34 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.34 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.34 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.34 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.34 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.34 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.34 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.34 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.34 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.34 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.34 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.34 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.34 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.34 130.72/78.34 The set Q consists of the following terms: 130.72/78.34 130.72/78.34 new_primPlusNat1(Succ(x0)) 130.72/78.34 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.34 new_primMulNat0(x0) 130.72/78.34 new_primPlusNat1(Zero) 130.72/78.34 new_primPlusNat2(Zero) 130.72/78.34 new_primPlusNat3(Succ(x0)) 130.72/78.34 new_primPlusNat8(Succ(x0), x1) 130.72/78.34 new_primMulNat3(x0) 130.72/78.34 new_primMulNat2(x0) 130.72/78.34 new_primPlusNat6(x0, Succ(x1)) 130.72/78.34 new_primPlusNat0(Succ(x0), Zero) 130.72/78.34 new_primPlusNat6(x0, Zero) 130.72/78.34 new_primPlusNat5(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.34 new_primMulNat4 130.72/78.34 new_primPlusNat4(Succ(x0)) 130.72/78.34 new_primPlusNat8(Zero, x0) 130.72/78.34 new_primPlusNat3(Zero) 130.72/78.34 new_primPlusNat7(x0, Zero) 130.72/78.34 new_primPlusNat5(Zero) 130.72/78.34 new_primMulNat1(x0) 130.72/78.34 new_primPlusNat7(x0, Succ(x1)) 130.72/78.34 new_primPlusNat4(Zero) 130.72/78.34 new_primPlusNat2(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Zero) 130.72/78.34 130.72/78.34 We have to consider all minimal (P,Q,R)-chains. 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (433) UsableRulesProof (EQUIVALENT) 130.72/78.34 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (434) 130.72/78.34 Obligation: 130.72/78.34 Q DP problem: 130.72/78.34 The TRS P consists of the following rules: 130.72/78.34 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.34 130.72/78.34 The TRS R consists of the following rules: 130.72/78.34 130.72/78.34 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.34 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.34 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.34 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primMulNat2(zzz4739) -> Zero 130.72/78.34 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.34 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.34 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.34 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.34 new_primPlusNat2(Zero) -> Zero 130.72/78.34 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.34 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.34 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.34 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.34 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.34 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.34 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.34 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.34 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.34 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.34 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.34 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.34 130.72/78.34 The set Q consists of the following terms: 130.72/78.34 130.72/78.34 new_primPlusNat1(Succ(x0)) 130.72/78.34 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.34 new_primMulNat0(x0) 130.72/78.34 new_primPlusNat1(Zero) 130.72/78.34 new_primPlusNat2(Zero) 130.72/78.34 new_primPlusNat3(Succ(x0)) 130.72/78.34 new_primPlusNat8(Succ(x0), x1) 130.72/78.34 new_primMulNat3(x0) 130.72/78.34 new_primMulNat2(x0) 130.72/78.34 new_primPlusNat6(x0, Succ(x1)) 130.72/78.34 new_primPlusNat0(Succ(x0), Zero) 130.72/78.34 new_primPlusNat6(x0, Zero) 130.72/78.34 new_primPlusNat5(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.34 new_primMulNat4 130.72/78.34 new_primPlusNat4(Succ(x0)) 130.72/78.34 new_primPlusNat8(Zero, x0) 130.72/78.34 new_primPlusNat3(Zero) 130.72/78.34 new_primPlusNat7(x0, Zero) 130.72/78.34 new_primPlusNat5(Zero) 130.72/78.34 new_primMulNat1(x0) 130.72/78.34 new_primPlusNat7(x0, Succ(x1)) 130.72/78.34 new_primPlusNat4(Zero) 130.72/78.34 new_primPlusNat2(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Zero) 130.72/78.34 130.72/78.34 We have to consider all minimal (P,Q,R)-chains. 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (435) QReductionProof (EQUIVALENT) 130.72/78.34 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.72/78.34 130.72/78.34 new_primMulNat3(x0) 130.72/78.34 130.72/78.34 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (436) 130.72/78.34 Obligation: 130.72/78.34 Q DP problem: 130.72/78.34 The TRS P consists of the following rules: 130.72/78.34 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.34 130.72/78.34 The TRS R consists of the following rules: 130.72/78.34 130.72/78.34 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.34 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.34 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.34 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primMulNat2(zzz4739) -> Zero 130.72/78.34 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.34 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.34 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.34 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.34 new_primPlusNat2(Zero) -> Zero 130.72/78.34 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.34 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.34 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.34 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.34 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.34 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.34 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.34 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.34 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.34 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.34 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.34 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.34 130.72/78.34 The set Q consists of the following terms: 130.72/78.34 130.72/78.34 new_primPlusNat1(Succ(x0)) 130.72/78.34 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.34 new_primMulNat0(x0) 130.72/78.34 new_primPlusNat1(Zero) 130.72/78.34 new_primPlusNat2(Zero) 130.72/78.34 new_primPlusNat3(Succ(x0)) 130.72/78.34 new_primPlusNat8(Succ(x0), x1) 130.72/78.34 new_primMulNat2(x0) 130.72/78.34 new_primPlusNat6(x0, Succ(x1)) 130.72/78.34 new_primPlusNat0(Succ(x0), Zero) 130.72/78.34 new_primPlusNat6(x0, Zero) 130.72/78.34 new_primPlusNat5(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.34 new_primMulNat4 130.72/78.34 new_primPlusNat4(Succ(x0)) 130.72/78.34 new_primPlusNat8(Zero, x0) 130.72/78.34 new_primPlusNat3(Zero) 130.72/78.34 new_primPlusNat7(x0, Zero) 130.72/78.34 new_primPlusNat5(Zero) 130.72/78.34 new_primMulNat1(x0) 130.72/78.34 new_primPlusNat7(x0, Succ(x1)) 130.72/78.34 new_primPlusNat4(Zero) 130.72/78.34 new_primPlusNat2(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Zero) 130.72/78.34 130.72/78.34 We have to consider all minimal (P,Q,R)-chains. 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (437) TransformationProof (EQUIVALENT) 130.72/78.34 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), bb) at position [10,0] we obtained the following new rules [LPAR04]: 130.72/78.34 130.72/78.34 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb)) 130.72/78.34 130.72/78.34 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (438) 130.72/78.34 Obligation: 130.72/78.34 Q DP problem: 130.72/78.34 The TRS P consists of the following rules: 130.72/78.34 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.34 130.72/78.34 The TRS R consists of the following rules: 130.72/78.34 130.72/78.34 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.34 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.34 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.34 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primMulNat2(zzz4739) -> Zero 130.72/78.34 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.34 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.34 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.34 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.34 new_primPlusNat2(Zero) -> Zero 130.72/78.34 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.34 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.34 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.34 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.34 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.34 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.34 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.34 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.34 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.34 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.34 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.34 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.34 130.72/78.34 The set Q consists of the following terms: 130.72/78.34 130.72/78.34 new_primPlusNat1(Succ(x0)) 130.72/78.34 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.34 new_primMulNat0(x0) 130.72/78.34 new_primPlusNat1(Zero) 130.72/78.34 new_primPlusNat2(Zero) 130.72/78.34 new_primPlusNat3(Succ(x0)) 130.72/78.34 new_primPlusNat8(Succ(x0), x1) 130.72/78.34 new_primMulNat2(x0) 130.72/78.34 new_primPlusNat6(x0, Succ(x1)) 130.72/78.34 new_primPlusNat0(Succ(x0), Zero) 130.72/78.34 new_primPlusNat6(x0, Zero) 130.72/78.34 new_primPlusNat5(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.34 new_primMulNat4 130.72/78.34 new_primPlusNat4(Succ(x0)) 130.72/78.34 new_primPlusNat8(Zero, x0) 130.72/78.34 new_primPlusNat3(Zero) 130.72/78.34 new_primPlusNat7(x0, Zero) 130.72/78.34 new_primPlusNat5(Zero) 130.72/78.34 new_primMulNat1(x0) 130.72/78.34 new_primPlusNat7(x0, Succ(x1)) 130.72/78.34 new_primPlusNat4(Zero) 130.72/78.34 new_primPlusNat2(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Zero) 130.72/78.34 130.72/78.34 We have to consider all minimal (P,Q,R)-chains. 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (439) TransformationProof (EQUIVALENT) 130.72/78.34 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primMulNat4), bb) at position [10,0] we obtained the following new rules [LPAR04]: 130.72/78.34 130.72/78.34 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb)) 130.72/78.34 130.72/78.34 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (440) 130.72/78.34 Obligation: 130.72/78.34 Q DP problem: 130.72/78.34 The TRS P consists of the following rules: 130.72/78.34 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.34 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.34 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.34 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.34 130.72/78.34 The TRS R consists of the following rules: 130.72/78.34 130.72/78.34 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.34 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.34 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.34 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.34 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.34 new_primMulNat2(zzz4739) -> Zero 130.72/78.34 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.34 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.34 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.34 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.34 new_primPlusNat2(Zero) -> Zero 130.72/78.34 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.34 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.34 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.34 new_primMulNat4 -> new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))) 130.72/78.34 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.34 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.34 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.34 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.34 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.34 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.34 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.34 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.34 130.72/78.34 The set Q consists of the following terms: 130.72/78.34 130.72/78.34 new_primPlusNat1(Succ(x0)) 130.72/78.34 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.34 new_primMulNat0(x0) 130.72/78.34 new_primPlusNat1(Zero) 130.72/78.34 new_primPlusNat2(Zero) 130.72/78.34 new_primPlusNat3(Succ(x0)) 130.72/78.34 new_primPlusNat8(Succ(x0), x1) 130.72/78.34 new_primMulNat2(x0) 130.72/78.34 new_primPlusNat6(x0, Succ(x1)) 130.72/78.34 new_primPlusNat0(Succ(x0), Zero) 130.72/78.34 new_primPlusNat6(x0, Zero) 130.72/78.34 new_primPlusNat5(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.34 new_primMulNat4 130.72/78.34 new_primPlusNat4(Succ(x0)) 130.72/78.34 new_primPlusNat8(Zero, x0) 130.72/78.34 new_primPlusNat3(Zero) 130.72/78.34 new_primPlusNat7(x0, Zero) 130.72/78.34 new_primPlusNat5(Zero) 130.72/78.34 new_primMulNat1(x0) 130.72/78.34 new_primPlusNat7(x0, Succ(x1)) 130.72/78.34 new_primPlusNat4(Zero) 130.72/78.34 new_primPlusNat2(Succ(x0)) 130.72/78.34 new_primPlusNat0(Zero, Zero) 130.72/78.34 130.72/78.34 We have to consider all minimal (P,Q,R)-chains. 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (441) UsableRulesProof (EQUIVALENT) 130.72/78.34 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.72/78.34 ---------------------------------------- 130.72/78.34 130.72/78.34 (442) 130.72/78.34 Obligation: 130.72/78.34 Q DP problem: 130.72/78.34 The TRS P consists of the following rules: 130.72/78.34 130.72/78.34 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.35 130.72/78.35 The TRS R consists of the following rules: 130.72/78.35 130.72/78.35 new_primMulNat2(zzz4739) -> Zero 130.72/78.35 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.35 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.35 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.35 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.35 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.35 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.35 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.35 new_primPlusNat2(Zero) -> Zero 130.72/78.35 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.35 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.35 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.35 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.35 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.35 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.35 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.35 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.35 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.35 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.35 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.35 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.35 130.72/78.35 The set Q consists of the following terms: 130.72/78.35 130.72/78.35 new_primPlusNat1(Succ(x0)) 130.72/78.35 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.35 new_primMulNat0(x0) 130.72/78.35 new_primPlusNat1(Zero) 130.72/78.35 new_primPlusNat2(Zero) 130.72/78.35 new_primPlusNat3(Succ(x0)) 130.72/78.35 new_primPlusNat8(Succ(x0), x1) 130.72/78.35 new_primMulNat2(x0) 130.72/78.35 new_primPlusNat6(x0, Succ(x1)) 130.72/78.35 new_primPlusNat0(Succ(x0), Zero) 130.72/78.35 new_primPlusNat6(x0, Zero) 130.72/78.35 new_primPlusNat5(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.35 new_primMulNat4 130.72/78.35 new_primPlusNat4(Succ(x0)) 130.72/78.35 new_primPlusNat8(Zero, x0) 130.72/78.35 new_primPlusNat3(Zero) 130.72/78.35 new_primPlusNat7(x0, Zero) 130.72/78.35 new_primPlusNat5(Zero) 130.72/78.35 new_primMulNat1(x0) 130.72/78.35 new_primPlusNat7(x0, Succ(x1)) 130.72/78.35 new_primPlusNat4(Zero) 130.72/78.35 new_primPlusNat2(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Zero) 130.72/78.35 130.72/78.35 We have to consider all minimal (P,Q,R)-chains. 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (443) QReductionProof (EQUIVALENT) 130.72/78.35 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.72/78.35 130.72/78.35 new_primMulNat4 130.72/78.35 130.72/78.35 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (444) 130.72/78.35 Obligation: 130.72/78.35 Q DP problem: 130.72/78.35 The TRS P consists of the following rules: 130.72/78.35 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.35 130.72/78.35 The TRS R consists of the following rules: 130.72/78.35 130.72/78.35 new_primMulNat2(zzz4739) -> Zero 130.72/78.35 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.35 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.35 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.35 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.35 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.35 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.35 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.35 new_primPlusNat2(Zero) -> Zero 130.72/78.35 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.35 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.35 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.35 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.35 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.35 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.35 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.35 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.35 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.35 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.35 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.35 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.35 130.72/78.35 The set Q consists of the following terms: 130.72/78.35 130.72/78.35 new_primPlusNat1(Succ(x0)) 130.72/78.35 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.35 new_primMulNat0(x0) 130.72/78.35 new_primPlusNat1(Zero) 130.72/78.35 new_primPlusNat2(Zero) 130.72/78.35 new_primPlusNat3(Succ(x0)) 130.72/78.35 new_primPlusNat8(Succ(x0), x1) 130.72/78.35 new_primMulNat2(x0) 130.72/78.35 new_primPlusNat6(x0, Succ(x1)) 130.72/78.35 new_primPlusNat0(Succ(x0), Zero) 130.72/78.35 new_primPlusNat6(x0, Zero) 130.72/78.35 new_primPlusNat5(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.35 new_primPlusNat4(Succ(x0)) 130.72/78.35 new_primPlusNat8(Zero, x0) 130.72/78.35 new_primPlusNat3(Zero) 130.72/78.35 new_primPlusNat7(x0, Zero) 130.72/78.35 new_primPlusNat5(Zero) 130.72/78.35 new_primMulNat1(x0) 130.72/78.35 new_primPlusNat7(x0, Succ(x1)) 130.72/78.35 new_primPlusNat4(Zero) 130.72/78.35 new_primPlusNat2(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Zero) 130.72/78.35 130.72/78.35 We have to consider all minimal (P,Q,R)-chains. 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (445) TransformationProof (EQUIVALENT) 130.72/78.35 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) at position [10,0] we obtained the following new rules [LPAR04]: 130.72/78.35 130.72/78.35 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb)) 130.72/78.35 130.72/78.35 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (446) 130.72/78.35 Obligation: 130.72/78.35 Q DP problem: 130.72/78.35 The TRS P consists of the following rules: 130.72/78.35 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 130.72/78.35 The TRS R consists of the following rules: 130.72/78.35 130.72/78.35 new_primMulNat2(zzz4739) -> Zero 130.72/78.35 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.35 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.35 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.35 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.35 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.35 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.35 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.35 new_primPlusNat2(Zero) -> Zero 130.72/78.35 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.35 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.35 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.35 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.35 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.35 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.35 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.35 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.35 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.35 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.35 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.35 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.35 130.72/78.35 The set Q consists of the following terms: 130.72/78.35 130.72/78.35 new_primPlusNat1(Succ(x0)) 130.72/78.35 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.35 new_primMulNat0(x0) 130.72/78.35 new_primPlusNat1(Zero) 130.72/78.35 new_primPlusNat2(Zero) 130.72/78.35 new_primPlusNat3(Succ(x0)) 130.72/78.35 new_primPlusNat8(Succ(x0), x1) 130.72/78.35 new_primMulNat2(x0) 130.72/78.35 new_primPlusNat6(x0, Succ(x1)) 130.72/78.35 new_primPlusNat0(Succ(x0), Zero) 130.72/78.35 new_primPlusNat6(x0, Zero) 130.72/78.35 new_primPlusNat5(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.35 new_primPlusNat4(Succ(x0)) 130.72/78.35 new_primPlusNat8(Zero, x0) 130.72/78.35 new_primPlusNat3(Zero) 130.72/78.35 new_primPlusNat7(x0, Zero) 130.72/78.35 new_primPlusNat5(Zero) 130.72/78.35 new_primMulNat1(x0) 130.72/78.35 new_primPlusNat7(x0, Succ(x1)) 130.72/78.35 new_primPlusNat4(Zero) 130.72/78.35 new_primPlusNat2(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Zero) 130.72/78.35 130.72/78.35 We have to consider all minimal (P,Q,R)-chains. 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (447) TransformationProof (EQUIVALENT) 130.72/78.35 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))), zzz34200000, bb) at position [11,0] we obtained the following new rules [LPAR04]: 130.72/78.35 130.72/78.35 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb)) 130.72/78.35 130.72/78.35 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (448) 130.72/78.35 Obligation: 130.72/78.35 Q DP problem: 130.72/78.35 The TRS P consists of the following rules: 130.72/78.35 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.35 130.72/78.35 The TRS R consists of the following rules: 130.72/78.35 130.72/78.35 new_primMulNat2(zzz4739) -> Zero 130.72/78.35 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.35 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.35 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.35 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.35 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.35 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.35 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.35 new_primPlusNat2(Zero) -> Zero 130.72/78.35 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.35 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.35 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.35 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.35 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.35 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.35 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.35 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.35 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.35 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.35 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.35 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.35 130.72/78.35 The set Q consists of the following terms: 130.72/78.35 130.72/78.35 new_primPlusNat1(Succ(x0)) 130.72/78.35 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.35 new_primMulNat0(x0) 130.72/78.35 new_primPlusNat1(Zero) 130.72/78.35 new_primPlusNat2(Zero) 130.72/78.35 new_primPlusNat3(Succ(x0)) 130.72/78.35 new_primPlusNat8(Succ(x0), x1) 130.72/78.35 new_primMulNat2(x0) 130.72/78.35 new_primPlusNat6(x0, Succ(x1)) 130.72/78.35 new_primPlusNat0(Succ(x0), Zero) 130.72/78.35 new_primPlusNat6(x0, Zero) 130.72/78.35 new_primPlusNat5(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.35 new_primPlusNat4(Succ(x0)) 130.72/78.35 new_primPlusNat8(Zero, x0) 130.72/78.35 new_primPlusNat3(Zero) 130.72/78.35 new_primPlusNat7(x0, Zero) 130.72/78.35 new_primPlusNat5(Zero) 130.72/78.35 new_primMulNat1(x0) 130.72/78.35 new_primPlusNat7(x0, Succ(x1)) 130.72/78.35 new_primPlusNat4(Zero) 130.72/78.35 new_primPlusNat2(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Zero) 130.72/78.35 130.72/78.35 We have to consider all minimal (P,Q,R)-chains. 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (449) TransformationProof (EQUIVALENT) 130.72/78.35 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) at position [11,0] we obtained the following new rules [LPAR04]: 130.72/78.35 130.72/78.35 (new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc)) 130.72/78.35 130.72/78.35 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (450) 130.72/78.35 Obligation: 130.72/78.35 Q DP problem: 130.72/78.35 The TRS P consists of the following rules: 130.72/78.35 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 130.72/78.35 The TRS R consists of the following rules: 130.72/78.35 130.72/78.35 new_primMulNat2(zzz4739) -> Zero 130.72/78.35 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.35 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.35 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.35 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.35 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.35 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.35 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.35 new_primPlusNat2(Zero) -> Zero 130.72/78.35 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.35 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.35 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.35 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.35 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.35 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.35 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.35 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.35 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.35 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.35 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.35 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.35 130.72/78.35 The set Q consists of the following terms: 130.72/78.35 130.72/78.35 new_primPlusNat1(Succ(x0)) 130.72/78.35 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.35 new_primMulNat0(x0) 130.72/78.35 new_primPlusNat1(Zero) 130.72/78.35 new_primPlusNat2(Zero) 130.72/78.35 new_primPlusNat3(Succ(x0)) 130.72/78.35 new_primPlusNat8(Succ(x0), x1) 130.72/78.35 new_primMulNat2(x0) 130.72/78.35 new_primPlusNat6(x0, Succ(x1)) 130.72/78.35 new_primPlusNat0(Succ(x0), Zero) 130.72/78.35 new_primPlusNat6(x0, Zero) 130.72/78.35 new_primPlusNat5(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.35 new_primPlusNat4(Succ(x0)) 130.72/78.35 new_primPlusNat8(Zero, x0) 130.72/78.35 new_primPlusNat3(Zero) 130.72/78.35 new_primPlusNat7(x0, Zero) 130.72/78.35 new_primPlusNat5(Zero) 130.72/78.35 new_primMulNat1(x0) 130.72/78.35 new_primPlusNat7(x0, Succ(x1)) 130.72/78.35 new_primPlusNat4(Zero) 130.72/78.35 new_primPlusNat2(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Zero) 130.72/78.35 130.72/78.35 We have to consider all minimal (P,Q,R)-chains. 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (451) TransformationProof (EQUIVALENT) 130.72/78.35 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) at position [11,0] we obtained the following new rules [LPAR04]: 130.72/78.35 130.72/78.35 (new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc)) 130.72/78.35 130.72/78.35 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (452) 130.72/78.35 Obligation: 130.72/78.35 Q DP problem: 130.72/78.35 The TRS P consists of the following rules: 130.72/78.35 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 130.72/78.35 The TRS R consists of the following rules: 130.72/78.35 130.72/78.35 new_primMulNat2(zzz4739) -> Zero 130.72/78.35 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.35 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.35 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.35 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.35 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.35 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.35 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.35 new_primPlusNat2(Zero) -> Zero 130.72/78.35 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.35 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.35 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.35 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.35 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.35 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.35 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.35 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.35 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.35 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.35 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.35 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.35 130.72/78.35 The set Q consists of the following terms: 130.72/78.35 130.72/78.35 new_primPlusNat1(Succ(x0)) 130.72/78.35 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.35 new_primMulNat0(x0) 130.72/78.35 new_primPlusNat1(Zero) 130.72/78.35 new_primPlusNat2(Zero) 130.72/78.35 new_primPlusNat3(Succ(x0)) 130.72/78.35 new_primPlusNat8(Succ(x0), x1) 130.72/78.35 new_primMulNat2(x0) 130.72/78.35 new_primPlusNat6(x0, Succ(x1)) 130.72/78.35 new_primPlusNat0(Succ(x0), Zero) 130.72/78.35 new_primPlusNat6(x0, Zero) 130.72/78.35 new_primPlusNat5(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.35 new_primPlusNat4(Succ(x0)) 130.72/78.35 new_primPlusNat8(Zero, x0) 130.72/78.35 new_primPlusNat3(Zero) 130.72/78.35 new_primPlusNat7(x0, Zero) 130.72/78.35 new_primPlusNat5(Zero) 130.72/78.35 new_primMulNat1(x0) 130.72/78.35 new_primPlusNat7(x0, Succ(x1)) 130.72/78.35 new_primPlusNat4(Zero) 130.72/78.35 new_primPlusNat2(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Zero) 130.72/78.35 130.72/78.35 We have to consider all minimal (P,Q,R)-chains. 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (453) TransformationProof (EQUIVALENT) 130.72/78.35 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primMulNat0(zzz3882), Succ(zzz3882)), bc) at position [11,0] we obtained the following new rules [LPAR04]: 130.72/78.35 130.72/78.35 (new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc)) 130.72/78.35 130.72/78.35 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (454) 130.72/78.35 Obligation: 130.72/78.35 Q DP problem: 130.72/78.35 The TRS P consists of the following rules: 130.72/78.35 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 130.72/78.35 The TRS R consists of the following rules: 130.72/78.35 130.72/78.35 new_primMulNat2(zzz4739) -> Zero 130.72/78.35 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.35 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.35 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.35 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.35 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.35 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.35 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.35 new_primPlusNat2(Zero) -> Zero 130.72/78.35 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.35 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.35 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.35 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.35 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.35 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.35 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.35 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.35 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.35 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.35 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.35 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.35 130.72/78.35 The set Q consists of the following terms: 130.72/78.35 130.72/78.35 new_primPlusNat1(Succ(x0)) 130.72/78.35 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.35 new_primMulNat0(x0) 130.72/78.35 new_primPlusNat1(Zero) 130.72/78.35 new_primPlusNat2(Zero) 130.72/78.35 new_primPlusNat3(Succ(x0)) 130.72/78.35 new_primPlusNat8(Succ(x0), x1) 130.72/78.35 new_primMulNat2(x0) 130.72/78.35 new_primPlusNat6(x0, Succ(x1)) 130.72/78.35 new_primPlusNat0(Succ(x0), Zero) 130.72/78.35 new_primPlusNat6(x0, Zero) 130.72/78.35 new_primPlusNat5(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.35 new_primPlusNat4(Succ(x0)) 130.72/78.35 new_primPlusNat8(Zero, x0) 130.72/78.35 new_primPlusNat3(Zero) 130.72/78.35 new_primPlusNat7(x0, Zero) 130.72/78.35 new_primPlusNat5(Zero) 130.72/78.35 new_primMulNat1(x0) 130.72/78.35 new_primPlusNat7(x0, Succ(x1)) 130.72/78.35 new_primPlusNat4(Zero) 130.72/78.35 new_primPlusNat2(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Zero) 130.72/78.35 130.72/78.35 We have to consider all minimal (P,Q,R)-chains. 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (455) TransformationProof (EQUIVALENT) 130.72/78.35 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.35 130.72/78.35 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb)) 130.72/78.35 130.72/78.35 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (456) 130.72/78.35 Obligation: 130.72/78.35 Q DP problem: 130.72/78.35 The TRS P consists of the following rules: 130.72/78.35 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.35 130.72/78.35 The TRS R consists of the following rules: 130.72/78.35 130.72/78.35 new_primMulNat2(zzz4739) -> Zero 130.72/78.35 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.35 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.35 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.35 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.35 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.35 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.35 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.35 new_primPlusNat2(Zero) -> Zero 130.72/78.35 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.35 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.35 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.35 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.35 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.35 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.35 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.35 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.35 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.35 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.35 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.35 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.35 130.72/78.35 The set Q consists of the following terms: 130.72/78.35 130.72/78.35 new_primPlusNat1(Succ(x0)) 130.72/78.35 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.35 new_primMulNat0(x0) 130.72/78.35 new_primPlusNat1(Zero) 130.72/78.35 new_primPlusNat2(Zero) 130.72/78.35 new_primPlusNat3(Succ(x0)) 130.72/78.35 new_primPlusNat8(Succ(x0), x1) 130.72/78.35 new_primMulNat2(x0) 130.72/78.35 new_primPlusNat6(x0, Succ(x1)) 130.72/78.35 new_primPlusNat0(Succ(x0), Zero) 130.72/78.35 new_primPlusNat6(x0, Zero) 130.72/78.35 new_primPlusNat5(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.35 new_primPlusNat4(Succ(x0)) 130.72/78.35 new_primPlusNat8(Zero, x0) 130.72/78.35 new_primPlusNat3(Zero) 130.72/78.35 new_primPlusNat7(x0, Zero) 130.72/78.35 new_primPlusNat5(Zero) 130.72/78.35 new_primMulNat1(x0) 130.72/78.35 new_primPlusNat7(x0, Succ(x1)) 130.72/78.35 new_primPlusNat4(Zero) 130.72/78.35 new_primPlusNat2(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Zero) 130.72/78.35 130.72/78.35 We have to consider all minimal (P,Q,R)-chains. 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (457) TransformationProof (EQUIVALENT) 130.72/78.35 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Zero))))), bb) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.35 130.72/78.35 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Zero))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Zero))))), bb)) 130.72/78.35 130.72/78.35 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (458) 130.72/78.35 Obligation: 130.72/78.35 Q DP problem: 130.72/78.35 The TRS P consists of the following rules: 130.72/78.35 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Zero))))), bb) 130.72/78.35 130.72/78.35 The TRS R consists of the following rules: 130.72/78.35 130.72/78.35 new_primMulNat2(zzz4739) -> Zero 130.72/78.35 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.35 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.35 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.35 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.35 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.35 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.35 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.35 new_primPlusNat2(Zero) -> Zero 130.72/78.35 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.35 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.35 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.35 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.35 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.35 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.35 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.35 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.35 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.35 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.35 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.35 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.35 130.72/78.35 The set Q consists of the following terms: 130.72/78.35 130.72/78.35 new_primPlusNat1(Succ(x0)) 130.72/78.35 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.35 new_primMulNat0(x0) 130.72/78.35 new_primPlusNat1(Zero) 130.72/78.35 new_primPlusNat2(Zero) 130.72/78.35 new_primPlusNat3(Succ(x0)) 130.72/78.35 new_primPlusNat8(Succ(x0), x1) 130.72/78.35 new_primMulNat2(x0) 130.72/78.35 new_primPlusNat6(x0, Succ(x1)) 130.72/78.35 new_primPlusNat0(Succ(x0), Zero) 130.72/78.35 new_primPlusNat6(x0, Zero) 130.72/78.35 new_primPlusNat5(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.35 new_primPlusNat4(Succ(x0)) 130.72/78.35 new_primPlusNat8(Zero, x0) 130.72/78.35 new_primPlusNat3(Zero) 130.72/78.35 new_primPlusNat7(x0, Zero) 130.72/78.35 new_primPlusNat5(Zero) 130.72/78.35 new_primMulNat1(x0) 130.72/78.35 new_primPlusNat7(x0, Succ(x1)) 130.72/78.35 new_primPlusNat4(Zero) 130.72/78.35 new_primPlusNat2(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Zero) 130.72/78.35 130.72/78.35 We have to consider all minimal (P,Q,R)-chains. 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (459) TransformationProof (EQUIVALENT) 130.72/78.35 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.35 130.72/78.35 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb)) 130.72/78.35 130.72/78.35 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (460) 130.72/78.35 Obligation: 130.72/78.35 Q DP problem: 130.72/78.35 The TRS P consists of the following rules: 130.72/78.35 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 130.72/78.35 The TRS R consists of the following rules: 130.72/78.35 130.72/78.35 new_primMulNat2(zzz4739) -> Zero 130.72/78.35 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.35 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.35 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.35 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.35 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.35 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.35 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.35 new_primPlusNat2(Zero) -> Zero 130.72/78.35 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.35 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.35 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.35 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.35 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.35 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.35 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.35 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.35 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.35 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.35 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.35 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.35 130.72/78.35 The set Q consists of the following terms: 130.72/78.35 130.72/78.35 new_primPlusNat1(Succ(x0)) 130.72/78.35 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.35 new_primMulNat0(x0) 130.72/78.35 new_primPlusNat1(Zero) 130.72/78.35 new_primPlusNat2(Zero) 130.72/78.35 new_primPlusNat3(Succ(x0)) 130.72/78.35 new_primPlusNat8(Succ(x0), x1) 130.72/78.35 new_primMulNat2(x0) 130.72/78.35 new_primPlusNat6(x0, Succ(x1)) 130.72/78.35 new_primPlusNat0(Succ(x0), Zero) 130.72/78.35 new_primPlusNat6(x0, Zero) 130.72/78.35 new_primPlusNat5(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.35 new_primPlusNat4(Succ(x0)) 130.72/78.35 new_primPlusNat8(Zero, x0) 130.72/78.35 new_primPlusNat3(Zero) 130.72/78.35 new_primPlusNat7(x0, Zero) 130.72/78.35 new_primPlusNat5(Zero) 130.72/78.35 new_primMulNat1(x0) 130.72/78.35 new_primPlusNat7(x0, Succ(x1)) 130.72/78.35 new_primPlusNat4(Zero) 130.72/78.35 new_primPlusNat2(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Zero) 130.72/78.35 130.72/78.35 We have to consider all minimal (P,Q,R)-chains. 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (461) TransformationProof (EQUIVALENT) 130.72/78.35 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Zero))))), bb) at position [10,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.35 130.72/78.35 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb)) 130.72/78.35 130.72/78.35 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (462) 130.72/78.35 Obligation: 130.72/78.35 Q DP problem: 130.72/78.35 The TRS P consists of the following rules: 130.72/78.35 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.35 130.72/78.35 The TRS R consists of the following rules: 130.72/78.35 130.72/78.35 new_primMulNat2(zzz4739) -> Zero 130.72/78.35 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.35 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.35 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.35 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.35 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.35 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.35 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.35 new_primPlusNat2(Zero) -> Zero 130.72/78.35 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.35 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.35 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.35 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.35 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.35 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.35 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.35 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.35 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.35 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.35 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.35 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.35 130.72/78.35 The set Q consists of the following terms: 130.72/78.35 130.72/78.35 new_primPlusNat1(Succ(x0)) 130.72/78.35 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.35 new_primMulNat0(x0) 130.72/78.35 new_primPlusNat1(Zero) 130.72/78.35 new_primPlusNat2(Zero) 130.72/78.35 new_primPlusNat3(Succ(x0)) 130.72/78.35 new_primPlusNat8(Succ(x0), x1) 130.72/78.35 new_primMulNat2(x0) 130.72/78.35 new_primPlusNat6(x0, Succ(x1)) 130.72/78.35 new_primPlusNat0(Succ(x0), Zero) 130.72/78.35 new_primPlusNat6(x0, Zero) 130.72/78.35 new_primPlusNat5(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.35 new_primPlusNat4(Succ(x0)) 130.72/78.35 new_primPlusNat8(Zero, x0) 130.72/78.35 new_primPlusNat3(Zero) 130.72/78.35 new_primPlusNat7(x0, Zero) 130.72/78.35 new_primPlusNat5(Zero) 130.72/78.35 new_primMulNat1(x0) 130.72/78.35 new_primPlusNat7(x0, Succ(x1)) 130.72/78.35 new_primPlusNat4(Zero) 130.72/78.35 new_primPlusNat2(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Zero) 130.72/78.35 130.72/78.35 We have to consider all minimal (P,Q,R)-chains. 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (463) TransformationProof (EQUIVALENT) 130.72/78.35 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) at position [12,0] we obtained the following new rules [LPAR04]: 130.72/78.35 130.72/78.35 (new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h),new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h)) 130.72/78.35 130.72/78.35 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (464) 130.72/78.35 Obligation: 130.72/78.35 Q DP problem: 130.72/78.35 The TRS P consists of the following rules: 130.72/78.35 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.35 130.72/78.35 The TRS R consists of the following rules: 130.72/78.35 130.72/78.35 new_primMulNat2(zzz4739) -> Zero 130.72/78.35 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.35 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.35 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.35 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.35 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.35 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.35 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.35 new_primPlusNat2(Zero) -> Zero 130.72/78.35 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.35 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.35 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.35 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.35 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.35 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.35 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.35 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.35 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.35 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.35 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.35 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.35 130.72/78.35 The set Q consists of the following terms: 130.72/78.35 130.72/78.35 new_primPlusNat1(Succ(x0)) 130.72/78.35 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.35 new_primMulNat0(x0) 130.72/78.35 new_primPlusNat1(Zero) 130.72/78.35 new_primPlusNat2(Zero) 130.72/78.35 new_primPlusNat3(Succ(x0)) 130.72/78.35 new_primPlusNat8(Succ(x0), x1) 130.72/78.35 new_primMulNat2(x0) 130.72/78.35 new_primPlusNat6(x0, Succ(x1)) 130.72/78.35 new_primPlusNat0(Succ(x0), Zero) 130.72/78.35 new_primPlusNat6(x0, Zero) 130.72/78.35 new_primPlusNat5(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.35 new_primPlusNat4(Succ(x0)) 130.72/78.35 new_primPlusNat8(Zero, x0) 130.72/78.35 new_primPlusNat3(Zero) 130.72/78.35 new_primPlusNat7(x0, Zero) 130.72/78.35 new_primPlusNat5(Zero) 130.72/78.35 new_primMulNat1(x0) 130.72/78.35 new_primPlusNat7(x0, Succ(x1)) 130.72/78.35 new_primPlusNat4(Zero) 130.72/78.35 new_primPlusNat2(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Zero) 130.72/78.35 130.72/78.35 We have to consider all minimal (P,Q,R)-chains. 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (465) TransformationProof (EQUIVALENT) 130.72/78.35 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primMulNat0(zzz4708), Succ(zzz4708)), h) at position [12,0] we obtained the following new rules [LPAR04]: 130.72/78.35 130.72/78.35 (new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h),new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h)) 130.72/78.35 130.72/78.35 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (466) 130.72/78.35 Obligation: 130.72/78.35 Q DP problem: 130.72/78.35 The TRS P consists of the following rules: 130.72/78.35 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.35 130.72/78.35 The TRS R consists of the following rules: 130.72/78.35 130.72/78.35 new_primMulNat2(zzz4739) -> Zero 130.72/78.35 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.35 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.35 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.35 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.35 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.35 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.35 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.35 new_primPlusNat2(Zero) -> Zero 130.72/78.35 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.35 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.35 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.35 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.72/78.35 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.35 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.35 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.35 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.35 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.35 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.35 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.35 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.35 130.72/78.35 The set Q consists of the following terms: 130.72/78.35 130.72/78.35 new_primPlusNat1(Succ(x0)) 130.72/78.35 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.35 new_primMulNat0(x0) 130.72/78.35 new_primPlusNat1(Zero) 130.72/78.35 new_primPlusNat2(Zero) 130.72/78.35 new_primPlusNat3(Succ(x0)) 130.72/78.35 new_primPlusNat8(Succ(x0), x1) 130.72/78.35 new_primMulNat2(x0) 130.72/78.35 new_primPlusNat6(x0, Succ(x1)) 130.72/78.35 new_primPlusNat0(Succ(x0), Zero) 130.72/78.35 new_primPlusNat6(x0, Zero) 130.72/78.35 new_primPlusNat5(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.35 new_primPlusNat4(Succ(x0)) 130.72/78.35 new_primPlusNat8(Zero, x0) 130.72/78.35 new_primPlusNat3(Zero) 130.72/78.35 new_primPlusNat7(x0, Zero) 130.72/78.35 new_primPlusNat5(Zero) 130.72/78.35 new_primMulNat1(x0) 130.72/78.35 new_primPlusNat7(x0, Succ(x1)) 130.72/78.35 new_primPlusNat4(Zero) 130.72/78.35 new_primPlusNat2(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Zero) 130.72/78.35 130.72/78.35 We have to consider all minimal (P,Q,R)-chains. 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (467) UsableRulesProof (EQUIVALENT) 130.72/78.35 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (468) 130.72/78.35 Obligation: 130.72/78.35 Q DP problem: 130.72/78.35 The TRS P consists of the following rules: 130.72/78.35 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Zero))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.35 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.35 130.72/78.35 The TRS R consists of the following rules: 130.72/78.35 130.72/78.35 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.35 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.35 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.35 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.35 new_primMulNat2(zzz4739) -> Zero 130.72/78.35 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.35 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.35 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.35 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.35 new_primPlusNat2(Zero) -> Zero 130.72/78.35 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.35 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.35 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.35 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.35 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.35 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.35 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.35 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.35 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.35 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.35 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.35 130.72/78.35 The set Q consists of the following terms: 130.72/78.35 130.72/78.35 new_primPlusNat1(Succ(x0)) 130.72/78.35 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.35 new_primMulNat0(x0) 130.72/78.35 new_primPlusNat1(Zero) 130.72/78.35 new_primPlusNat2(Zero) 130.72/78.35 new_primPlusNat3(Succ(x0)) 130.72/78.35 new_primPlusNat8(Succ(x0), x1) 130.72/78.35 new_primMulNat2(x0) 130.72/78.35 new_primPlusNat6(x0, Succ(x1)) 130.72/78.35 new_primPlusNat0(Succ(x0), Zero) 130.72/78.35 new_primPlusNat6(x0, Zero) 130.72/78.35 new_primPlusNat5(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.35 new_primPlusNat4(Succ(x0)) 130.72/78.35 new_primPlusNat8(Zero, x0) 130.72/78.35 new_primPlusNat3(Zero) 130.72/78.35 new_primPlusNat7(x0, Zero) 130.72/78.35 new_primPlusNat5(Zero) 130.72/78.35 new_primMulNat1(x0) 130.72/78.35 new_primPlusNat7(x0, Succ(x1)) 130.72/78.35 new_primPlusNat4(Zero) 130.72/78.35 new_primPlusNat2(Succ(x0)) 130.72/78.35 new_primPlusNat0(Zero, Zero) 130.72/78.35 130.72/78.35 We have to consider all minimal (P,Q,R)-chains. 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (469) QReductionProof (EQUIVALENT) 130.72/78.35 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.72/78.35 130.72/78.35 new_primMulNat0(x0) 130.72/78.35 130.72/78.35 130.72/78.35 ---------------------------------------- 130.72/78.35 130.72/78.35 (470) 130.72/78.35 Obligation: 130.72/78.35 Q DP problem: 130.72/78.35 The TRS P consists of the following rules: 130.72/78.35 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.35 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.35 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 130.72/78.36 The TRS R consists of the following rules: 130.72/78.36 130.72/78.36 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.36 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.36 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.36 new_primMulNat2(zzz4739) -> Zero 130.72/78.36 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.36 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.36 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.36 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.36 new_primPlusNat2(Zero) -> Zero 130.72/78.36 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.36 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.36 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.36 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.36 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.36 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.36 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.36 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.36 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.36 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.36 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.36 130.72/78.36 The set Q consists of the following terms: 130.72/78.36 130.72/78.36 new_primPlusNat1(Succ(x0)) 130.72/78.36 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.36 new_primPlusNat1(Zero) 130.72/78.36 new_primPlusNat2(Zero) 130.72/78.36 new_primPlusNat3(Succ(x0)) 130.72/78.36 new_primPlusNat8(Succ(x0), x1) 130.72/78.36 new_primMulNat2(x0) 130.72/78.36 new_primPlusNat6(x0, Succ(x1)) 130.72/78.36 new_primPlusNat0(Succ(x0), Zero) 130.72/78.36 new_primPlusNat6(x0, Zero) 130.72/78.36 new_primPlusNat5(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.36 new_primPlusNat4(Succ(x0)) 130.72/78.36 new_primPlusNat8(Zero, x0) 130.72/78.36 new_primPlusNat3(Zero) 130.72/78.36 new_primPlusNat7(x0, Zero) 130.72/78.36 new_primPlusNat5(Zero) 130.72/78.36 new_primMulNat1(x0) 130.72/78.36 new_primPlusNat7(x0, Succ(x1)) 130.72/78.36 new_primPlusNat4(Zero) 130.72/78.36 new_primPlusNat2(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Zero) 130.72/78.36 130.72/78.36 We have to consider all minimal (P,Q,R)-chains. 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (471) TransformationProof (EQUIVALENT) 130.72/78.36 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) at position [10,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.36 130.72/78.36 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb)) 130.72/78.36 130.72/78.36 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (472) 130.72/78.36 Obligation: 130.72/78.36 Q DP problem: 130.72/78.36 The TRS P consists of the following rules: 130.72/78.36 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.36 130.72/78.36 The TRS R consists of the following rules: 130.72/78.36 130.72/78.36 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.36 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.36 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.36 new_primMulNat2(zzz4739) -> Zero 130.72/78.36 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.36 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.36 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.36 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.36 new_primPlusNat2(Zero) -> Zero 130.72/78.36 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.36 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.36 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.36 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.36 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.36 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.36 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.36 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.36 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.36 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.36 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.36 130.72/78.36 The set Q consists of the following terms: 130.72/78.36 130.72/78.36 new_primPlusNat1(Succ(x0)) 130.72/78.36 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.36 new_primPlusNat1(Zero) 130.72/78.36 new_primPlusNat2(Zero) 130.72/78.36 new_primPlusNat3(Succ(x0)) 130.72/78.36 new_primPlusNat8(Succ(x0), x1) 130.72/78.36 new_primMulNat2(x0) 130.72/78.36 new_primPlusNat6(x0, Succ(x1)) 130.72/78.36 new_primPlusNat0(Succ(x0), Zero) 130.72/78.36 new_primPlusNat6(x0, Zero) 130.72/78.36 new_primPlusNat5(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.36 new_primPlusNat4(Succ(x0)) 130.72/78.36 new_primPlusNat8(Zero, x0) 130.72/78.36 new_primPlusNat3(Zero) 130.72/78.36 new_primPlusNat7(x0, Zero) 130.72/78.36 new_primPlusNat5(Zero) 130.72/78.36 new_primMulNat1(x0) 130.72/78.36 new_primPlusNat7(x0, Succ(x1)) 130.72/78.36 new_primPlusNat4(Zero) 130.72/78.36 new_primPlusNat2(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Zero) 130.72/78.36 130.72/78.36 We have to consider all minimal (P,Q,R)-chains. 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (473) TransformationProof (EQUIVALENT) 130.72/78.36 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) at position [10,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.36 130.72/78.36 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb)) 130.72/78.36 130.72/78.36 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (474) 130.72/78.36 Obligation: 130.72/78.36 Q DP problem: 130.72/78.36 The TRS P consists of the following rules: 130.72/78.36 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.36 130.72/78.36 The TRS R consists of the following rules: 130.72/78.36 130.72/78.36 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.36 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.36 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.36 new_primMulNat2(zzz4739) -> Zero 130.72/78.36 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.36 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.36 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.36 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.36 new_primPlusNat2(Zero) -> Zero 130.72/78.36 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.36 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.36 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.36 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.36 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.36 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.36 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.36 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.36 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.36 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.36 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.36 130.72/78.36 The set Q consists of the following terms: 130.72/78.36 130.72/78.36 new_primPlusNat1(Succ(x0)) 130.72/78.36 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.36 new_primPlusNat1(Zero) 130.72/78.36 new_primPlusNat2(Zero) 130.72/78.36 new_primPlusNat3(Succ(x0)) 130.72/78.36 new_primPlusNat8(Succ(x0), x1) 130.72/78.36 new_primMulNat2(x0) 130.72/78.36 new_primPlusNat6(x0, Succ(x1)) 130.72/78.36 new_primPlusNat0(Succ(x0), Zero) 130.72/78.36 new_primPlusNat6(x0, Zero) 130.72/78.36 new_primPlusNat5(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.36 new_primPlusNat4(Succ(x0)) 130.72/78.36 new_primPlusNat8(Zero, x0) 130.72/78.36 new_primPlusNat3(Zero) 130.72/78.36 new_primPlusNat7(x0, Zero) 130.72/78.36 new_primPlusNat5(Zero) 130.72/78.36 new_primMulNat1(x0) 130.72/78.36 new_primPlusNat7(x0, Succ(x1)) 130.72/78.36 new_primPlusNat4(Zero) 130.72/78.36 new_primPlusNat2(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Zero) 130.72/78.36 130.72/78.36 We have to consider all minimal (P,Q,R)-chains. 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (475) TransformationProof (EQUIVALENT) 130.72/78.36 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) at position [10,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.36 130.72/78.36 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb)) 130.72/78.36 130.72/78.36 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (476) 130.72/78.36 Obligation: 130.72/78.36 Q DP problem: 130.72/78.36 The TRS P consists of the following rules: 130.72/78.36 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 130.72/78.36 The TRS R consists of the following rules: 130.72/78.36 130.72/78.36 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.36 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.36 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.36 new_primMulNat2(zzz4739) -> Zero 130.72/78.36 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.36 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.36 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.36 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.36 new_primPlusNat2(Zero) -> Zero 130.72/78.36 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.36 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.36 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.36 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.36 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.36 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.36 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.36 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.36 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.36 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.36 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.36 130.72/78.36 The set Q consists of the following terms: 130.72/78.36 130.72/78.36 new_primPlusNat1(Succ(x0)) 130.72/78.36 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.36 new_primPlusNat1(Zero) 130.72/78.36 new_primPlusNat2(Zero) 130.72/78.36 new_primPlusNat3(Succ(x0)) 130.72/78.36 new_primPlusNat8(Succ(x0), x1) 130.72/78.36 new_primMulNat2(x0) 130.72/78.36 new_primPlusNat6(x0, Succ(x1)) 130.72/78.36 new_primPlusNat0(Succ(x0), Zero) 130.72/78.36 new_primPlusNat6(x0, Zero) 130.72/78.36 new_primPlusNat5(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.36 new_primPlusNat4(Succ(x0)) 130.72/78.36 new_primPlusNat8(Zero, x0) 130.72/78.36 new_primPlusNat3(Zero) 130.72/78.36 new_primPlusNat7(x0, Zero) 130.72/78.36 new_primPlusNat5(Zero) 130.72/78.36 new_primMulNat1(x0) 130.72/78.36 new_primPlusNat7(x0, Succ(x1)) 130.72/78.36 new_primPlusNat4(Zero) 130.72/78.36 new_primPlusNat2(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Zero) 130.72/78.36 130.72/78.36 We have to consider all minimal (P,Q,R)-chains. 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (477) TransformationProof (EQUIVALENT) 130.72/78.36 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))), zzz34200000, bb) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.36 130.72/78.36 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), zzz34200000, bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), zzz34200000, bb)) 130.72/78.36 130.72/78.36 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (478) 130.72/78.36 Obligation: 130.72/78.36 Q DP problem: 130.72/78.36 The TRS P consists of the following rules: 130.72/78.36 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), zzz34200000, bb) 130.72/78.36 130.72/78.36 The TRS R consists of the following rules: 130.72/78.36 130.72/78.36 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.36 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.36 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.36 new_primMulNat2(zzz4739) -> Zero 130.72/78.36 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.36 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.36 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.36 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.36 new_primPlusNat2(Zero) -> Zero 130.72/78.36 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.36 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.36 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.36 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.36 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.36 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.36 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.36 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.36 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.36 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.36 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.36 130.72/78.36 The set Q consists of the following terms: 130.72/78.36 130.72/78.36 new_primPlusNat1(Succ(x0)) 130.72/78.36 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.36 new_primPlusNat1(Zero) 130.72/78.36 new_primPlusNat2(Zero) 130.72/78.36 new_primPlusNat3(Succ(x0)) 130.72/78.36 new_primPlusNat8(Succ(x0), x1) 130.72/78.36 new_primMulNat2(x0) 130.72/78.36 new_primPlusNat6(x0, Succ(x1)) 130.72/78.36 new_primPlusNat0(Succ(x0), Zero) 130.72/78.36 new_primPlusNat6(x0, Zero) 130.72/78.36 new_primPlusNat5(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.36 new_primPlusNat4(Succ(x0)) 130.72/78.36 new_primPlusNat8(Zero, x0) 130.72/78.36 new_primPlusNat3(Zero) 130.72/78.36 new_primPlusNat7(x0, Zero) 130.72/78.36 new_primPlusNat5(Zero) 130.72/78.36 new_primMulNat1(x0) 130.72/78.36 new_primPlusNat7(x0, Succ(x1)) 130.72/78.36 new_primPlusNat4(Zero) 130.72/78.36 new_primPlusNat2(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Zero) 130.72/78.36 130.72/78.36 We have to consider all minimal (P,Q,R)-chains. 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (479) TransformationProof (EQUIVALENT) 130.72/78.36 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.36 130.72/78.36 (new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc)) 130.72/78.36 130.72/78.36 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (480) 130.72/78.36 Obligation: 130.72/78.36 Q DP problem: 130.72/78.36 The TRS P consists of the following rules: 130.72/78.36 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 130.72/78.36 The TRS R consists of the following rules: 130.72/78.36 130.72/78.36 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.36 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.36 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.36 new_primMulNat2(zzz4739) -> Zero 130.72/78.36 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.36 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.36 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.36 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.36 new_primPlusNat2(Zero) -> Zero 130.72/78.36 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.36 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.36 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.36 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.36 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.36 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.36 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.36 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.36 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.36 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.36 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.36 130.72/78.36 The set Q consists of the following terms: 130.72/78.36 130.72/78.36 new_primPlusNat1(Succ(x0)) 130.72/78.36 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.36 new_primPlusNat1(Zero) 130.72/78.36 new_primPlusNat2(Zero) 130.72/78.36 new_primPlusNat3(Succ(x0)) 130.72/78.36 new_primPlusNat8(Succ(x0), x1) 130.72/78.36 new_primMulNat2(x0) 130.72/78.36 new_primPlusNat6(x0, Succ(x1)) 130.72/78.36 new_primPlusNat0(Succ(x0), Zero) 130.72/78.36 new_primPlusNat6(x0, Zero) 130.72/78.36 new_primPlusNat5(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.36 new_primPlusNat4(Succ(x0)) 130.72/78.36 new_primPlusNat8(Zero, x0) 130.72/78.36 new_primPlusNat3(Zero) 130.72/78.36 new_primPlusNat7(x0, Zero) 130.72/78.36 new_primPlusNat5(Zero) 130.72/78.36 new_primMulNat1(x0) 130.72/78.36 new_primPlusNat7(x0, Succ(x1)) 130.72/78.36 new_primPlusNat4(Zero) 130.72/78.36 new_primPlusNat2(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Zero) 130.72/78.36 130.72/78.36 We have to consider all minimal (P,Q,R)-chains. 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (481) TransformationProof (EQUIVALENT) 130.72/78.36 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.36 130.72/78.36 (new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc)) 130.72/78.36 130.72/78.36 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (482) 130.72/78.36 Obligation: 130.72/78.36 Q DP problem: 130.72/78.36 The TRS P consists of the following rules: 130.72/78.36 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 130.72/78.36 The TRS R consists of the following rules: 130.72/78.36 130.72/78.36 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.36 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.36 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.36 new_primMulNat2(zzz4739) -> Zero 130.72/78.36 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.36 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.36 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.36 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.36 new_primPlusNat2(Zero) -> Zero 130.72/78.36 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.36 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.36 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.36 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.36 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.36 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.36 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.36 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.36 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.36 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.36 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.36 130.72/78.36 The set Q consists of the following terms: 130.72/78.36 130.72/78.36 new_primPlusNat1(Succ(x0)) 130.72/78.36 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.36 new_primPlusNat1(Zero) 130.72/78.36 new_primPlusNat2(Zero) 130.72/78.36 new_primPlusNat3(Succ(x0)) 130.72/78.36 new_primPlusNat8(Succ(x0), x1) 130.72/78.36 new_primMulNat2(x0) 130.72/78.36 new_primPlusNat6(x0, Succ(x1)) 130.72/78.36 new_primPlusNat0(Succ(x0), Zero) 130.72/78.36 new_primPlusNat6(x0, Zero) 130.72/78.36 new_primPlusNat5(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.36 new_primPlusNat4(Succ(x0)) 130.72/78.36 new_primPlusNat8(Zero, x0) 130.72/78.36 new_primPlusNat3(Zero) 130.72/78.36 new_primPlusNat7(x0, Zero) 130.72/78.36 new_primPlusNat5(Zero) 130.72/78.36 new_primMulNat1(x0) 130.72/78.36 new_primPlusNat7(x0, Succ(x1)) 130.72/78.36 new_primPlusNat4(Zero) 130.72/78.36 new_primPlusNat2(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Zero) 130.72/78.36 130.72/78.36 We have to consider all minimal (P,Q,R)-chains. 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (483) TransformationProof (EQUIVALENT) 130.72/78.36 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.36 130.72/78.36 (new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc)) 130.72/78.36 130.72/78.36 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (484) 130.72/78.36 Obligation: 130.72/78.36 Q DP problem: 130.72/78.36 The TRS P consists of the following rules: 130.72/78.36 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 130.72/78.36 The TRS R consists of the following rules: 130.72/78.36 130.72/78.36 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.36 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.36 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.36 new_primMulNat2(zzz4739) -> Zero 130.72/78.36 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.36 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.36 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.36 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.36 new_primPlusNat2(Zero) -> Zero 130.72/78.36 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.36 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.36 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.36 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.36 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.36 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.36 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.36 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.36 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.36 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.36 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.36 130.72/78.36 The set Q consists of the following terms: 130.72/78.36 130.72/78.36 new_primPlusNat1(Succ(x0)) 130.72/78.36 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.36 new_primPlusNat1(Zero) 130.72/78.36 new_primPlusNat2(Zero) 130.72/78.36 new_primPlusNat3(Succ(x0)) 130.72/78.36 new_primPlusNat8(Succ(x0), x1) 130.72/78.36 new_primMulNat2(x0) 130.72/78.36 new_primPlusNat6(x0, Succ(x1)) 130.72/78.36 new_primPlusNat0(Succ(x0), Zero) 130.72/78.36 new_primPlusNat6(x0, Zero) 130.72/78.36 new_primPlusNat5(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.36 new_primPlusNat4(Succ(x0)) 130.72/78.36 new_primPlusNat8(Zero, x0) 130.72/78.36 new_primPlusNat3(Zero) 130.72/78.36 new_primPlusNat7(x0, Zero) 130.72/78.36 new_primPlusNat5(Zero) 130.72/78.36 new_primMulNat1(x0) 130.72/78.36 new_primPlusNat7(x0, Succ(x1)) 130.72/78.36 new_primPlusNat4(Zero) 130.72/78.36 new_primPlusNat2(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Zero) 130.72/78.36 130.72/78.36 We have to consider all minimal (P,Q,R)-chains. 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (485) TransformationProof (EQUIVALENT) 130.72/78.36 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.36 130.72/78.36 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb)) 130.72/78.36 130.72/78.36 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (486) 130.72/78.36 Obligation: 130.72/78.36 Q DP problem: 130.72/78.36 The TRS P consists of the following rules: 130.72/78.36 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.72/78.36 130.72/78.36 The TRS R consists of the following rules: 130.72/78.36 130.72/78.36 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.36 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.36 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.36 new_primMulNat2(zzz4739) -> Zero 130.72/78.36 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.36 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.36 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.36 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.36 new_primPlusNat2(Zero) -> Zero 130.72/78.36 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.36 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.36 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.36 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.36 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.36 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.36 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.36 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.36 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.36 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.36 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.36 130.72/78.36 The set Q consists of the following terms: 130.72/78.36 130.72/78.36 new_primPlusNat1(Succ(x0)) 130.72/78.36 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.36 new_primPlusNat1(Zero) 130.72/78.36 new_primPlusNat2(Zero) 130.72/78.36 new_primPlusNat3(Succ(x0)) 130.72/78.36 new_primPlusNat8(Succ(x0), x1) 130.72/78.36 new_primMulNat2(x0) 130.72/78.36 new_primPlusNat6(x0, Succ(x1)) 130.72/78.36 new_primPlusNat0(Succ(x0), Zero) 130.72/78.36 new_primPlusNat6(x0, Zero) 130.72/78.36 new_primPlusNat5(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.36 new_primPlusNat4(Succ(x0)) 130.72/78.36 new_primPlusNat8(Zero, x0) 130.72/78.36 new_primPlusNat3(Zero) 130.72/78.36 new_primPlusNat7(x0, Zero) 130.72/78.36 new_primPlusNat5(Zero) 130.72/78.36 new_primMulNat1(x0) 130.72/78.36 new_primPlusNat7(x0, Succ(x1)) 130.72/78.36 new_primPlusNat4(Zero) 130.72/78.36 new_primPlusNat2(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Zero) 130.72/78.36 130.72/78.36 We have to consider all minimal (P,Q,R)-chains. 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (487) TransformationProof (EQUIVALENT) 130.72/78.36 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Zero))))), bb) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.36 130.72/78.36 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Zero)))))), bb)) 130.72/78.36 130.72/78.36 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (488) 130.72/78.36 Obligation: 130.72/78.36 Q DP problem: 130.72/78.36 The TRS P consists of the following rules: 130.72/78.36 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.36 130.72/78.36 The TRS R consists of the following rules: 130.72/78.36 130.72/78.36 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.36 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.36 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.36 new_primMulNat2(zzz4739) -> Zero 130.72/78.36 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.36 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.36 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.36 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.36 new_primPlusNat2(Zero) -> Zero 130.72/78.36 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.36 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.36 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.36 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.36 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.36 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.36 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.36 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.36 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.36 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.36 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.36 130.72/78.36 The set Q consists of the following terms: 130.72/78.36 130.72/78.36 new_primPlusNat1(Succ(x0)) 130.72/78.36 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.36 new_primPlusNat1(Zero) 130.72/78.36 new_primPlusNat2(Zero) 130.72/78.36 new_primPlusNat3(Succ(x0)) 130.72/78.36 new_primPlusNat8(Succ(x0), x1) 130.72/78.36 new_primMulNat2(x0) 130.72/78.36 new_primPlusNat6(x0, Succ(x1)) 130.72/78.36 new_primPlusNat0(Succ(x0), Zero) 130.72/78.36 new_primPlusNat6(x0, Zero) 130.72/78.36 new_primPlusNat5(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.36 new_primPlusNat4(Succ(x0)) 130.72/78.36 new_primPlusNat8(Zero, x0) 130.72/78.36 new_primPlusNat3(Zero) 130.72/78.36 new_primPlusNat7(x0, Zero) 130.72/78.36 new_primPlusNat5(Zero) 130.72/78.36 new_primMulNat1(x0) 130.72/78.36 new_primPlusNat7(x0, Succ(x1)) 130.72/78.36 new_primPlusNat4(Zero) 130.72/78.36 new_primPlusNat2(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Zero) 130.72/78.36 130.72/78.36 We have to consider all minimal (P,Q,R)-chains. 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (489) TransformationProof (EQUIVALENT) 130.72/78.36 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero)))))), bb) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.36 130.72/78.36 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), bb)) 130.72/78.36 130.72/78.36 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (490) 130.72/78.36 Obligation: 130.72/78.36 Q DP problem: 130.72/78.36 The TRS P consists of the following rules: 130.72/78.36 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 130.72/78.36 The TRS R consists of the following rules: 130.72/78.36 130.72/78.36 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.36 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.36 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.36 new_primMulNat2(zzz4739) -> Zero 130.72/78.36 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.36 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.36 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.36 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.36 new_primPlusNat2(Zero) -> Zero 130.72/78.36 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.36 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.36 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.36 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.36 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.36 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.36 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.36 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.36 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.36 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.36 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.36 130.72/78.36 The set Q consists of the following terms: 130.72/78.36 130.72/78.36 new_primPlusNat1(Succ(x0)) 130.72/78.36 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.36 new_primPlusNat1(Zero) 130.72/78.36 new_primPlusNat2(Zero) 130.72/78.36 new_primPlusNat3(Succ(x0)) 130.72/78.36 new_primPlusNat8(Succ(x0), x1) 130.72/78.36 new_primMulNat2(x0) 130.72/78.36 new_primPlusNat6(x0, Succ(x1)) 130.72/78.36 new_primPlusNat0(Succ(x0), Zero) 130.72/78.36 new_primPlusNat6(x0, Zero) 130.72/78.36 new_primPlusNat5(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.36 new_primPlusNat4(Succ(x0)) 130.72/78.36 new_primPlusNat8(Zero, x0) 130.72/78.36 new_primPlusNat3(Zero) 130.72/78.36 new_primPlusNat7(x0, Zero) 130.72/78.36 new_primPlusNat5(Zero) 130.72/78.36 new_primMulNat1(x0) 130.72/78.36 new_primPlusNat7(x0, Succ(x1)) 130.72/78.36 new_primPlusNat4(Zero) 130.72/78.36 new_primPlusNat2(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Zero) 130.72/78.36 130.72/78.36 We have to consider all minimal (P,Q,R)-chains. 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (491) TransformationProof (EQUIVALENT) 130.72/78.36 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(Zero)))))), bb) at position [10,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.36 130.72/78.36 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb)) 130.72/78.36 130.72/78.36 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (492) 130.72/78.36 Obligation: 130.72/78.36 Q DP problem: 130.72/78.36 The TRS P consists of the following rules: 130.72/78.36 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.72/78.36 130.72/78.36 The TRS R consists of the following rules: 130.72/78.36 130.72/78.36 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.36 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.36 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.36 new_primMulNat2(zzz4739) -> Zero 130.72/78.36 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.36 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.36 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.36 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.36 new_primPlusNat2(Zero) -> Zero 130.72/78.36 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.36 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.36 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.36 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.36 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.36 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.36 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.36 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.36 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.36 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.36 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.36 130.72/78.36 The set Q consists of the following terms: 130.72/78.36 130.72/78.36 new_primPlusNat1(Succ(x0)) 130.72/78.36 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.36 new_primPlusNat1(Zero) 130.72/78.36 new_primPlusNat2(Zero) 130.72/78.36 new_primPlusNat3(Succ(x0)) 130.72/78.36 new_primPlusNat8(Succ(x0), x1) 130.72/78.36 new_primMulNat2(x0) 130.72/78.36 new_primPlusNat6(x0, Succ(x1)) 130.72/78.36 new_primPlusNat0(Succ(x0), Zero) 130.72/78.36 new_primPlusNat6(x0, Zero) 130.72/78.36 new_primPlusNat5(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.36 new_primPlusNat4(Succ(x0)) 130.72/78.36 new_primPlusNat8(Zero, x0) 130.72/78.36 new_primPlusNat3(Zero) 130.72/78.36 new_primPlusNat7(x0, Zero) 130.72/78.36 new_primPlusNat5(Zero) 130.72/78.36 new_primMulNat1(x0) 130.72/78.36 new_primPlusNat7(x0, Succ(x1)) 130.72/78.36 new_primPlusNat4(Zero) 130.72/78.36 new_primPlusNat2(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Zero) 130.72/78.36 130.72/78.36 We have to consider all minimal (P,Q,R)-chains. 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (493) TransformationProof (EQUIVALENT) 130.72/78.36 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.36 130.72/78.36 (new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h),new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h)) 130.72/78.36 130.72/78.36 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (494) 130.72/78.36 Obligation: 130.72/78.36 Q DP problem: 130.72/78.36 The TRS P consists of the following rules: 130.72/78.36 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 130.72/78.36 The TRS R consists of the following rules: 130.72/78.36 130.72/78.36 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.36 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.36 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.36 new_primMulNat2(zzz4739) -> Zero 130.72/78.36 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.36 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.36 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.36 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.36 new_primPlusNat2(Zero) -> Zero 130.72/78.36 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.36 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.36 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.36 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.36 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.36 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.36 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.36 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.36 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.36 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.36 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.36 130.72/78.36 The set Q consists of the following terms: 130.72/78.36 130.72/78.36 new_primPlusNat1(Succ(x0)) 130.72/78.36 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.36 new_primPlusNat1(Zero) 130.72/78.36 new_primPlusNat2(Zero) 130.72/78.36 new_primPlusNat3(Succ(x0)) 130.72/78.36 new_primPlusNat8(Succ(x0), x1) 130.72/78.36 new_primMulNat2(x0) 130.72/78.36 new_primPlusNat6(x0, Succ(x1)) 130.72/78.36 new_primPlusNat0(Succ(x0), Zero) 130.72/78.36 new_primPlusNat6(x0, Zero) 130.72/78.36 new_primPlusNat5(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.36 new_primPlusNat4(Succ(x0)) 130.72/78.36 new_primPlusNat8(Zero, x0) 130.72/78.36 new_primPlusNat3(Zero) 130.72/78.36 new_primPlusNat7(x0, Zero) 130.72/78.36 new_primPlusNat5(Zero) 130.72/78.36 new_primMulNat1(x0) 130.72/78.36 new_primPlusNat7(x0, Succ(x1)) 130.72/78.36 new_primPlusNat4(Zero) 130.72/78.36 new_primPlusNat2(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Zero) 130.72/78.36 130.72/78.36 We have to consider all minimal (P,Q,R)-chains. 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (495) TransformationProof (EQUIVALENT) 130.72/78.36 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.72/78.36 130.72/78.36 (new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h),new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h)) 130.72/78.36 130.72/78.36 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (496) 130.72/78.36 Obligation: 130.72/78.36 Q DP problem: 130.72/78.36 The TRS P consists of the following rules: 130.72/78.36 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.72/78.36 130.72/78.36 The TRS R consists of the following rules: 130.72/78.36 130.72/78.36 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.72/78.36 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.72/78.36 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.72/78.36 new_primPlusNat0(Zero, Zero) -> Zero 130.72/78.36 new_primMulNat2(zzz4739) -> Zero 130.72/78.36 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.72/78.36 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.72/78.36 new_primPlusNat3(Zero) -> Succ(Zero) 130.72/78.36 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.72/78.36 new_primPlusNat2(Zero) -> Zero 130.72/78.36 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.72/78.36 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.72/78.36 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.72/78.36 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.72/78.36 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.72/78.36 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.72/78.36 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.72/78.36 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.72/78.36 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.72/78.36 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.72/78.36 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.72/78.36 130.72/78.36 The set Q consists of the following terms: 130.72/78.36 130.72/78.36 new_primPlusNat1(Succ(x0)) 130.72/78.36 new_primPlusNat0(Succ(x0), Succ(x1)) 130.72/78.36 new_primPlusNat1(Zero) 130.72/78.36 new_primPlusNat2(Zero) 130.72/78.36 new_primPlusNat3(Succ(x0)) 130.72/78.36 new_primPlusNat8(Succ(x0), x1) 130.72/78.36 new_primMulNat2(x0) 130.72/78.36 new_primPlusNat6(x0, Succ(x1)) 130.72/78.36 new_primPlusNat0(Succ(x0), Zero) 130.72/78.36 new_primPlusNat6(x0, Zero) 130.72/78.36 new_primPlusNat5(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Succ(x0)) 130.72/78.36 new_primPlusNat4(Succ(x0)) 130.72/78.36 new_primPlusNat8(Zero, x0) 130.72/78.36 new_primPlusNat3(Zero) 130.72/78.36 new_primPlusNat7(x0, Zero) 130.72/78.36 new_primPlusNat5(Zero) 130.72/78.36 new_primMulNat1(x0) 130.72/78.36 new_primPlusNat7(x0, Succ(x1)) 130.72/78.36 new_primPlusNat4(Zero) 130.72/78.36 new_primPlusNat2(Succ(x0)) 130.72/78.36 new_primPlusNat0(Zero, Zero) 130.72/78.36 130.72/78.36 We have to consider all minimal (P,Q,R)-chains. 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (497) UsableRulesProof (EQUIVALENT) 130.72/78.36 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.72/78.36 ---------------------------------------- 130.72/78.36 130.72/78.36 (498) 130.72/78.36 Obligation: 130.72/78.36 Q DP problem: 130.72/78.36 The TRS P consists of the following rules: 130.72/78.36 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.72/78.36 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.72/78.36 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.72/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.72/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.72/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), zzz34200000, bb) 130.72/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 130.73/78.37 The TRS R consists of the following rules: 130.73/78.37 130.73/78.37 new_primMulNat2(zzz4739) -> Zero 130.73/78.37 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.37 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.37 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.37 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.37 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.37 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.37 new_primPlusNat2(Zero) -> Zero 130.73/78.37 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.37 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.37 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.37 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.37 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.37 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.37 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.37 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.37 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.37 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.37 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.37 130.73/78.37 The set Q consists of the following terms: 130.73/78.37 130.73/78.37 new_primPlusNat1(Succ(x0)) 130.73/78.37 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.37 new_primPlusNat1(Zero) 130.73/78.37 new_primPlusNat2(Zero) 130.73/78.37 new_primPlusNat3(Succ(x0)) 130.73/78.37 new_primPlusNat8(Succ(x0), x1) 130.73/78.37 new_primMulNat2(x0) 130.73/78.37 new_primPlusNat6(x0, Succ(x1)) 130.73/78.37 new_primPlusNat0(Succ(x0), Zero) 130.73/78.37 new_primPlusNat6(x0, Zero) 130.73/78.37 new_primPlusNat5(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.37 new_primPlusNat4(Succ(x0)) 130.73/78.37 new_primPlusNat8(Zero, x0) 130.73/78.37 new_primPlusNat3(Zero) 130.73/78.37 new_primPlusNat7(x0, Zero) 130.73/78.37 new_primPlusNat5(Zero) 130.73/78.37 new_primMulNat1(x0) 130.73/78.37 new_primPlusNat7(x0, Succ(x1)) 130.73/78.37 new_primPlusNat4(Zero) 130.73/78.37 new_primPlusNat2(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Zero) 130.73/78.37 130.73/78.37 We have to consider all minimal (P,Q,R)-chains. 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (499) QReductionProof (EQUIVALENT) 130.73/78.37 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.73/78.37 130.73/78.37 new_primMulNat1(x0) 130.73/78.37 130.73/78.37 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (500) 130.73/78.37 Obligation: 130.73/78.37 Q DP problem: 130.73/78.37 The TRS P consists of the following rules: 130.73/78.37 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 130.73/78.37 The TRS R consists of the following rules: 130.73/78.37 130.73/78.37 new_primMulNat2(zzz4739) -> Zero 130.73/78.37 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.37 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.37 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.37 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.37 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.37 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.37 new_primPlusNat2(Zero) -> Zero 130.73/78.37 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.37 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.37 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.37 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.37 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.37 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.37 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.37 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.37 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.37 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.37 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.37 130.73/78.37 The set Q consists of the following terms: 130.73/78.37 130.73/78.37 new_primPlusNat1(Succ(x0)) 130.73/78.37 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.37 new_primPlusNat1(Zero) 130.73/78.37 new_primPlusNat2(Zero) 130.73/78.37 new_primPlusNat3(Succ(x0)) 130.73/78.37 new_primPlusNat8(Succ(x0), x1) 130.73/78.37 new_primMulNat2(x0) 130.73/78.37 new_primPlusNat6(x0, Succ(x1)) 130.73/78.37 new_primPlusNat0(Succ(x0), Zero) 130.73/78.37 new_primPlusNat6(x0, Zero) 130.73/78.37 new_primPlusNat5(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.37 new_primPlusNat4(Succ(x0)) 130.73/78.37 new_primPlusNat8(Zero, x0) 130.73/78.37 new_primPlusNat3(Zero) 130.73/78.37 new_primPlusNat7(x0, Zero) 130.73/78.37 new_primPlusNat5(Zero) 130.73/78.37 new_primPlusNat7(x0, Succ(x1)) 130.73/78.37 new_primPlusNat4(Zero) 130.73/78.37 new_primPlusNat2(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Zero) 130.73/78.37 130.73/78.37 We have to consider all minimal (P,Q,R)-chains. 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (501) TransformationProof (EQUIVALENT) 130.73/78.37 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) at position [10,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.73/78.37 130.73/78.37 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb)) 130.73/78.37 130.73/78.37 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (502) 130.73/78.37 Obligation: 130.73/78.37 Q DP problem: 130.73/78.37 The TRS P consists of the following rules: 130.73/78.37 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.37 130.73/78.37 The TRS R consists of the following rules: 130.73/78.37 130.73/78.37 new_primMulNat2(zzz4739) -> Zero 130.73/78.37 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.37 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.37 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.37 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.37 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.37 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.37 new_primPlusNat2(Zero) -> Zero 130.73/78.37 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.37 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.37 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.37 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.37 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.37 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.37 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.37 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.37 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.37 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.37 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.37 130.73/78.37 The set Q consists of the following terms: 130.73/78.37 130.73/78.37 new_primPlusNat1(Succ(x0)) 130.73/78.37 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.37 new_primPlusNat1(Zero) 130.73/78.37 new_primPlusNat2(Zero) 130.73/78.37 new_primPlusNat3(Succ(x0)) 130.73/78.37 new_primPlusNat8(Succ(x0), x1) 130.73/78.37 new_primMulNat2(x0) 130.73/78.37 new_primPlusNat6(x0, Succ(x1)) 130.73/78.37 new_primPlusNat0(Succ(x0), Zero) 130.73/78.37 new_primPlusNat6(x0, Zero) 130.73/78.37 new_primPlusNat5(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.37 new_primPlusNat4(Succ(x0)) 130.73/78.37 new_primPlusNat8(Zero, x0) 130.73/78.37 new_primPlusNat3(Zero) 130.73/78.37 new_primPlusNat7(x0, Zero) 130.73/78.37 new_primPlusNat5(Zero) 130.73/78.37 new_primPlusNat7(x0, Succ(x1)) 130.73/78.37 new_primPlusNat4(Zero) 130.73/78.37 new_primPlusNat2(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Zero) 130.73/78.37 130.73/78.37 We have to consider all minimal (P,Q,R)-chains. 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (503) TransformationProof (EQUIVALENT) 130.73/78.37 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Zero))))))), bb) at position [10,0,0,0,0] we obtained the following new rules [LPAR04]: 130.73/78.37 130.73/78.37 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))))), bb)) 130.73/78.37 130.73/78.37 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (504) 130.73/78.37 Obligation: 130.73/78.37 Q DP problem: 130.73/78.37 The TRS P consists of the following rules: 130.73/78.37 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))))), bb) 130.73/78.37 130.73/78.37 The TRS R consists of the following rules: 130.73/78.37 130.73/78.37 new_primMulNat2(zzz4739) -> Zero 130.73/78.37 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.37 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.37 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.37 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.37 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.37 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.37 new_primPlusNat2(Zero) -> Zero 130.73/78.37 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.37 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.37 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.37 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.37 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.37 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.37 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.37 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.37 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.37 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.37 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.37 130.73/78.37 The set Q consists of the following terms: 130.73/78.37 130.73/78.37 new_primPlusNat1(Succ(x0)) 130.73/78.37 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.37 new_primPlusNat1(Zero) 130.73/78.37 new_primPlusNat2(Zero) 130.73/78.37 new_primPlusNat3(Succ(x0)) 130.73/78.37 new_primPlusNat8(Succ(x0), x1) 130.73/78.37 new_primMulNat2(x0) 130.73/78.37 new_primPlusNat6(x0, Succ(x1)) 130.73/78.37 new_primPlusNat0(Succ(x0), Zero) 130.73/78.37 new_primPlusNat6(x0, Zero) 130.73/78.37 new_primPlusNat5(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.37 new_primPlusNat4(Succ(x0)) 130.73/78.37 new_primPlusNat8(Zero, x0) 130.73/78.37 new_primPlusNat3(Zero) 130.73/78.37 new_primPlusNat7(x0, Zero) 130.73/78.37 new_primPlusNat5(Zero) 130.73/78.37 new_primPlusNat7(x0, Succ(x1)) 130.73/78.37 new_primPlusNat4(Zero) 130.73/78.37 new_primPlusNat2(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Zero) 130.73/78.37 130.73/78.37 We have to consider all minimal (P,Q,R)-chains. 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (505) TransformationProof (EQUIVALENT) 130.73/78.37 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) at position [10,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.73/78.37 130.73/78.37 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb)) 130.73/78.37 130.73/78.37 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (506) 130.73/78.37 Obligation: 130.73/78.37 Q DP problem: 130.73/78.37 The TRS P consists of the following rules: 130.73/78.37 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 130.73/78.37 The TRS R consists of the following rules: 130.73/78.37 130.73/78.37 new_primMulNat2(zzz4739) -> Zero 130.73/78.37 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.37 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.37 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.37 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.37 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.37 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.37 new_primPlusNat2(Zero) -> Zero 130.73/78.37 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.37 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.37 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.37 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.37 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.37 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.37 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.37 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.37 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.37 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.37 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.37 130.73/78.37 The set Q consists of the following terms: 130.73/78.37 130.73/78.37 new_primPlusNat1(Succ(x0)) 130.73/78.37 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.37 new_primPlusNat1(Zero) 130.73/78.37 new_primPlusNat2(Zero) 130.73/78.37 new_primPlusNat3(Succ(x0)) 130.73/78.37 new_primPlusNat8(Succ(x0), x1) 130.73/78.37 new_primMulNat2(x0) 130.73/78.37 new_primPlusNat6(x0, Succ(x1)) 130.73/78.37 new_primPlusNat0(Succ(x0), Zero) 130.73/78.37 new_primPlusNat6(x0, Zero) 130.73/78.37 new_primPlusNat5(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.37 new_primPlusNat4(Succ(x0)) 130.73/78.37 new_primPlusNat8(Zero, x0) 130.73/78.37 new_primPlusNat3(Zero) 130.73/78.37 new_primPlusNat7(x0, Zero) 130.73/78.37 new_primPlusNat5(Zero) 130.73/78.37 new_primPlusNat7(x0, Succ(x1)) 130.73/78.37 new_primPlusNat4(Zero) 130.73/78.37 new_primPlusNat2(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Zero) 130.73/78.37 130.73/78.37 We have to consider all minimal (P,Q,R)-chains. 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (507) TransformationProof (EQUIVALENT) 130.73/78.37 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero))))))), zzz34200000, bb) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.73/78.37 130.73/78.37 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), zzz34200000, bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), zzz34200000, bb)) 130.73/78.37 130.73/78.37 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (508) 130.73/78.37 Obligation: 130.73/78.37 Q DP problem: 130.73/78.37 The TRS P consists of the following rules: 130.73/78.37 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), zzz34200000, bb) 130.73/78.37 130.73/78.37 The TRS R consists of the following rules: 130.73/78.37 130.73/78.37 new_primMulNat2(zzz4739) -> Zero 130.73/78.37 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.37 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.37 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.37 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.37 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.37 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.37 new_primPlusNat2(Zero) -> Zero 130.73/78.37 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.37 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.37 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.37 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.37 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.37 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.37 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.37 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.37 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.37 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.37 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.37 130.73/78.37 The set Q consists of the following terms: 130.73/78.37 130.73/78.37 new_primPlusNat1(Succ(x0)) 130.73/78.37 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.37 new_primPlusNat1(Zero) 130.73/78.37 new_primPlusNat2(Zero) 130.73/78.37 new_primPlusNat3(Succ(x0)) 130.73/78.37 new_primPlusNat8(Succ(x0), x1) 130.73/78.37 new_primMulNat2(x0) 130.73/78.37 new_primPlusNat6(x0, Succ(x1)) 130.73/78.37 new_primPlusNat0(Succ(x0), Zero) 130.73/78.37 new_primPlusNat6(x0, Zero) 130.73/78.37 new_primPlusNat5(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.37 new_primPlusNat4(Succ(x0)) 130.73/78.37 new_primPlusNat8(Zero, x0) 130.73/78.37 new_primPlusNat3(Zero) 130.73/78.37 new_primPlusNat7(x0, Zero) 130.73/78.37 new_primPlusNat5(Zero) 130.73/78.37 new_primPlusNat7(x0, Succ(x1)) 130.73/78.37 new_primPlusNat4(Zero) 130.73/78.37 new_primPlusNat2(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Zero) 130.73/78.37 130.73/78.37 We have to consider all minimal (P,Q,R)-chains. 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (509) TransformationProof (EQUIVALENT) 130.73/78.37 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.73/78.37 130.73/78.37 (new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc)) 130.73/78.37 130.73/78.37 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (510) 130.73/78.37 Obligation: 130.73/78.37 Q DP problem: 130.73/78.37 The TRS P consists of the following rules: 130.73/78.37 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 130.73/78.37 The TRS R consists of the following rules: 130.73/78.37 130.73/78.37 new_primMulNat2(zzz4739) -> Zero 130.73/78.37 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.37 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.37 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.37 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.37 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.37 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.37 new_primPlusNat2(Zero) -> Zero 130.73/78.37 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.37 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.37 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.37 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.37 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.37 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.37 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.37 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.37 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.37 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.37 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.37 130.73/78.37 The set Q consists of the following terms: 130.73/78.37 130.73/78.37 new_primPlusNat1(Succ(x0)) 130.73/78.37 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.37 new_primPlusNat1(Zero) 130.73/78.37 new_primPlusNat2(Zero) 130.73/78.37 new_primPlusNat3(Succ(x0)) 130.73/78.37 new_primPlusNat8(Succ(x0), x1) 130.73/78.37 new_primMulNat2(x0) 130.73/78.37 new_primPlusNat6(x0, Succ(x1)) 130.73/78.37 new_primPlusNat0(Succ(x0), Zero) 130.73/78.37 new_primPlusNat6(x0, Zero) 130.73/78.37 new_primPlusNat5(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.37 new_primPlusNat4(Succ(x0)) 130.73/78.37 new_primPlusNat8(Zero, x0) 130.73/78.37 new_primPlusNat3(Zero) 130.73/78.37 new_primPlusNat7(x0, Zero) 130.73/78.37 new_primPlusNat5(Zero) 130.73/78.37 new_primPlusNat7(x0, Succ(x1)) 130.73/78.37 new_primPlusNat4(Zero) 130.73/78.37 new_primPlusNat2(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Zero) 130.73/78.37 130.73/78.37 We have to consider all minimal (P,Q,R)-chains. 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (511) TransformationProof (EQUIVALENT) 130.73/78.37 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.73/78.37 130.73/78.37 (new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc)) 130.73/78.37 130.73/78.37 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (512) 130.73/78.37 Obligation: 130.73/78.37 Q DP problem: 130.73/78.37 The TRS P consists of the following rules: 130.73/78.37 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 130.73/78.37 The TRS R consists of the following rules: 130.73/78.37 130.73/78.37 new_primMulNat2(zzz4739) -> Zero 130.73/78.37 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.37 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.37 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.37 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.37 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.37 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.37 new_primPlusNat2(Zero) -> Zero 130.73/78.37 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.37 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.37 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.37 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.37 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.37 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.37 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.37 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.37 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.37 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.37 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.37 130.73/78.37 The set Q consists of the following terms: 130.73/78.37 130.73/78.37 new_primPlusNat1(Succ(x0)) 130.73/78.37 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.37 new_primPlusNat1(Zero) 130.73/78.37 new_primPlusNat2(Zero) 130.73/78.37 new_primPlusNat3(Succ(x0)) 130.73/78.37 new_primPlusNat8(Succ(x0), x1) 130.73/78.37 new_primMulNat2(x0) 130.73/78.37 new_primPlusNat6(x0, Succ(x1)) 130.73/78.37 new_primPlusNat0(Succ(x0), Zero) 130.73/78.37 new_primPlusNat6(x0, Zero) 130.73/78.37 new_primPlusNat5(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.37 new_primPlusNat4(Succ(x0)) 130.73/78.37 new_primPlusNat8(Zero, x0) 130.73/78.37 new_primPlusNat3(Zero) 130.73/78.37 new_primPlusNat7(x0, Zero) 130.73/78.37 new_primPlusNat5(Zero) 130.73/78.37 new_primPlusNat7(x0, Succ(x1)) 130.73/78.37 new_primPlusNat4(Zero) 130.73/78.37 new_primPlusNat2(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Zero) 130.73/78.37 130.73/78.37 We have to consider all minimal (P,Q,R)-chains. 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (513) TransformationProof (EQUIVALENT) 130.73/78.37 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.73/78.37 130.73/78.37 (new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc)) 130.73/78.37 130.73/78.37 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (514) 130.73/78.37 Obligation: 130.73/78.37 Q DP problem: 130.73/78.37 The TRS P consists of the following rules: 130.73/78.37 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 130.73/78.37 The TRS R consists of the following rules: 130.73/78.37 130.73/78.37 new_primMulNat2(zzz4739) -> Zero 130.73/78.37 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.37 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.37 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.37 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.37 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.37 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.37 new_primPlusNat2(Zero) -> Zero 130.73/78.37 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.37 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.37 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.37 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.37 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.37 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.37 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.37 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.37 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.37 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.37 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.37 130.73/78.37 The set Q consists of the following terms: 130.73/78.37 130.73/78.37 new_primPlusNat1(Succ(x0)) 130.73/78.37 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.37 new_primPlusNat1(Zero) 130.73/78.37 new_primPlusNat2(Zero) 130.73/78.37 new_primPlusNat3(Succ(x0)) 130.73/78.37 new_primPlusNat8(Succ(x0), x1) 130.73/78.37 new_primMulNat2(x0) 130.73/78.37 new_primPlusNat6(x0, Succ(x1)) 130.73/78.37 new_primPlusNat0(Succ(x0), Zero) 130.73/78.37 new_primPlusNat6(x0, Zero) 130.73/78.37 new_primPlusNat5(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.37 new_primPlusNat4(Succ(x0)) 130.73/78.37 new_primPlusNat8(Zero, x0) 130.73/78.37 new_primPlusNat3(Zero) 130.73/78.37 new_primPlusNat7(x0, Zero) 130.73/78.37 new_primPlusNat5(Zero) 130.73/78.37 new_primPlusNat7(x0, Succ(x1)) 130.73/78.37 new_primPlusNat4(Zero) 130.73/78.37 new_primPlusNat2(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Zero) 130.73/78.37 130.73/78.37 We have to consider all minimal (P,Q,R)-chains. 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (515) TransformationProof (EQUIVALENT) 130.73/78.37 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.73/78.37 130.73/78.37 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb)) 130.73/78.37 130.73/78.37 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (516) 130.73/78.37 Obligation: 130.73/78.37 Q DP problem: 130.73/78.37 The TRS P consists of the following rules: 130.73/78.37 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.37 130.73/78.37 The TRS R consists of the following rules: 130.73/78.37 130.73/78.37 new_primMulNat2(zzz4739) -> Zero 130.73/78.37 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.37 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.37 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.37 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.37 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.37 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.37 new_primPlusNat2(Zero) -> Zero 130.73/78.37 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.37 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.37 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.37 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.37 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.37 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.37 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.37 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.37 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.37 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.37 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.37 130.73/78.37 The set Q consists of the following terms: 130.73/78.37 130.73/78.37 new_primPlusNat1(Succ(x0)) 130.73/78.37 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.37 new_primPlusNat1(Zero) 130.73/78.37 new_primPlusNat2(Zero) 130.73/78.37 new_primPlusNat3(Succ(x0)) 130.73/78.37 new_primPlusNat8(Succ(x0), x1) 130.73/78.37 new_primMulNat2(x0) 130.73/78.37 new_primPlusNat6(x0, Succ(x1)) 130.73/78.37 new_primPlusNat0(Succ(x0), Zero) 130.73/78.37 new_primPlusNat6(x0, Zero) 130.73/78.37 new_primPlusNat5(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.37 new_primPlusNat4(Succ(x0)) 130.73/78.37 new_primPlusNat8(Zero, x0) 130.73/78.37 new_primPlusNat3(Zero) 130.73/78.37 new_primPlusNat7(x0, Zero) 130.73/78.37 new_primPlusNat5(Zero) 130.73/78.37 new_primPlusNat7(x0, Succ(x1)) 130.73/78.37 new_primPlusNat4(Zero) 130.73/78.37 new_primPlusNat2(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Zero) 130.73/78.37 130.73/78.37 We have to consider all minimal (P,Q,R)-chains. 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (517) TransformationProof (EQUIVALENT) 130.73/78.37 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Zero)))))), bb) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.73/78.37 130.73/78.37 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb)) 130.73/78.37 130.73/78.37 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (518) 130.73/78.37 Obligation: 130.73/78.37 Q DP problem: 130.73/78.37 The TRS P consists of the following rules: 130.73/78.37 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.73/78.37 130.73/78.37 The TRS R consists of the following rules: 130.73/78.37 130.73/78.37 new_primMulNat2(zzz4739) -> Zero 130.73/78.37 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.37 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.37 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.37 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.37 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.37 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.37 new_primPlusNat2(Zero) -> Zero 130.73/78.37 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.37 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.37 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.37 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.37 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.37 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.37 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.37 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.37 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.37 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.37 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.37 130.73/78.37 The set Q consists of the following terms: 130.73/78.37 130.73/78.37 new_primPlusNat1(Succ(x0)) 130.73/78.37 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.37 new_primPlusNat1(Zero) 130.73/78.37 new_primPlusNat2(Zero) 130.73/78.37 new_primPlusNat3(Succ(x0)) 130.73/78.37 new_primPlusNat8(Succ(x0), x1) 130.73/78.37 new_primMulNat2(x0) 130.73/78.37 new_primPlusNat6(x0, Succ(x1)) 130.73/78.37 new_primPlusNat0(Succ(x0), Zero) 130.73/78.37 new_primPlusNat6(x0, Zero) 130.73/78.37 new_primPlusNat5(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.37 new_primPlusNat4(Succ(x0)) 130.73/78.37 new_primPlusNat8(Zero, x0) 130.73/78.37 new_primPlusNat3(Zero) 130.73/78.37 new_primPlusNat7(x0, Zero) 130.73/78.37 new_primPlusNat5(Zero) 130.73/78.37 new_primPlusNat7(x0, Succ(x1)) 130.73/78.37 new_primPlusNat4(Zero) 130.73/78.37 new_primPlusNat2(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Zero) 130.73/78.37 130.73/78.37 We have to consider all minimal (P,Q,R)-chains. 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (519) TransformationProof (EQUIVALENT) 130.73/78.37 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), bb) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.73/78.37 130.73/78.37 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))), bb)) 130.73/78.37 130.73/78.37 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (520) 130.73/78.37 Obligation: 130.73/78.37 Q DP problem: 130.73/78.37 The TRS P consists of the following rules: 130.73/78.37 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))), bb) 130.73/78.37 130.73/78.37 The TRS R consists of the following rules: 130.73/78.37 130.73/78.37 new_primMulNat2(zzz4739) -> Zero 130.73/78.37 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.37 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.37 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.37 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.37 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.37 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.37 new_primPlusNat2(Zero) -> Zero 130.73/78.37 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.37 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.37 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.37 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.37 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.37 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.37 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.37 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.37 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.37 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.37 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.37 130.73/78.37 The set Q consists of the following terms: 130.73/78.37 130.73/78.37 new_primPlusNat1(Succ(x0)) 130.73/78.37 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.37 new_primPlusNat1(Zero) 130.73/78.37 new_primPlusNat2(Zero) 130.73/78.37 new_primPlusNat3(Succ(x0)) 130.73/78.37 new_primPlusNat8(Succ(x0), x1) 130.73/78.37 new_primMulNat2(x0) 130.73/78.37 new_primPlusNat6(x0, Succ(x1)) 130.73/78.37 new_primPlusNat0(Succ(x0), Zero) 130.73/78.37 new_primPlusNat6(x0, Zero) 130.73/78.37 new_primPlusNat5(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.37 new_primPlusNat4(Succ(x0)) 130.73/78.37 new_primPlusNat8(Zero, x0) 130.73/78.37 new_primPlusNat3(Zero) 130.73/78.37 new_primPlusNat7(x0, Zero) 130.73/78.37 new_primPlusNat5(Zero) 130.73/78.37 new_primPlusNat7(x0, Succ(x1)) 130.73/78.37 new_primPlusNat4(Zero) 130.73/78.37 new_primPlusNat2(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Zero) 130.73/78.37 130.73/78.37 We have to consider all minimal (P,Q,R)-chains. 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (521) TransformationProof (EQUIVALENT) 130.73/78.37 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(Zero))))))), bb) at position [10,0,0] we obtained the following new rules [LPAR04]: 130.73/78.37 130.73/78.37 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb)) 130.73/78.37 130.73/78.37 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (522) 130.73/78.37 Obligation: 130.73/78.37 Q DP problem: 130.73/78.37 The TRS P consists of the following rules: 130.73/78.37 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.37 130.73/78.37 The TRS R consists of the following rules: 130.73/78.37 130.73/78.37 new_primMulNat2(zzz4739) -> Zero 130.73/78.37 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.37 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.37 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.37 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.37 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.37 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.37 new_primPlusNat2(Zero) -> Zero 130.73/78.37 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.37 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.37 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.37 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.37 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.37 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.37 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.37 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.37 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.37 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.37 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.37 130.73/78.37 The set Q consists of the following terms: 130.73/78.37 130.73/78.37 new_primPlusNat1(Succ(x0)) 130.73/78.37 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.37 new_primPlusNat1(Zero) 130.73/78.37 new_primPlusNat2(Zero) 130.73/78.37 new_primPlusNat3(Succ(x0)) 130.73/78.37 new_primPlusNat8(Succ(x0), x1) 130.73/78.37 new_primMulNat2(x0) 130.73/78.37 new_primPlusNat6(x0, Succ(x1)) 130.73/78.37 new_primPlusNat0(Succ(x0), Zero) 130.73/78.37 new_primPlusNat6(x0, Zero) 130.73/78.37 new_primPlusNat5(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.37 new_primPlusNat4(Succ(x0)) 130.73/78.37 new_primPlusNat8(Zero, x0) 130.73/78.37 new_primPlusNat3(Zero) 130.73/78.37 new_primPlusNat7(x0, Zero) 130.73/78.37 new_primPlusNat5(Zero) 130.73/78.37 new_primPlusNat7(x0, Succ(x1)) 130.73/78.37 new_primPlusNat4(Zero) 130.73/78.37 new_primPlusNat2(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Zero) 130.73/78.37 130.73/78.37 We have to consider all minimal (P,Q,R)-chains. 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (523) TransformationProof (EQUIVALENT) 130.73/78.37 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) at position [12,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.73/78.37 130.73/78.37 (new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h),new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h)) 130.73/78.37 130.73/78.37 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (524) 130.73/78.37 Obligation: 130.73/78.37 Q DP problem: 130.73/78.37 The TRS P consists of the following rules: 130.73/78.37 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 130.73/78.37 The TRS R consists of the following rules: 130.73/78.37 130.73/78.37 new_primMulNat2(zzz4739) -> Zero 130.73/78.37 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.37 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.37 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.37 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.37 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.37 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.37 new_primPlusNat2(Zero) -> Zero 130.73/78.37 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.37 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.37 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.37 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.37 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.37 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.37 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.37 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.37 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.37 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.37 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.37 130.73/78.37 The set Q consists of the following terms: 130.73/78.37 130.73/78.37 new_primPlusNat1(Succ(x0)) 130.73/78.37 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.37 new_primPlusNat1(Zero) 130.73/78.37 new_primPlusNat2(Zero) 130.73/78.37 new_primPlusNat3(Succ(x0)) 130.73/78.37 new_primPlusNat8(Succ(x0), x1) 130.73/78.37 new_primMulNat2(x0) 130.73/78.37 new_primPlusNat6(x0, Succ(x1)) 130.73/78.37 new_primPlusNat0(Succ(x0), Zero) 130.73/78.37 new_primPlusNat6(x0, Zero) 130.73/78.37 new_primPlusNat5(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.37 new_primPlusNat4(Succ(x0)) 130.73/78.37 new_primPlusNat8(Zero, x0) 130.73/78.37 new_primPlusNat3(Zero) 130.73/78.37 new_primPlusNat7(x0, Zero) 130.73/78.37 new_primPlusNat5(Zero) 130.73/78.37 new_primPlusNat7(x0, Succ(x1)) 130.73/78.37 new_primPlusNat4(Zero) 130.73/78.37 new_primPlusNat2(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Zero) 130.73/78.37 130.73/78.37 We have to consider all minimal (P,Q,R)-chains. 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (525) TransformationProof (EQUIVALENT) 130.73/78.37 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) at position [12,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.73/78.37 130.73/78.37 (new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h),new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h)) 130.73/78.37 130.73/78.37 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (526) 130.73/78.37 Obligation: 130.73/78.37 Q DP problem: 130.73/78.37 The TRS P consists of the following rules: 130.73/78.37 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), zzz34200000, bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))), bb) 130.73/78.37 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.37 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.37 130.73/78.37 The TRS R consists of the following rules: 130.73/78.37 130.73/78.37 new_primMulNat2(zzz4739) -> Zero 130.73/78.37 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.37 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.37 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.37 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.37 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.37 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.37 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.37 new_primPlusNat2(Zero) -> Zero 130.73/78.37 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.37 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.37 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.37 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.37 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.37 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.37 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.37 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.37 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.37 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.37 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.37 130.73/78.37 The set Q consists of the following terms: 130.73/78.37 130.73/78.37 new_primPlusNat1(Succ(x0)) 130.73/78.37 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.37 new_primPlusNat1(Zero) 130.73/78.37 new_primPlusNat2(Zero) 130.73/78.37 new_primPlusNat3(Succ(x0)) 130.73/78.37 new_primPlusNat8(Succ(x0), x1) 130.73/78.37 new_primMulNat2(x0) 130.73/78.37 new_primPlusNat6(x0, Succ(x1)) 130.73/78.37 new_primPlusNat0(Succ(x0), Zero) 130.73/78.37 new_primPlusNat6(x0, Zero) 130.73/78.37 new_primPlusNat5(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.37 new_primPlusNat4(Succ(x0)) 130.73/78.37 new_primPlusNat8(Zero, x0) 130.73/78.37 new_primPlusNat3(Zero) 130.73/78.37 new_primPlusNat7(x0, Zero) 130.73/78.37 new_primPlusNat5(Zero) 130.73/78.37 new_primPlusNat7(x0, Succ(x1)) 130.73/78.37 new_primPlusNat4(Zero) 130.73/78.37 new_primPlusNat2(Succ(x0)) 130.73/78.37 new_primPlusNat0(Zero, Zero) 130.73/78.37 130.73/78.37 We have to consider all minimal (P,Q,R)-chains. 130.73/78.37 ---------------------------------------- 130.73/78.37 130.73/78.37 (527) UsableRulesProof (EQUIVALENT) 130.73/78.37 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (528) 130.73/78.38 Obligation: 130.73/78.38 Q DP problem: 130.73/78.38 The TRS P consists of the following rules: 130.73/78.38 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 130.73/78.38 The TRS R consists of the following rules: 130.73/78.38 130.73/78.38 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.38 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.38 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.38 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.38 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.38 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.38 new_primPlusNat2(Zero) -> Zero 130.73/78.38 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.38 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.38 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.38 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.38 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.38 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.38 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.38 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.38 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.38 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.38 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.38 130.73/78.38 The set Q consists of the following terms: 130.73/78.38 130.73/78.38 new_primPlusNat1(Succ(x0)) 130.73/78.38 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.38 new_primPlusNat1(Zero) 130.73/78.38 new_primPlusNat2(Zero) 130.73/78.38 new_primPlusNat3(Succ(x0)) 130.73/78.38 new_primPlusNat8(Succ(x0), x1) 130.73/78.38 new_primMulNat2(x0) 130.73/78.38 new_primPlusNat6(x0, Succ(x1)) 130.73/78.38 new_primPlusNat0(Succ(x0), Zero) 130.73/78.38 new_primPlusNat6(x0, Zero) 130.73/78.38 new_primPlusNat5(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.38 new_primPlusNat4(Succ(x0)) 130.73/78.38 new_primPlusNat8(Zero, x0) 130.73/78.38 new_primPlusNat3(Zero) 130.73/78.38 new_primPlusNat7(x0, Zero) 130.73/78.38 new_primPlusNat5(Zero) 130.73/78.38 new_primPlusNat7(x0, Succ(x1)) 130.73/78.38 new_primPlusNat4(Zero) 130.73/78.38 new_primPlusNat2(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Zero) 130.73/78.38 130.73/78.38 We have to consider all minimal (P,Q,R)-chains. 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (529) QReductionProof (EQUIVALENT) 130.73/78.38 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.73/78.38 130.73/78.38 new_primMulNat2(x0) 130.73/78.38 130.73/78.38 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (530) 130.73/78.38 Obligation: 130.73/78.38 Q DP problem: 130.73/78.38 The TRS P consists of the following rules: 130.73/78.38 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 130.73/78.38 The TRS R consists of the following rules: 130.73/78.38 130.73/78.38 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.38 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.38 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.38 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.38 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.38 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.38 new_primPlusNat2(Zero) -> Zero 130.73/78.38 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.38 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.38 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.38 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.38 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.38 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.38 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.38 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.38 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.38 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.38 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.38 130.73/78.38 The set Q consists of the following terms: 130.73/78.38 130.73/78.38 new_primPlusNat1(Succ(x0)) 130.73/78.38 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.38 new_primPlusNat1(Zero) 130.73/78.38 new_primPlusNat2(Zero) 130.73/78.38 new_primPlusNat3(Succ(x0)) 130.73/78.38 new_primPlusNat8(Succ(x0), x1) 130.73/78.38 new_primPlusNat6(x0, Succ(x1)) 130.73/78.38 new_primPlusNat0(Succ(x0), Zero) 130.73/78.38 new_primPlusNat6(x0, Zero) 130.73/78.38 new_primPlusNat5(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.38 new_primPlusNat4(Succ(x0)) 130.73/78.38 new_primPlusNat8(Zero, x0) 130.73/78.38 new_primPlusNat3(Zero) 130.73/78.38 new_primPlusNat7(x0, Zero) 130.73/78.38 new_primPlusNat5(Zero) 130.73/78.38 new_primPlusNat7(x0, Succ(x1)) 130.73/78.38 new_primPlusNat4(Zero) 130.73/78.38 new_primPlusNat2(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Zero) 130.73/78.38 130.73/78.38 We have to consider all minimal (P,Q,R)-chains. 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (531) TransformationProof (EQUIVALENT) 130.73/78.38 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) at position [10,0,0,0,0] we obtained the following new rules [LPAR04]: 130.73/78.38 130.73/78.38 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb)) 130.73/78.38 130.73/78.38 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (532) 130.73/78.38 Obligation: 130.73/78.38 Q DP problem: 130.73/78.38 The TRS P consists of the following rules: 130.73/78.38 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.38 130.73/78.38 The TRS R consists of the following rules: 130.73/78.38 130.73/78.38 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.38 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.38 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.38 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.38 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.38 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.38 new_primPlusNat2(Zero) -> Zero 130.73/78.38 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.38 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.38 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.38 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.38 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.38 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.38 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.38 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.38 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.38 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.38 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.38 130.73/78.38 The set Q consists of the following terms: 130.73/78.38 130.73/78.38 new_primPlusNat1(Succ(x0)) 130.73/78.38 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.38 new_primPlusNat1(Zero) 130.73/78.38 new_primPlusNat2(Zero) 130.73/78.38 new_primPlusNat3(Succ(x0)) 130.73/78.38 new_primPlusNat8(Succ(x0), x1) 130.73/78.38 new_primPlusNat6(x0, Succ(x1)) 130.73/78.38 new_primPlusNat0(Succ(x0), Zero) 130.73/78.38 new_primPlusNat6(x0, Zero) 130.73/78.38 new_primPlusNat5(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.38 new_primPlusNat4(Succ(x0)) 130.73/78.38 new_primPlusNat8(Zero, x0) 130.73/78.38 new_primPlusNat3(Zero) 130.73/78.38 new_primPlusNat7(x0, Zero) 130.73/78.38 new_primPlusNat5(Zero) 130.73/78.38 new_primPlusNat7(x0, Succ(x1)) 130.73/78.38 new_primPlusNat4(Zero) 130.73/78.38 new_primPlusNat2(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Zero) 130.73/78.38 130.73/78.38 We have to consider all minimal (P,Q,R)-chains. 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (533) TransformationProof (EQUIVALENT) 130.73/78.38 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))))), bb) at position [10,0,0,0] we obtained the following new rules [LPAR04]: 130.73/78.38 130.73/78.38 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb)) 130.73/78.38 130.73/78.38 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (534) 130.73/78.38 Obligation: 130.73/78.38 Q DP problem: 130.73/78.38 The TRS P consists of the following rules: 130.73/78.38 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.73/78.38 130.73/78.38 The TRS R consists of the following rules: 130.73/78.38 130.73/78.38 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.38 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.38 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.38 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.38 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.38 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.38 new_primPlusNat2(Zero) -> Zero 130.73/78.38 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.38 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.38 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.38 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.38 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.38 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.38 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.38 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.38 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.38 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.38 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.38 130.73/78.38 The set Q consists of the following terms: 130.73/78.38 130.73/78.38 new_primPlusNat1(Succ(x0)) 130.73/78.38 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.38 new_primPlusNat1(Zero) 130.73/78.38 new_primPlusNat2(Zero) 130.73/78.38 new_primPlusNat3(Succ(x0)) 130.73/78.38 new_primPlusNat8(Succ(x0), x1) 130.73/78.38 new_primPlusNat6(x0, Succ(x1)) 130.73/78.38 new_primPlusNat0(Succ(x0), Zero) 130.73/78.38 new_primPlusNat6(x0, Zero) 130.73/78.38 new_primPlusNat5(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.38 new_primPlusNat4(Succ(x0)) 130.73/78.38 new_primPlusNat8(Zero, x0) 130.73/78.38 new_primPlusNat3(Zero) 130.73/78.38 new_primPlusNat7(x0, Zero) 130.73/78.38 new_primPlusNat5(Zero) 130.73/78.38 new_primPlusNat7(x0, Succ(x1)) 130.73/78.38 new_primPlusNat4(Zero) 130.73/78.38 new_primPlusNat2(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Zero) 130.73/78.38 130.73/78.38 We have to consider all minimal (P,Q,R)-chains. 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (535) TransformationProof (EQUIVALENT) 130.73/78.38 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) at position [10,0,0,0,0] we obtained the following new rules [LPAR04]: 130.73/78.38 130.73/78.38 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb)) 130.73/78.38 130.73/78.38 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (536) 130.73/78.38 Obligation: 130.73/78.38 Q DP problem: 130.73/78.38 The TRS P consists of the following rules: 130.73/78.38 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.38 130.73/78.38 The TRS R consists of the following rules: 130.73/78.38 130.73/78.38 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.38 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.38 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.38 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.38 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.38 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.38 new_primPlusNat2(Zero) -> Zero 130.73/78.38 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.38 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.38 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.38 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.38 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.38 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.38 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.38 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.38 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.38 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.38 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.38 130.73/78.38 The set Q consists of the following terms: 130.73/78.38 130.73/78.38 new_primPlusNat1(Succ(x0)) 130.73/78.38 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.38 new_primPlusNat1(Zero) 130.73/78.38 new_primPlusNat2(Zero) 130.73/78.38 new_primPlusNat3(Succ(x0)) 130.73/78.38 new_primPlusNat8(Succ(x0), x1) 130.73/78.38 new_primPlusNat6(x0, Succ(x1)) 130.73/78.38 new_primPlusNat0(Succ(x0), Zero) 130.73/78.38 new_primPlusNat6(x0, Zero) 130.73/78.38 new_primPlusNat5(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.38 new_primPlusNat4(Succ(x0)) 130.73/78.38 new_primPlusNat8(Zero, x0) 130.73/78.38 new_primPlusNat3(Zero) 130.73/78.38 new_primPlusNat7(x0, Zero) 130.73/78.38 new_primPlusNat5(Zero) 130.73/78.38 new_primPlusNat7(x0, Succ(x1)) 130.73/78.38 new_primPlusNat4(Zero) 130.73/78.38 new_primPlusNat2(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Zero) 130.73/78.38 130.73/78.38 We have to consider all minimal (P,Q,R)-chains. 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (537) TransformationProof (EQUIVALENT) 130.73/78.38 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), zzz34200000, bb) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.73/78.38 130.73/78.38 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb)) 130.73/78.38 130.73/78.38 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (538) 130.73/78.38 Obligation: 130.73/78.38 Q DP problem: 130.73/78.38 The TRS P consists of the following rules: 130.73/78.38 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.73/78.38 130.73/78.38 The TRS R consists of the following rules: 130.73/78.38 130.73/78.38 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.38 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.38 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.38 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.38 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.38 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.38 new_primPlusNat2(Zero) -> Zero 130.73/78.38 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.38 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.38 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.38 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.38 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.38 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.38 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.38 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.38 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.38 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.38 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.38 130.73/78.38 The set Q consists of the following terms: 130.73/78.38 130.73/78.38 new_primPlusNat1(Succ(x0)) 130.73/78.38 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.38 new_primPlusNat1(Zero) 130.73/78.38 new_primPlusNat2(Zero) 130.73/78.38 new_primPlusNat3(Succ(x0)) 130.73/78.38 new_primPlusNat8(Succ(x0), x1) 130.73/78.38 new_primPlusNat6(x0, Succ(x1)) 130.73/78.38 new_primPlusNat0(Succ(x0), Zero) 130.73/78.38 new_primPlusNat6(x0, Zero) 130.73/78.38 new_primPlusNat5(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.38 new_primPlusNat4(Succ(x0)) 130.73/78.38 new_primPlusNat8(Zero, x0) 130.73/78.38 new_primPlusNat3(Zero) 130.73/78.38 new_primPlusNat7(x0, Zero) 130.73/78.38 new_primPlusNat5(Zero) 130.73/78.38 new_primPlusNat7(x0, Succ(x1)) 130.73/78.38 new_primPlusNat4(Zero) 130.73/78.38 new_primPlusNat2(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Zero) 130.73/78.38 130.73/78.38 We have to consider all minimal (P,Q,R)-chains. 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (539) TransformationProof (EQUIVALENT) 130.73/78.38 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.73/78.38 130.73/78.38 (new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc)) 130.73/78.38 130.73/78.38 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (540) 130.73/78.38 Obligation: 130.73/78.38 Q DP problem: 130.73/78.38 The TRS P consists of the following rules: 130.73/78.38 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 130.73/78.38 The TRS R consists of the following rules: 130.73/78.38 130.73/78.38 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.38 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.38 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.38 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.38 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.38 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.38 new_primPlusNat2(Zero) -> Zero 130.73/78.38 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.38 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.38 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.38 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.38 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.38 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.38 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.38 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.38 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.38 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.38 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.38 130.73/78.38 The set Q consists of the following terms: 130.73/78.38 130.73/78.38 new_primPlusNat1(Succ(x0)) 130.73/78.38 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.38 new_primPlusNat1(Zero) 130.73/78.38 new_primPlusNat2(Zero) 130.73/78.38 new_primPlusNat3(Succ(x0)) 130.73/78.38 new_primPlusNat8(Succ(x0), x1) 130.73/78.38 new_primPlusNat6(x0, Succ(x1)) 130.73/78.38 new_primPlusNat0(Succ(x0), Zero) 130.73/78.38 new_primPlusNat6(x0, Zero) 130.73/78.38 new_primPlusNat5(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.38 new_primPlusNat4(Succ(x0)) 130.73/78.38 new_primPlusNat8(Zero, x0) 130.73/78.38 new_primPlusNat3(Zero) 130.73/78.38 new_primPlusNat7(x0, Zero) 130.73/78.38 new_primPlusNat5(Zero) 130.73/78.38 new_primPlusNat7(x0, Succ(x1)) 130.73/78.38 new_primPlusNat4(Zero) 130.73/78.38 new_primPlusNat2(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Zero) 130.73/78.38 130.73/78.38 We have to consider all minimal (P,Q,R)-chains. 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (541) TransformationProof (EQUIVALENT) 130.73/78.38 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.73/78.38 130.73/78.38 (new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc)) 130.73/78.38 130.73/78.38 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (542) 130.73/78.38 Obligation: 130.73/78.38 Q DP problem: 130.73/78.38 The TRS P consists of the following rules: 130.73/78.38 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 130.73/78.38 The TRS R consists of the following rules: 130.73/78.38 130.73/78.38 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.38 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.38 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.38 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.38 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.38 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.38 new_primPlusNat2(Zero) -> Zero 130.73/78.38 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.38 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.38 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.38 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.38 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.38 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.38 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.38 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.38 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.38 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.38 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.38 130.73/78.38 The set Q consists of the following terms: 130.73/78.38 130.73/78.38 new_primPlusNat1(Succ(x0)) 130.73/78.38 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.38 new_primPlusNat1(Zero) 130.73/78.38 new_primPlusNat2(Zero) 130.73/78.38 new_primPlusNat3(Succ(x0)) 130.73/78.38 new_primPlusNat8(Succ(x0), x1) 130.73/78.38 new_primPlusNat6(x0, Succ(x1)) 130.73/78.38 new_primPlusNat0(Succ(x0), Zero) 130.73/78.38 new_primPlusNat6(x0, Zero) 130.73/78.38 new_primPlusNat5(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.38 new_primPlusNat4(Succ(x0)) 130.73/78.38 new_primPlusNat8(Zero, x0) 130.73/78.38 new_primPlusNat3(Zero) 130.73/78.38 new_primPlusNat7(x0, Zero) 130.73/78.38 new_primPlusNat5(Zero) 130.73/78.38 new_primPlusNat7(x0, Succ(x1)) 130.73/78.38 new_primPlusNat4(Zero) 130.73/78.38 new_primPlusNat2(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Zero) 130.73/78.38 130.73/78.38 We have to consider all minimal (P,Q,R)-chains. 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (543) TransformationProof (EQUIVALENT) 130.73/78.38 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.73/78.38 130.73/78.38 (new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc)) 130.73/78.38 130.73/78.38 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (544) 130.73/78.38 Obligation: 130.73/78.38 Q DP problem: 130.73/78.38 The TRS P consists of the following rules: 130.73/78.38 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 130.73/78.38 The TRS R consists of the following rules: 130.73/78.38 130.73/78.38 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.38 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.38 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.38 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.38 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.38 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.38 new_primPlusNat2(Zero) -> Zero 130.73/78.38 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.38 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.38 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.38 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.38 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.38 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.38 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.38 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.38 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.38 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.38 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.38 130.73/78.38 The set Q consists of the following terms: 130.73/78.38 130.73/78.38 new_primPlusNat1(Succ(x0)) 130.73/78.38 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.38 new_primPlusNat1(Zero) 130.73/78.38 new_primPlusNat2(Zero) 130.73/78.38 new_primPlusNat3(Succ(x0)) 130.73/78.38 new_primPlusNat8(Succ(x0), x1) 130.73/78.38 new_primPlusNat6(x0, Succ(x1)) 130.73/78.38 new_primPlusNat0(Succ(x0), Zero) 130.73/78.38 new_primPlusNat6(x0, Zero) 130.73/78.38 new_primPlusNat5(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.38 new_primPlusNat4(Succ(x0)) 130.73/78.38 new_primPlusNat8(Zero, x0) 130.73/78.38 new_primPlusNat3(Zero) 130.73/78.38 new_primPlusNat7(x0, Zero) 130.73/78.38 new_primPlusNat5(Zero) 130.73/78.38 new_primPlusNat7(x0, Succ(x1)) 130.73/78.38 new_primPlusNat4(Zero) 130.73/78.38 new_primPlusNat2(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Zero) 130.73/78.38 130.73/78.38 We have to consider all minimal (P,Q,R)-chains. 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (545) TransformationProof (EQUIVALENT) 130.73/78.38 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) at position [11,0] we obtained the following new rules [LPAR04]: 130.73/78.38 130.73/78.38 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb)) 130.73/78.38 130.73/78.38 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (546) 130.73/78.38 Obligation: 130.73/78.38 Q DP problem: 130.73/78.38 The TRS P consists of the following rules: 130.73/78.38 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.73/78.38 130.73/78.38 The TRS R consists of the following rules: 130.73/78.38 130.73/78.38 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.38 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.38 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.38 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.38 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.38 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.38 new_primPlusNat2(Zero) -> Zero 130.73/78.38 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.38 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.38 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.38 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.38 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.38 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.38 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.38 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.38 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.38 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.38 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.38 130.73/78.38 The set Q consists of the following terms: 130.73/78.38 130.73/78.38 new_primPlusNat1(Succ(x0)) 130.73/78.38 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.38 new_primPlusNat1(Zero) 130.73/78.38 new_primPlusNat2(Zero) 130.73/78.38 new_primPlusNat3(Succ(x0)) 130.73/78.38 new_primPlusNat8(Succ(x0), x1) 130.73/78.38 new_primPlusNat6(x0, Succ(x1)) 130.73/78.38 new_primPlusNat0(Succ(x0), Zero) 130.73/78.38 new_primPlusNat6(x0, Zero) 130.73/78.38 new_primPlusNat5(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.38 new_primPlusNat4(Succ(x0)) 130.73/78.38 new_primPlusNat8(Zero, x0) 130.73/78.38 new_primPlusNat3(Zero) 130.73/78.38 new_primPlusNat7(x0, Zero) 130.73/78.38 new_primPlusNat5(Zero) 130.73/78.38 new_primPlusNat7(x0, Succ(x1)) 130.73/78.38 new_primPlusNat4(Zero) 130.73/78.38 new_primPlusNat2(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Zero) 130.73/78.38 130.73/78.38 We have to consider all minimal (P,Q,R)-chains. 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (547) TransformationProof (EQUIVALENT) 130.73/78.38 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) at position [11,0] we obtained the following new rules [LPAR04]: 130.73/78.38 130.73/78.38 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb)) 130.73/78.38 130.73/78.38 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (548) 130.73/78.38 Obligation: 130.73/78.38 Q DP problem: 130.73/78.38 The TRS P consists of the following rules: 130.73/78.38 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.73/78.38 130.73/78.38 The TRS R consists of the following rules: 130.73/78.38 130.73/78.38 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.38 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.38 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.38 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.38 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.38 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.38 new_primPlusNat2(Zero) -> Zero 130.73/78.38 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.38 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.38 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.38 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.38 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.38 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.38 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.38 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.38 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.38 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.38 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.38 130.73/78.38 The set Q consists of the following terms: 130.73/78.38 130.73/78.38 new_primPlusNat1(Succ(x0)) 130.73/78.38 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.38 new_primPlusNat1(Zero) 130.73/78.38 new_primPlusNat2(Zero) 130.73/78.38 new_primPlusNat3(Succ(x0)) 130.73/78.38 new_primPlusNat8(Succ(x0), x1) 130.73/78.38 new_primPlusNat6(x0, Succ(x1)) 130.73/78.38 new_primPlusNat0(Succ(x0), Zero) 130.73/78.38 new_primPlusNat6(x0, Zero) 130.73/78.38 new_primPlusNat5(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.38 new_primPlusNat4(Succ(x0)) 130.73/78.38 new_primPlusNat8(Zero, x0) 130.73/78.38 new_primPlusNat3(Zero) 130.73/78.38 new_primPlusNat7(x0, Zero) 130.73/78.38 new_primPlusNat5(Zero) 130.73/78.38 new_primPlusNat7(x0, Succ(x1)) 130.73/78.38 new_primPlusNat4(Zero) 130.73/78.38 new_primPlusNat2(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Zero) 130.73/78.38 130.73/78.38 We have to consider all minimal (P,Q,R)-chains. 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (549) TransformationProof (EQUIVALENT) 130.73/78.38 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))), bb) at position [11,0] we obtained the following new rules [LPAR04]: 130.73/78.38 130.73/78.38 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb)) 130.73/78.38 130.73/78.38 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (550) 130.73/78.38 Obligation: 130.73/78.38 Q DP problem: 130.73/78.38 The TRS P consists of the following rules: 130.73/78.38 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.73/78.38 130.73/78.38 The TRS R consists of the following rules: 130.73/78.38 130.73/78.38 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.38 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.38 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.38 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.38 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.38 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.38 new_primPlusNat2(Zero) -> Zero 130.73/78.38 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.38 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.38 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.38 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.38 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.38 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.38 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.38 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.38 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.38 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.38 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.38 130.73/78.38 The set Q consists of the following terms: 130.73/78.38 130.73/78.38 new_primPlusNat1(Succ(x0)) 130.73/78.38 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.38 new_primPlusNat1(Zero) 130.73/78.38 new_primPlusNat2(Zero) 130.73/78.38 new_primPlusNat3(Succ(x0)) 130.73/78.38 new_primPlusNat8(Succ(x0), x1) 130.73/78.38 new_primPlusNat6(x0, Succ(x1)) 130.73/78.38 new_primPlusNat0(Succ(x0), Zero) 130.73/78.38 new_primPlusNat6(x0, Zero) 130.73/78.38 new_primPlusNat5(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.38 new_primPlusNat4(Succ(x0)) 130.73/78.38 new_primPlusNat8(Zero, x0) 130.73/78.38 new_primPlusNat3(Zero) 130.73/78.38 new_primPlusNat7(x0, Zero) 130.73/78.38 new_primPlusNat5(Zero) 130.73/78.38 new_primPlusNat7(x0, Succ(x1)) 130.73/78.38 new_primPlusNat4(Zero) 130.73/78.38 new_primPlusNat2(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Zero) 130.73/78.38 130.73/78.38 We have to consider all minimal (P,Q,R)-chains. 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (551) TransformationProof (EQUIVALENT) 130.73/78.38 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))), bb) at position [10,0] we obtained the following new rules [LPAR04]: 130.73/78.38 130.73/78.38 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb)) 130.73/78.38 130.73/78.38 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (552) 130.73/78.38 Obligation: 130.73/78.38 Q DP problem: 130.73/78.38 The TRS P consists of the following rules: 130.73/78.38 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.73/78.38 130.73/78.38 The TRS R consists of the following rules: 130.73/78.38 130.73/78.38 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.38 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.38 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.38 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.38 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.38 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.38 new_primPlusNat2(Zero) -> Zero 130.73/78.38 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.38 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.38 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.38 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.38 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.38 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.38 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.38 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.38 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.38 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.38 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.38 130.73/78.38 The set Q consists of the following terms: 130.73/78.38 130.73/78.38 new_primPlusNat1(Succ(x0)) 130.73/78.38 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.38 new_primPlusNat1(Zero) 130.73/78.38 new_primPlusNat2(Zero) 130.73/78.38 new_primPlusNat3(Succ(x0)) 130.73/78.38 new_primPlusNat8(Succ(x0), x1) 130.73/78.38 new_primPlusNat6(x0, Succ(x1)) 130.73/78.38 new_primPlusNat0(Succ(x0), Zero) 130.73/78.38 new_primPlusNat6(x0, Zero) 130.73/78.38 new_primPlusNat5(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.38 new_primPlusNat4(Succ(x0)) 130.73/78.38 new_primPlusNat8(Zero, x0) 130.73/78.38 new_primPlusNat3(Zero) 130.73/78.38 new_primPlusNat7(x0, Zero) 130.73/78.38 new_primPlusNat5(Zero) 130.73/78.38 new_primPlusNat7(x0, Succ(x1)) 130.73/78.38 new_primPlusNat4(Zero) 130.73/78.38 new_primPlusNat2(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Zero) 130.73/78.38 130.73/78.38 We have to consider all minimal (P,Q,R)-chains. 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (553) TransformationProof (EQUIVALENT) 130.73/78.38 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.73/78.38 130.73/78.38 (new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h),new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h)) 130.73/78.38 130.73/78.38 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (554) 130.73/78.38 Obligation: 130.73/78.38 Q DP problem: 130.73/78.38 The TRS P consists of the following rules: 130.73/78.38 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 130.73/78.38 The TRS R consists of the following rules: 130.73/78.38 130.73/78.38 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.38 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.38 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.38 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.38 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.38 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.38 new_primPlusNat2(Zero) -> Zero 130.73/78.38 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.38 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.38 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.38 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.38 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.38 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.38 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.38 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.38 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.38 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.38 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.38 130.73/78.38 The set Q consists of the following terms: 130.73/78.38 130.73/78.38 new_primPlusNat1(Succ(x0)) 130.73/78.38 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.38 new_primPlusNat1(Zero) 130.73/78.38 new_primPlusNat2(Zero) 130.73/78.38 new_primPlusNat3(Succ(x0)) 130.73/78.38 new_primPlusNat8(Succ(x0), x1) 130.73/78.38 new_primPlusNat6(x0, Succ(x1)) 130.73/78.38 new_primPlusNat0(Succ(x0), Zero) 130.73/78.38 new_primPlusNat6(x0, Zero) 130.73/78.38 new_primPlusNat5(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.38 new_primPlusNat4(Succ(x0)) 130.73/78.38 new_primPlusNat8(Zero, x0) 130.73/78.38 new_primPlusNat3(Zero) 130.73/78.38 new_primPlusNat7(x0, Zero) 130.73/78.38 new_primPlusNat5(Zero) 130.73/78.38 new_primPlusNat7(x0, Succ(x1)) 130.73/78.38 new_primPlusNat4(Zero) 130.73/78.38 new_primPlusNat2(Succ(x0)) 130.73/78.38 new_primPlusNat0(Zero, Zero) 130.73/78.38 130.73/78.38 We have to consider all minimal (P,Q,R)-chains. 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (555) TransformationProof (EQUIVALENT) 130.73/78.38 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.73/78.38 130.73/78.38 (new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h),new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h)) 130.73/78.38 130.73/78.38 130.73/78.38 ---------------------------------------- 130.73/78.38 130.73/78.38 (556) 130.73/78.38 Obligation: 130.73/78.38 Q DP problem: 130.73/78.38 The TRS P consists of the following rules: 130.73/78.38 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.73/78.38 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.73/78.38 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.38 130.73/78.38 The TRS R consists of the following rules: 130.73/78.38 130.73/78.38 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.38 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.38 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.38 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.38 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.38 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.38 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.38 new_primPlusNat2(Zero) -> Zero 130.73/78.39 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.73/78.39 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.73/78.39 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.73/78.39 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.73/78.39 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.73/78.39 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.73/78.39 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.73/78.39 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.73/78.39 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.73/78.39 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.73/78.39 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.73/78.39 130.73/78.39 The set Q consists of the following terms: 130.73/78.39 130.73/78.39 new_primPlusNat1(Succ(x0)) 130.73/78.39 new_primPlusNat0(Succ(x0), Succ(x1)) 130.73/78.39 new_primPlusNat1(Zero) 130.73/78.39 new_primPlusNat2(Zero) 130.73/78.39 new_primPlusNat3(Succ(x0)) 130.73/78.39 new_primPlusNat8(Succ(x0), x1) 130.73/78.39 new_primPlusNat6(x0, Succ(x1)) 130.73/78.39 new_primPlusNat0(Succ(x0), Zero) 130.73/78.39 new_primPlusNat6(x0, Zero) 130.73/78.39 new_primPlusNat5(Succ(x0)) 130.73/78.39 new_primPlusNat0(Zero, Succ(x0)) 130.73/78.39 new_primPlusNat4(Succ(x0)) 130.73/78.39 new_primPlusNat8(Zero, x0) 130.73/78.39 new_primPlusNat3(Zero) 130.73/78.39 new_primPlusNat7(x0, Zero) 130.73/78.39 new_primPlusNat5(Zero) 130.73/78.39 new_primPlusNat7(x0, Succ(x1)) 130.73/78.39 new_primPlusNat4(Zero) 130.73/78.39 new_primPlusNat2(Succ(x0)) 130.73/78.39 new_primPlusNat0(Zero, Zero) 130.73/78.39 130.73/78.39 We have to consider all minimal (P,Q,R)-chains. 130.73/78.39 ---------------------------------------- 130.73/78.39 130.73/78.39 (557) TransformationProof (EQUIVALENT) 130.73/78.39 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) at position [10,0,0,0] we obtained the following new rules [LPAR04]: 130.73/78.39 130.73/78.39 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb)) 130.73/78.39 130.73/78.39 130.73/78.39 ---------------------------------------- 130.73/78.39 130.73/78.39 (558) 130.73/78.39 Obligation: 130.73/78.39 Q DP problem: 130.73/78.39 The TRS P consists of the following rules: 130.73/78.39 130.73/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.73/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.73/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.73/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.73/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.73/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.73/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.73/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.73/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.73/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.73/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.73/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.73/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.73/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.73/78.39 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.73/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.73/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.73/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.73/78.39 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.73/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.73/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.73/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.73/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.73/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.73/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.73/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.73/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.73/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.73/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.73/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.73/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.39 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.39 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.73/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.73/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.73/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.73/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.73/78.39 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.73/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.73/78.39 130.73/78.39 The TRS R consists of the following rules: 130.73/78.39 130.73/78.39 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.73/78.39 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.73/78.39 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.73/78.39 new_primPlusNat0(Zero, Zero) -> Zero 130.73/78.39 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.73/78.39 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.73/78.39 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.73/78.39 new_primPlusNat3(Zero) -> Succ(Zero) 130.73/78.39 new_primPlusNat2(Zero) -> Zero 130.73/78.39 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.39 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.39 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.74/78.39 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.39 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.39 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.39 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.39 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.39 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.39 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.39 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.39 130.74/78.39 The set Q consists of the following terms: 130.74/78.39 130.74/78.39 new_primPlusNat1(Succ(x0)) 130.74/78.39 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.39 new_primPlusNat1(Zero) 130.74/78.39 new_primPlusNat2(Zero) 130.74/78.39 new_primPlusNat3(Succ(x0)) 130.74/78.39 new_primPlusNat8(Succ(x0), x1) 130.74/78.39 new_primPlusNat6(x0, Succ(x1)) 130.74/78.39 new_primPlusNat0(Succ(x0), Zero) 130.74/78.39 new_primPlusNat6(x0, Zero) 130.74/78.39 new_primPlusNat5(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.39 new_primPlusNat4(Succ(x0)) 130.74/78.39 new_primPlusNat8(Zero, x0) 130.74/78.39 new_primPlusNat3(Zero) 130.74/78.39 new_primPlusNat7(x0, Zero) 130.74/78.39 new_primPlusNat5(Zero) 130.74/78.39 new_primPlusNat7(x0, Succ(x1)) 130.74/78.39 new_primPlusNat4(Zero) 130.74/78.39 new_primPlusNat2(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Zero) 130.74/78.39 130.74/78.39 We have to consider all minimal (P,Q,R)-chains. 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (559) TransformationProof (EQUIVALENT) 130.74/78.39 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) at position [10,0,0] we obtained the following new rules [LPAR04]: 130.74/78.39 130.74/78.39 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb)) 130.74/78.39 130.74/78.39 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (560) 130.74/78.39 Obligation: 130.74/78.39 Q DP problem: 130.74/78.39 The TRS P consists of the following rules: 130.74/78.39 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.39 130.74/78.39 The TRS R consists of the following rules: 130.74/78.39 130.74/78.39 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.39 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.39 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.39 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.39 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.39 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.39 new_primPlusNat2(Zero) -> Zero 130.74/78.39 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.39 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.39 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.74/78.39 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.39 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.39 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.39 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.39 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.39 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.39 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.39 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.39 130.74/78.39 The set Q consists of the following terms: 130.74/78.39 130.74/78.39 new_primPlusNat1(Succ(x0)) 130.74/78.39 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.39 new_primPlusNat1(Zero) 130.74/78.39 new_primPlusNat2(Zero) 130.74/78.39 new_primPlusNat3(Succ(x0)) 130.74/78.39 new_primPlusNat8(Succ(x0), x1) 130.74/78.39 new_primPlusNat6(x0, Succ(x1)) 130.74/78.39 new_primPlusNat0(Succ(x0), Zero) 130.74/78.39 new_primPlusNat6(x0, Zero) 130.74/78.39 new_primPlusNat5(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.39 new_primPlusNat4(Succ(x0)) 130.74/78.39 new_primPlusNat8(Zero, x0) 130.74/78.39 new_primPlusNat3(Zero) 130.74/78.39 new_primPlusNat7(x0, Zero) 130.74/78.39 new_primPlusNat5(Zero) 130.74/78.39 new_primPlusNat7(x0, Succ(x1)) 130.74/78.39 new_primPlusNat4(Zero) 130.74/78.39 new_primPlusNat2(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Zero) 130.74/78.39 130.74/78.39 We have to consider all minimal (P,Q,R)-chains. 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (561) TransformationProof (EQUIVALENT) 130.74/78.39 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) at position [10,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.39 130.74/78.39 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb)) 130.74/78.39 130.74/78.39 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (562) 130.74/78.39 Obligation: 130.74/78.39 Q DP problem: 130.74/78.39 The TRS P consists of the following rules: 130.74/78.39 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.39 130.74/78.39 The TRS R consists of the following rules: 130.74/78.39 130.74/78.39 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.39 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.39 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.39 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.39 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.39 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.39 new_primPlusNat2(Zero) -> Zero 130.74/78.39 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.39 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.39 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.74/78.39 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.39 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.39 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.39 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.39 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.39 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.39 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.39 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.39 130.74/78.39 The set Q consists of the following terms: 130.74/78.39 130.74/78.39 new_primPlusNat1(Succ(x0)) 130.74/78.39 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.39 new_primPlusNat1(Zero) 130.74/78.39 new_primPlusNat2(Zero) 130.74/78.39 new_primPlusNat3(Succ(x0)) 130.74/78.39 new_primPlusNat8(Succ(x0), x1) 130.74/78.39 new_primPlusNat6(x0, Succ(x1)) 130.74/78.39 new_primPlusNat0(Succ(x0), Zero) 130.74/78.39 new_primPlusNat6(x0, Zero) 130.74/78.39 new_primPlusNat5(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.39 new_primPlusNat4(Succ(x0)) 130.74/78.39 new_primPlusNat8(Zero, x0) 130.74/78.39 new_primPlusNat3(Zero) 130.74/78.39 new_primPlusNat7(x0, Zero) 130.74/78.39 new_primPlusNat5(Zero) 130.74/78.39 new_primPlusNat7(x0, Succ(x1)) 130.74/78.39 new_primPlusNat4(Zero) 130.74/78.39 new_primPlusNat2(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Zero) 130.74/78.39 130.74/78.39 We have to consider all minimal (P,Q,R)-chains. 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (563) TransformationProof (EQUIVALENT) 130.74/78.39 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.39 130.74/78.39 (new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc)) 130.74/78.39 130.74/78.39 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (564) 130.74/78.39 Obligation: 130.74/78.39 Q DP problem: 130.74/78.39 The TRS P consists of the following rules: 130.74/78.39 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 130.74/78.39 The TRS R consists of the following rules: 130.74/78.39 130.74/78.39 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.39 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.39 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.39 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.39 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.39 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.39 new_primPlusNat2(Zero) -> Zero 130.74/78.39 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.39 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.39 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.74/78.39 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.39 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.39 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.39 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.39 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.39 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.39 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.39 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.39 130.74/78.39 The set Q consists of the following terms: 130.74/78.39 130.74/78.39 new_primPlusNat1(Succ(x0)) 130.74/78.39 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.39 new_primPlusNat1(Zero) 130.74/78.39 new_primPlusNat2(Zero) 130.74/78.39 new_primPlusNat3(Succ(x0)) 130.74/78.39 new_primPlusNat8(Succ(x0), x1) 130.74/78.39 new_primPlusNat6(x0, Succ(x1)) 130.74/78.39 new_primPlusNat0(Succ(x0), Zero) 130.74/78.39 new_primPlusNat6(x0, Zero) 130.74/78.39 new_primPlusNat5(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.39 new_primPlusNat4(Succ(x0)) 130.74/78.39 new_primPlusNat8(Zero, x0) 130.74/78.39 new_primPlusNat3(Zero) 130.74/78.39 new_primPlusNat7(x0, Zero) 130.74/78.39 new_primPlusNat5(Zero) 130.74/78.39 new_primPlusNat7(x0, Succ(x1)) 130.74/78.39 new_primPlusNat4(Zero) 130.74/78.39 new_primPlusNat2(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Zero) 130.74/78.39 130.74/78.39 We have to consider all minimal (P,Q,R)-chains. 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (565) TransformationProof (EQUIVALENT) 130.74/78.39 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.39 130.74/78.39 (new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc)) 130.74/78.39 130.74/78.39 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (566) 130.74/78.39 Obligation: 130.74/78.39 Q DP problem: 130.74/78.39 The TRS P consists of the following rules: 130.74/78.39 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 130.74/78.39 The TRS R consists of the following rules: 130.74/78.39 130.74/78.39 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.39 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.39 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.39 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.39 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.39 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.39 new_primPlusNat2(Zero) -> Zero 130.74/78.39 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.39 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.39 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.74/78.39 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.39 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.39 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.39 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.39 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.39 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.39 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.39 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.39 130.74/78.39 The set Q consists of the following terms: 130.74/78.39 130.74/78.39 new_primPlusNat1(Succ(x0)) 130.74/78.39 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.39 new_primPlusNat1(Zero) 130.74/78.39 new_primPlusNat2(Zero) 130.74/78.39 new_primPlusNat3(Succ(x0)) 130.74/78.39 new_primPlusNat8(Succ(x0), x1) 130.74/78.39 new_primPlusNat6(x0, Succ(x1)) 130.74/78.39 new_primPlusNat0(Succ(x0), Zero) 130.74/78.39 new_primPlusNat6(x0, Zero) 130.74/78.39 new_primPlusNat5(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.39 new_primPlusNat4(Succ(x0)) 130.74/78.39 new_primPlusNat8(Zero, x0) 130.74/78.39 new_primPlusNat3(Zero) 130.74/78.39 new_primPlusNat7(x0, Zero) 130.74/78.39 new_primPlusNat5(Zero) 130.74/78.39 new_primPlusNat7(x0, Succ(x1)) 130.74/78.39 new_primPlusNat4(Zero) 130.74/78.39 new_primPlusNat2(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Zero) 130.74/78.39 130.74/78.39 We have to consider all minimal (P,Q,R)-chains. 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (567) TransformationProof (EQUIVALENT) 130.74/78.39 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz3882), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.39 130.74/78.39 (new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc)) 130.74/78.39 130.74/78.39 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (568) 130.74/78.39 Obligation: 130.74/78.39 Q DP problem: 130.74/78.39 The TRS P consists of the following rules: 130.74/78.39 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 130.74/78.39 The TRS R consists of the following rules: 130.74/78.39 130.74/78.39 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.39 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.39 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.39 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.39 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.39 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.39 new_primPlusNat2(Zero) -> Zero 130.74/78.39 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.39 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.39 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.74/78.39 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.39 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.39 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.39 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.39 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.39 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.39 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.39 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.39 130.74/78.39 The set Q consists of the following terms: 130.74/78.39 130.74/78.39 new_primPlusNat1(Succ(x0)) 130.74/78.39 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.39 new_primPlusNat1(Zero) 130.74/78.39 new_primPlusNat2(Zero) 130.74/78.39 new_primPlusNat3(Succ(x0)) 130.74/78.39 new_primPlusNat8(Succ(x0), x1) 130.74/78.39 new_primPlusNat6(x0, Succ(x1)) 130.74/78.39 new_primPlusNat0(Succ(x0), Zero) 130.74/78.39 new_primPlusNat6(x0, Zero) 130.74/78.39 new_primPlusNat5(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.39 new_primPlusNat4(Succ(x0)) 130.74/78.39 new_primPlusNat8(Zero, x0) 130.74/78.39 new_primPlusNat3(Zero) 130.74/78.39 new_primPlusNat7(x0, Zero) 130.74/78.39 new_primPlusNat5(Zero) 130.74/78.39 new_primPlusNat7(x0, Succ(x1)) 130.74/78.39 new_primPlusNat4(Zero) 130.74/78.39 new_primPlusNat2(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Zero) 130.74/78.39 130.74/78.39 We have to consider all minimal (P,Q,R)-chains. 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (569) TransformationProof (EQUIVALENT) 130.74/78.39 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) at position [11] we obtained the following new rules [LPAR04]: 130.74/78.39 130.74/78.39 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb)) 130.74/78.39 130.74/78.39 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (570) 130.74/78.39 Obligation: 130.74/78.39 Q DP problem: 130.74/78.39 The TRS P consists of the following rules: 130.74/78.39 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.39 130.74/78.39 The TRS R consists of the following rules: 130.74/78.39 130.74/78.39 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.39 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.39 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.39 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.39 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.39 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.39 new_primPlusNat2(Zero) -> Zero 130.74/78.39 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.39 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.39 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.74/78.39 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.39 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.39 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.39 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.39 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.39 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.39 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.39 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.39 130.74/78.39 The set Q consists of the following terms: 130.74/78.39 130.74/78.39 new_primPlusNat1(Succ(x0)) 130.74/78.39 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.39 new_primPlusNat1(Zero) 130.74/78.39 new_primPlusNat2(Zero) 130.74/78.39 new_primPlusNat3(Succ(x0)) 130.74/78.39 new_primPlusNat8(Succ(x0), x1) 130.74/78.39 new_primPlusNat6(x0, Succ(x1)) 130.74/78.39 new_primPlusNat0(Succ(x0), Zero) 130.74/78.39 new_primPlusNat6(x0, Zero) 130.74/78.39 new_primPlusNat5(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.39 new_primPlusNat4(Succ(x0)) 130.74/78.39 new_primPlusNat8(Zero, x0) 130.74/78.39 new_primPlusNat3(Zero) 130.74/78.39 new_primPlusNat7(x0, Zero) 130.74/78.39 new_primPlusNat5(Zero) 130.74/78.39 new_primPlusNat7(x0, Succ(x1)) 130.74/78.39 new_primPlusNat4(Zero) 130.74/78.39 new_primPlusNat2(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Zero) 130.74/78.39 130.74/78.39 We have to consider all minimal (P,Q,R)-chains. 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (571) DependencyGraphProof (EQUIVALENT) 130.74/78.39 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (572) 130.74/78.39 Obligation: 130.74/78.39 Q DP problem: 130.74/78.39 The TRS P consists of the following rules: 130.74/78.39 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 130.74/78.39 The TRS R consists of the following rules: 130.74/78.39 130.74/78.39 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.39 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.39 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.39 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.39 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.39 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.39 new_primPlusNat2(Zero) -> Zero 130.74/78.39 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.39 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.39 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.74/78.39 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.39 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.39 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.39 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.39 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.39 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.39 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.39 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.39 130.74/78.39 The set Q consists of the following terms: 130.74/78.39 130.74/78.39 new_primPlusNat1(Succ(x0)) 130.74/78.39 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.39 new_primPlusNat1(Zero) 130.74/78.39 new_primPlusNat2(Zero) 130.74/78.39 new_primPlusNat3(Succ(x0)) 130.74/78.39 new_primPlusNat8(Succ(x0), x1) 130.74/78.39 new_primPlusNat6(x0, Succ(x1)) 130.74/78.39 new_primPlusNat0(Succ(x0), Zero) 130.74/78.39 new_primPlusNat6(x0, Zero) 130.74/78.39 new_primPlusNat5(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.39 new_primPlusNat4(Succ(x0)) 130.74/78.39 new_primPlusNat8(Zero, x0) 130.74/78.39 new_primPlusNat3(Zero) 130.74/78.39 new_primPlusNat7(x0, Zero) 130.74/78.39 new_primPlusNat5(Zero) 130.74/78.39 new_primPlusNat7(x0, Succ(x1)) 130.74/78.39 new_primPlusNat4(Zero) 130.74/78.39 new_primPlusNat2(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Zero) 130.74/78.39 130.74/78.39 We have to consider all minimal (P,Q,R)-chains. 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (573) TransformationProof (EQUIVALENT) 130.74/78.39 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat3(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) at position [11] we obtained the following new rules [LPAR04]: 130.74/78.39 130.74/78.39 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))))), bb)) 130.74/78.39 130.74/78.39 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (574) 130.74/78.39 Obligation: 130.74/78.39 Q DP problem: 130.74/78.39 The TRS P consists of the following rules: 130.74/78.39 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Zero, Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))))), bb) 130.74/78.39 130.74/78.39 The TRS R consists of the following rules: 130.74/78.39 130.74/78.39 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.39 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.39 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.39 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.39 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.39 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.39 new_primPlusNat2(Zero) -> Zero 130.74/78.39 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.39 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.39 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.74/78.39 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.39 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.39 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.39 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.39 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.39 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.39 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.39 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.39 130.74/78.39 The set Q consists of the following terms: 130.74/78.39 130.74/78.39 new_primPlusNat1(Succ(x0)) 130.74/78.39 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.39 new_primPlusNat1(Zero) 130.74/78.39 new_primPlusNat2(Zero) 130.74/78.39 new_primPlusNat3(Succ(x0)) 130.74/78.39 new_primPlusNat8(Succ(x0), x1) 130.74/78.39 new_primPlusNat6(x0, Succ(x1)) 130.74/78.39 new_primPlusNat0(Succ(x0), Zero) 130.74/78.39 new_primPlusNat6(x0, Zero) 130.74/78.39 new_primPlusNat5(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.39 new_primPlusNat4(Succ(x0)) 130.74/78.39 new_primPlusNat8(Zero, x0) 130.74/78.39 new_primPlusNat3(Zero) 130.74/78.39 new_primPlusNat7(x0, Zero) 130.74/78.39 new_primPlusNat5(Zero) 130.74/78.39 new_primPlusNat7(x0, Succ(x1)) 130.74/78.39 new_primPlusNat4(Zero) 130.74/78.39 new_primPlusNat2(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Zero) 130.74/78.39 130.74/78.39 We have to consider all minimal (P,Q,R)-chains. 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (575) DependencyGraphProof (EQUIVALENT) 130.74/78.39 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (576) 130.74/78.39 Obligation: 130.74/78.39 Q DP problem: 130.74/78.39 The TRS P consists of the following rules: 130.74/78.39 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 130.74/78.39 The TRS R consists of the following rules: 130.74/78.39 130.74/78.39 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.39 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.39 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.39 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.39 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.39 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.39 new_primPlusNat2(Zero) -> Zero 130.74/78.39 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.39 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.39 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.74/78.39 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.39 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.39 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.39 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.39 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.39 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.39 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.39 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.39 130.74/78.39 The set Q consists of the following terms: 130.74/78.39 130.74/78.39 new_primPlusNat1(Succ(x0)) 130.74/78.39 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.39 new_primPlusNat1(Zero) 130.74/78.39 new_primPlusNat2(Zero) 130.74/78.39 new_primPlusNat3(Succ(x0)) 130.74/78.39 new_primPlusNat8(Succ(x0), x1) 130.74/78.39 new_primPlusNat6(x0, Succ(x1)) 130.74/78.39 new_primPlusNat0(Succ(x0), Zero) 130.74/78.39 new_primPlusNat6(x0, Zero) 130.74/78.39 new_primPlusNat5(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.39 new_primPlusNat4(Succ(x0)) 130.74/78.39 new_primPlusNat8(Zero, x0) 130.74/78.39 new_primPlusNat3(Zero) 130.74/78.39 new_primPlusNat7(x0, Zero) 130.74/78.39 new_primPlusNat5(Zero) 130.74/78.39 new_primPlusNat7(x0, Succ(x1)) 130.74/78.39 new_primPlusNat4(Zero) 130.74/78.39 new_primPlusNat2(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Zero) 130.74/78.39 130.74/78.39 We have to consider all minimal (P,Q,R)-chains. 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (577) TransformationProof (EQUIVALENT) 130.74/78.39 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))), bb) at position [10] we obtained the following new rules [LPAR04]: 130.74/78.39 130.74/78.39 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb)) 130.74/78.39 130.74/78.39 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (578) 130.74/78.39 Obligation: 130.74/78.39 Q DP problem: 130.74/78.39 The TRS P consists of the following rules: 130.74/78.39 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.39 130.74/78.39 The TRS R consists of the following rules: 130.74/78.39 130.74/78.39 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.39 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.39 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.39 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.39 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.39 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.39 new_primPlusNat2(Zero) -> Zero 130.74/78.39 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.39 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.39 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.74/78.39 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.39 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.39 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.39 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.39 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.39 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.39 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.39 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.39 130.74/78.39 The set Q consists of the following terms: 130.74/78.39 130.74/78.39 new_primPlusNat1(Succ(x0)) 130.74/78.39 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.39 new_primPlusNat1(Zero) 130.74/78.39 new_primPlusNat2(Zero) 130.74/78.39 new_primPlusNat3(Succ(x0)) 130.74/78.39 new_primPlusNat8(Succ(x0), x1) 130.74/78.39 new_primPlusNat6(x0, Succ(x1)) 130.74/78.39 new_primPlusNat0(Succ(x0), Zero) 130.74/78.39 new_primPlusNat6(x0, Zero) 130.74/78.39 new_primPlusNat5(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.39 new_primPlusNat4(Succ(x0)) 130.74/78.39 new_primPlusNat8(Zero, x0) 130.74/78.39 new_primPlusNat3(Zero) 130.74/78.39 new_primPlusNat7(x0, Zero) 130.74/78.39 new_primPlusNat5(Zero) 130.74/78.39 new_primPlusNat7(x0, Succ(x1)) 130.74/78.39 new_primPlusNat4(Zero) 130.74/78.39 new_primPlusNat2(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Zero) 130.74/78.39 130.74/78.39 We have to consider all minimal (P,Q,R)-chains. 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (579) DependencyGraphProof (EQUIVALENT) 130.74/78.39 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (580) 130.74/78.39 Obligation: 130.74/78.39 Q DP problem: 130.74/78.39 The TRS P consists of the following rules: 130.74/78.39 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.39 130.74/78.39 The TRS R consists of the following rules: 130.74/78.39 130.74/78.39 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.39 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.39 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.39 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.39 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.39 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.39 new_primPlusNat2(Zero) -> Zero 130.74/78.39 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.39 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.39 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.74/78.39 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.39 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.39 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.39 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.39 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.39 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.39 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.39 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.39 130.74/78.39 The set Q consists of the following terms: 130.74/78.39 130.74/78.39 new_primPlusNat1(Succ(x0)) 130.74/78.39 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.39 new_primPlusNat1(Zero) 130.74/78.39 new_primPlusNat2(Zero) 130.74/78.39 new_primPlusNat3(Succ(x0)) 130.74/78.39 new_primPlusNat8(Succ(x0), x1) 130.74/78.39 new_primPlusNat6(x0, Succ(x1)) 130.74/78.39 new_primPlusNat0(Succ(x0), Zero) 130.74/78.39 new_primPlusNat6(x0, Zero) 130.74/78.39 new_primPlusNat5(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.39 new_primPlusNat4(Succ(x0)) 130.74/78.39 new_primPlusNat8(Zero, x0) 130.74/78.39 new_primPlusNat3(Zero) 130.74/78.39 new_primPlusNat7(x0, Zero) 130.74/78.39 new_primPlusNat5(Zero) 130.74/78.39 new_primPlusNat7(x0, Succ(x1)) 130.74/78.39 new_primPlusNat4(Zero) 130.74/78.39 new_primPlusNat2(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Zero) 130.74/78.39 130.74/78.39 We have to consider all minimal (P,Q,R)-chains. 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (581) TransformationProof (EQUIVALENT) 130.74/78.39 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) at position [10,0,0] we obtained the following new rules [LPAR04]: 130.74/78.39 130.74/78.39 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb)) 130.74/78.39 130.74/78.39 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (582) 130.74/78.39 Obligation: 130.74/78.39 Q DP problem: 130.74/78.39 The TRS P consists of the following rules: 130.74/78.39 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.39 130.74/78.39 The TRS R consists of the following rules: 130.74/78.39 130.74/78.39 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.39 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.39 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.39 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.39 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.39 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.39 new_primPlusNat2(Zero) -> Zero 130.74/78.39 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.39 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.39 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.74/78.39 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.39 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.39 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.39 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.39 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.39 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.39 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.39 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.39 130.74/78.39 The set Q consists of the following terms: 130.74/78.39 130.74/78.39 new_primPlusNat1(Succ(x0)) 130.74/78.39 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.39 new_primPlusNat1(Zero) 130.74/78.39 new_primPlusNat2(Zero) 130.74/78.39 new_primPlusNat3(Succ(x0)) 130.74/78.39 new_primPlusNat8(Succ(x0), x1) 130.74/78.39 new_primPlusNat6(x0, Succ(x1)) 130.74/78.39 new_primPlusNat0(Succ(x0), Zero) 130.74/78.39 new_primPlusNat6(x0, Zero) 130.74/78.39 new_primPlusNat5(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.39 new_primPlusNat4(Succ(x0)) 130.74/78.39 new_primPlusNat8(Zero, x0) 130.74/78.39 new_primPlusNat3(Zero) 130.74/78.39 new_primPlusNat7(x0, Zero) 130.74/78.39 new_primPlusNat5(Zero) 130.74/78.39 new_primPlusNat7(x0, Succ(x1)) 130.74/78.39 new_primPlusNat4(Zero) 130.74/78.39 new_primPlusNat2(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Zero) 130.74/78.39 130.74/78.39 We have to consider all minimal (P,Q,R)-chains. 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (583) TransformationProof (EQUIVALENT) 130.74/78.39 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) at position [12,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.39 130.74/78.39 (new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h),new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h)) 130.74/78.39 130.74/78.39 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (584) 130.74/78.39 Obligation: 130.74/78.39 Q DP problem: 130.74/78.39 The TRS P consists of the following rules: 130.74/78.39 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 130.74/78.39 The TRS R consists of the following rules: 130.74/78.39 130.74/78.39 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.39 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.39 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.39 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.39 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.39 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.39 new_primPlusNat2(Zero) -> Zero 130.74/78.39 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.39 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.39 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.74/78.39 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.39 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.39 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.39 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.39 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.39 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.39 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.39 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.39 130.74/78.39 The set Q consists of the following terms: 130.74/78.39 130.74/78.39 new_primPlusNat1(Succ(x0)) 130.74/78.39 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.39 new_primPlusNat1(Zero) 130.74/78.39 new_primPlusNat2(Zero) 130.74/78.39 new_primPlusNat3(Succ(x0)) 130.74/78.39 new_primPlusNat8(Succ(x0), x1) 130.74/78.39 new_primPlusNat6(x0, Succ(x1)) 130.74/78.39 new_primPlusNat0(Succ(x0), Zero) 130.74/78.39 new_primPlusNat6(x0, Zero) 130.74/78.39 new_primPlusNat5(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.39 new_primPlusNat4(Succ(x0)) 130.74/78.39 new_primPlusNat8(Zero, x0) 130.74/78.39 new_primPlusNat3(Zero) 130.74/78.39 new_primPlusNat7(x0, Zero) 130.74/78.39 new_primPlusNat5(Zero) 130.74/78.39 new_primPlusNat7(x0, Succ(x1)) 130.74/78.39 new_primPlusNat4(Zero) 130.74/78.39 new_primPlusNat2(Succ(x0)) 130.74/78.39 new_primPlusNat0(Zero, Zero) 130.74/78.39 130.74/78.39 We have to consider all minimal (P,Q,R)-chains. 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (585) TransformationProof (EQUIVALENT) 130.74/78.39 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))), bb) at position [11] we obtained the following new rules [LPAR04]: 130.74/78.39 130.74/78.39 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb)) 130.74/78.39 130.74/78.39 130.74/78.39 ---------------------------------------- 130.74/78.39 130.74/78.39 (586) 130.74/78.39 Obligation: 130.74/78.39 Q DP problem: 130.74/78.39 The TRS P consists of the following rules: 130.74/78.39 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.39 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.39 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.39 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.39 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.39 130.74/78.39 The TRS R consists of the following rules: 130.74/78.39 130.74/78.39 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.39 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.39 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.39 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.39 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.39 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.39 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.39 new_primPlusNat2(Zero) -> Zero 130.74/78.39 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.39 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.39 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.74/78.39 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.39 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.39 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.39 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.39 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.40 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.40 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.40 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.40 130.74/78.40 The set Q consists of the following terms: 130.74/78.40 130.74/78.40 new_primPlusNat1(Succ(x0)) 130.74/78.40 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.40 new_primPlusNat1(Zero) 130.74/78.40 new_primPlusNat2(Zero) 130.74/78.40 new_primPlusNat3(Succ(x0)) 130.74/78.40 new_primPlusNat8(Succ(x0), x1) 130.74/78.40 new_primPlusNat6(x0, Succ(x1)) 130.74/78.40 new_primPlusNat0(Succ(x0), Zero) 130.74/78.40 new_primPlusNat6(x0, Zero) 130.74/78.40 new_primPlusNat5(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.40 new_primPlusNat4(Succ(x0)) 130.74/78.40 new_primPlusNat8(Zero, x0) 130.74/78.40 new_primPlusNat3(Zero) 130.74/78.40 new_primPlusNat7(x0, Zero) 130.74/78.40 new_primPlusNat5(Zero) 130.74/78.40 new_primPlusNat7(x0, Succ(x1)) 130.74/78.40 new_primPlusNat4(Zero) 130.74/78.40 new_primPlusNat2(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Zero) 130.74/78.40 130.74/78.40 We have to consider all minimal (P,Q,R)-chains. 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (587) DependencyGraphProof (EQUIVALENT) 130.74/78.40 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (588) 130.74/78.40 Obligation: 130.74/78.40 Q DP problem: 130.74/78.40 The TRS P consists of the following rules: 130.74/78.40 130.74/78.40 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 130.74/78.40 The TRS R consists of the following rules: 130.74/78.40 130.74/78.40 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.40 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.40 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.40 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.40 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.40 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.40 new_primPlusNat2(Zero) -> Zero 130.74/78.40 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.40 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.40 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.74/78.40 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.40 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.40 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.40 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.40 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.40 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.40 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.40 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.40 130.74/78.40 The set Q consists of the following terms: 130.74/78.40 130.74/78.40 new_primPlusNat1(Succ(x0)) 130.74/78.40 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.40 new_primPlusNat1(Zero) 130.74/78.40 new_primPlusNat2(Zero) 130.74/78.40 new_primPlusNat3(Succ(x0)) 130.74/78.40 new_primPlusNat8(Succ(x0), x1) 130.74/78.40 new_primPlusNat6(x0, Succ(x1)) 130.74/78.40 new_primPlusNat0(Succ(x0), Zero) 130.74/78.40 new_primPlusNat6(x0, Zero) 130.74/78.40 new_primPlusNat5(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.40 new_primPlusNat4(Succ(x0)) 130.74/78.40 new_primPlusNat8(Zero, x0) 130.74/78.40 new_primPlusNat3(Zero) 130.74/78.40 new_primPlusNat7(x0, Zero) 130.74/78.40 new_primPlusNat5(Zero) 130.74/78.40 new_primPlusNat7(x0, Succ(x1)) 130.74/78.40 new_primPlusNat4(Zero) 130.74/78.40 new_primPlusNat2(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Zero) 130.74/78.40 130.74/78.40 We have to consider all minimal (P,Q,R)-chains. 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (589) TransformationProof (EQUIVALENT) 130.74/78.40 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) at position [10,0] we obtained the following new rules [LPAR04]: 130.74/78.40 130.74/78.40 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb)) 130.74/78.40 130.74/78.40 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (590) 130.74/78.40 Obligation: 130.74/78.40 Q DP problem: 130.74/78.40 The TRS P consists of the following rules: 130.74/78.40 130.74/78.40 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 130.74/78.40 The TRS R consists of the following rules: 130.74/78.40 130.74/78.40 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.40 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.40 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.40 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.40 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.40 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.40 new_primPlusNat2(Zero) -> Zero 130.74/78.40 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.40 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.40 new_primPlusNat5(Zero) -> Succ(Succ(Succ(Zero))) 130.74/78.40 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.40 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.40 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.40 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.40 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.40 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.40 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.40 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.40 130.74/78.40 The set Q consists of the following terms: 130.74/78.40 130.74/78.40 new_primPlusNat1(Succ(x0)) 130.74/78.40 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.40 new_primPlusNat1(Zero) 130.74/78.40 new_primPlusNat2(Zero) 130.74/78.40 new_primPlusNat3(Succ(x0)) 130.74/78.40 new_primPlusNat8(Succ(x0), x1) 130.74/78.40 new_primPlusNat6(x0, Succ(x1)) 130.74/78.40 new_primPlusNat0(Succ(x0), Zero) 130.74/78.40 new_primPlusNat6(x0, Zero) 130.74/78.40 new_primPlusNat5(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.40 new_primPlusNat4(Succ(x0)) 130.74/78.40 new_primPlusNat8(Zero, x0) 130.74/78.40 new_primPlusNat3(Zero) 130.74/78.40 new_primPlusNat7(x0, Zero) 130.74/78.40 new_primPlusNat5(Zero) 130.74/78.40 new_primPlusNat7(x0, Succ(x1)) 130.74/78.40 new_primPlusNat4(Zero) 130.74/78.40 new_primPlusNat2(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Zero) 130.74/78.40 130.74/78.40 We have to consider all minimal (P,Q,R)-chains. 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (591) UsableRulesProof (EQUIVALENT) 130.74/78.40 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (592) 130.74/78.40 Obligation: 130.74/78.40 Q DP problem: 130.74/78.40 The TRS P consists of the following rules: 130.74/78.40 130.74/78.40 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 130.74/78.40 The TRS R consists of the following rules: 130.74/78.40 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.40 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.40 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.40 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.40 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.40 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.40 new_primPlusNat2(Zero) -> Zero 130.74/78.40 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.40 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.40 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.40 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.40 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.40 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.40 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.40 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.40 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.40 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.40 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.40 130.74/78.40 The set Q consists of the following terms: 130.74/78.40 130.74/78.40 new_primPlusNat1(Succ(x0)) 130.74/78.40 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.40 new_primPlusNat1(Zero) 130.74/78.40 new_primPlusNat2(Zero) 130.74/78.40 new_primPlusNat3(Succ(x0)) 130.74/78.40 new_primPlusNat8(Succ(x0), x1) 130.74/78.40 new_primPlusNat6(x0, Succ(x1)) 130.74/78.40 new_primPlusNat0(Succ(x0), Zero) 130.74/78.40 new_primPlusNat6(x0, Zero) 130.74/78.40 new_primPlusNat5(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.40 new_primPlusNat4(Succ(x0)) 130.74/78.40 new_primPlusNat8(Zero, x0) 130.74/78.40 new_primPlusNat3(Zero) 130.74/78.40 new_primPlusNat7(x0, Zero) 130.74/78.40 new_primPlusNat5(Zero) 130.74/78.40 new_primPlusNat7(x0, Succ(x1)) 130.74/78.40 new_primPlusNat4(Zero) 130.74/78.40 new_primPlusNat2(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Zero) 130.74/78.40 130.74/78.40 We have to consider all minimal (P,Q,R)-chains. 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (593) TransformationProof (EQUIVALENT) 130.74/78.40 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) at position [12,0,0] we obtained the following new rules [LPAR04]: 130.74/78.40 130.74/78.40 (new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h),new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h)) 130.74/78.40 130.74/78.40 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (594) 130.74/78.40 Obligation: 130.74/78.40 Q DP problem: 130.74/78.40 The TRS P consists of the following rules: 130.74/78.40 130.74/78.40 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 130.74/78.40 The TRS R consists of the following rules: 130.74/78.40 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.40 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.40 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.40 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.40 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.40 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.40 new_primPlusNat2(Zero) -> Zero 130.74/78.40 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.40 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.40 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.40 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.40 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.40 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.40 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.40 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.40 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.40 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.40 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.40 130.74/78.40 The set Q consists of the following terms: 130.74/78.40 130.74/78.40 new_primPlusNat1(Succ(x0)) 130.74/78.40 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.40 new_primPlusNat1(Zero) 130.74/78.40 new_primPlusNat2(Zero) 130.74/78.40 new_primPlusNat3(Succ(x0)) 130.74/78.40 new_primPlusNat8(Succ(x0), x1) 130.74/78.40 new_primPlusNat6(x0, Succ(x1)) 130.74/78.40 new_primPlusNat0(Succ(x0), Zero) 130.74/78.40 new_primPlusNat6(x0, Zero) 130.74/78.40 new_primPlusNat5(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.40 new_primPlusNat4(Succ(x0)) 130.74/78.40 new_primPlusNat8(Zero, x0) 130.74/78.40 new_primPlusNat3(Zero) 130.74/78.40 new_primPlusNat7(x0, Zero) 130.74/78.40 new_primPlusNat5(Zero) 130.74/78.40 new_primPlusNat7(x0, Succ(x1)) 130.74/78.40 new_primPlusNat4(Zero) 130.74/78.40 new_primPlusNat2(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Zero) 130.74/78.40 130.74/78.40 We have to consider all minimal (P,Q,R)-chains. 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (595) TransformationProof (EQUIVALENT) 130.74/78.40 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.74/78.40 130.74/78.40 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb)) 130.74/78.40 130.74/78.40 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (596) 130.74/78.40 Obligation: 130.74/78.40 Q DP problem: 130.74/78.40 The TRS P consists of the following rules: 130.74/78.40 130.74/78.40 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.40 130.74/78.40 The TRS R consists of the following rules: 130.74/78.40 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.40 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.40 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.40 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.40 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.40 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.40 new_primPlusNat2(Zero) -> Zero 130.74/78.40 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.40 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.40 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.40 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.40 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.40 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.40 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.40 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.40 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.40 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.40 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.40 130.74/78.40 The set Q consists of the following terms: 130.74/78.40 130.74/78.40 new_primPlusNat1(Succ(x0)) 130.74/78.40 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.40 new_primPlusNat1(Zero) 130.74/78.40 new_primPlusNat2(Zero) 130.74/78.40 new_primPlusNat3(Succ(x0)) 130.74/78.40 new_primPlusNat8(Succ(x0), x1) 130.74/78.40 new_primPlusNat6(x0, Succ(x1)) 130.74/78.40 new_primPlusNat0(Succ(x0), Zero) 130.74/78.40 new_primPlusNat6(x0, Zero) 130.74/78.40 new_primPlusNat5(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.40 new_primPlusNat4(Succ(x0)) 130.74/78.40 new_primPlusNat8(Zero, x0) 130.74/78.40 new_primPlusNat3(Zero) 130.74/78.40 new_primPlusNat7(x0, Zero) 130.74/78.40 new_primPlusNat5(Zero) 130.74/78.40 new_primPlusNat7(x0, Succ(x1)) 130.74/78.40 new_primPlusNat4(Zero) 130.74/78.40 new_primPlusNat2(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Zero) 130.74/78.40 130.74/78.40 We have to consider all minimal (P,Q,R)-chains. 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (597) TransformationProof (EQUIVALENT) 130.74/78.40 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))))), bb) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.74/78.40 130.74/78.40 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb)) 130.74/78.40 130.74/78.40 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (598) 130.74/78.40 Obligation: 130.74/78.40 Q DP problem: 130.74/78.40 The TRS P consists of the following rules: 130.74/78.40 130.74/78.40 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.40 130.74/78.40 The TRS R consists of the following rules: 130.74/78.40 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.40 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.40 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.40 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.40 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.40 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.40 new_primPlusNat2(Zero) -> Zero 130.74/78.40 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.40 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.40 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.40 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.40 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.40 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.40 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.40 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.40 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.40 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.40 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.40 130.74/78.40 The set Q consists of the following terms: 130.74/78.40 130.74/78.40 new_primPlusNat1(Succ(x0)) 130.74/78.40 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.40 new_primPlusNat1(Zero) 130.74/78.40 new_primPlusNat2(Zero) 130.74/78.40 new_primPlusNat3(Succ(x0)) 130.74/78.40 new_primPlusNat8(Succ(x0), x1) 130.74/78.40 new_primPlusNat6(x0, Succ(x1)) 130.74/78.40 new_primPlusNat0(Succ(x0), Zero) 130.74/78.40 new_primPlusNat6(x0, Zero) 130.74/78.40 new_primPlusNat5(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.40 new_primPlusNat4(Succ(x0)) 130.74/78.40 new_primPlusNat8(Zero, x0) 130.74/78.40 new_primPlusNat3(Zero) 130.74/78.40 new_primPlusNat7(x0, Zero) 130.74/78.40 new_primPlusNat5(Zero) 130.74/78.40 new_primPlusNat7(x0, Succ(x1)) 130.74/78.40 new_primPlusNat4(Zero) 130.74/78.40 new_primPlusNat2(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Zero) 130.74/78.40 130.74/78.40 We have to consider all minimal (P,Q,R)-chains. 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (599) TransformationProof (EQUIVALENT) 130.74/78.40 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))), bb) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.74/78.40 130.74/78.40 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb)) 130.74/78.40 130.74/78.40 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (600) 130.74/78.40 Obligation: 130.74/78.40 Q DP problem: 130.74/78.40 The TRS P consists of the following rules: 130.74/78.40 130.74/78.40 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 130.74/78.40 The TRS R consists of the following rules: 130.74/78.40 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.40 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.40 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.40 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.40 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.40 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.40 new_primPlusNat2(Zero) -> Zero 130.74/78.40 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.40 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.40 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.40 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.40 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.40 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.40 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.40 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.40 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.40 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.40 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.40 130.74/78.40 The set Q consists of the following terms: 130.74/78.40 130.74/78.40 new_primPlusNat1(Succ(x0)) 130.74/78.40 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.40 new_primPlusNat1(Zero) 130.74/78.40 new_primPlusNat2(Zero) 130.74/78.40 new_primPlusNat3(Succ(x0)) 130.74/78.40 new_primPlusNat8(Succ(x0), x1) 130.74/78.40 new_primPlusNat6(x0, Succ(x1)) 130.74/78.40 new_primPlusNat0(Succ(x0), Zero) 130.74/78.40 new_primPlusNat6(x0, Zero) 130.74/78.40 new_primPlusNat5(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.40 new_primPlusNat4(Succ(x0)) 130.74/78.40 new_primPlusNat8(Zero, x0) 130.74/78.40 new_primPlusNat3(Zero) 130.74/78.40 new_primPlusNat7(x0, Zero) 130.74/78.40 new_primPlusNat5(Zero) 130.74/78.40 new_primPlusNat7(x0, Succ(x1)) 130.74/78.40 new_primPlusNat4(Zero) 130.74/78.40 new_primPlusNat2(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Zero) 130.74/78.40 130.74/78.40 We have to consider all minimal (P,Q,R)-chains. 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (601) TransformationProof (EQUIVALENT) 130.74/78.40 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz4708), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) at position [12,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.40 130.74/78.40 (new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h),new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h)) 130.74/78.40 130.74/78.40 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (602) 130.74/78.40 Obligation: 130.74/78.40 Q DP problem: 130.74/78.40 The TRS P consists of the following rules: 130.74/78.40 130.74/78.40 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 130.74/78.40 The TRS R consists of the following rules: 130.74/78.40 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.40 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.40 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.40 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.40 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.40 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.40 new_primPlusNat2(Zero) -> Zero 130.74/78.40 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.40 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.40 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.40 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.40 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.40 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.40 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.40 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.40 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.40 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.40 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.40 130.74/78.40 The set Q consists of the following terms: 130.74/78.40 130.74/78.40 new_primPlusNat1(Succ(x0)) 130.74/78.40 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.40 new_primPlusNat1(Zero) 130.74/78.40 new_primPlusNat2(Zero) 130.74/78.40 new_primPlusNat3(Succ(x0)) 130.74/78.40 new_primPlusNat8(Succ(x0), x1) 130.74/78.40 new_primPlusNat6(x0, Succ(x1)) 130.74/78.40 new_primPlusNat0(Succ(x0), Zero) 130.74/78.40 new_primPlusNat6(x0, Zero) 130.74/78.40 new_primPlusNat5(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.40 new_primPlusNat4(Succ(x0)) 130.74/78.40 new_primPlusNat8(Zero, x0) 130.74/78.40 new_primPlusNat3(Zero) 130.74/78.40 new_primPlusNat7(x0, Zero) 130.74/78.40 new_primPlusNat5(Zero) 130.74/78.40 new_primPlusNat7(x0, Succ(x1)) 130.74/78.40 new_primPlusNat4(Zero) 130.74/78.40 new_primPlusNat2(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Zero) 130.74/78.40 130.74/78.40 We have to consider all minimal (P,Q,R)-chains. 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (603) TransformationProof (EQUIVALENT) 130.74/78.40 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.74/78.40 130.74/78.40 (new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc)) 130.74/78.40 130.74/78.40 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (604) 130.74/78.40 Obligation: 130.74/78.40 Q DP problem: 130.74/78.40 The TRS P consists of the following rules: 130.74/78.40 130.74/78.40 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 130.74/78.40 The TRS R consists of the following rules: 130.74/78.40 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.40 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.40 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.40 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.40 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.40 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.40 new_primPlusNat2(Zero) -> Zero 130.74/78.40 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.40 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.40 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.40 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.40 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.40 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.40 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.40 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.40 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.40 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.40 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.40 130.74/78.40 The set Q consists of the following terms: 130.74/78.40 130.74/78.40 new_primPlusNat1(Succ(x0)) 130.74/78.40 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.40 new_primPlusNat1(Zero) 130.74/78.40 new_primPlusNat2(Zero) 130.74/78.40 new_primPlusNat3(Succ(x0)) 130.74/78.40 new_primPlusNat8(Succ(x0), x1) 130.74/78.40 new_primPlusNat6(x0, Succ(x1)) 130.74/78.40 new_primPlusNat0(Succ(x0), Zero) 130.74/78.40 new_primPlusNat6(x0, Zero) 130.74/78.40 new_primPlusNat5(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.40 new_primPlusNat4(Succ(x0)) 130.74/78.40 new_primPlusNat8(Zero, x0) 130.74/78.40 new_primPlusNat3(Zero) 130.74/78.40 new_primPlusNat7(x0, Zero) 130.74/78.40 new_primPlusNat5(Zero) 130.74/78.40 new_primPlusNat7(x0, Succ(x1)) 130.74/78.40 new_primPlusNat4(Zero) 130.74/78.40 new_primPlusNat2(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Zero) 130.74/78.40 130.74/78.40 We have to consider all minimal (P,Q,R)-chains. 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (605) TransformationProof (EQUIVALENT) 130.74/78.40 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.74/78.40 130.74/78.40 (new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc)) 130.74/78.40 130.74/78.40 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (606) 130.74/78.40 Obligation: 130.74/78.40 Q DP problem: 130.74/78.40 The TRS P consists of the following rules: 130.74/78.40 130.74/78.40 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 130.74/78.40 The TRS R consists of the following rules: 130.74/78.40 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.40 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.40 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.40 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.40 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.40 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.40 new_primPlusNat2(Zero) -> Zero 130.74/78.40 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.40 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.40 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.40 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.40 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.40 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.40 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.40 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.40 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.40 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.40 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.40 130.74/78.40 The set Q consists of the following terms: 130.74/78.40 130.74/78.40 new_primPlusNat1(Succ(x0)) 130.74/78.40 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.40 new_primPlusNat1(Zero) 130.74/78.40 new_primPlusNat2(Zero) 130.74/78.40 new_primPlusNat3(Succ(x0)) 130.74/78.40 new_primPlusNat8(Succ(x0), x1) 130.74/78.40 new_primPlusNat6(x0, Succ(x1)) 130.74/78.40 new_primPlusNat0(Succ(x0), Zero) 130.74/78.40 new_primPlusNat6(x0, Zero) 130.74/78.40 new_primPlusNat5(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.40 new_primPlusNat4(Succ(x0)) 130.74/78.40 new_primPlusNat8(Zero, x0) 130.74/78.40 new_primPlusNat3(Zero) 130.74/78.40 new_primPlusNat7(x0, Zero) 130.74/78.40 new_primPlusNat5(Zero) 130.74/78.40 new_primPlusNat7(x0, Succ(x1)) 130.74/78.40 new_primPlusNat4(Zero) 130.74/78.40 new_primPlusNat2(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Zero) 130.74/78.40 130.74/78.40 We have to consider all minimal (P,Q,R)-chains. 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (607) TransformationProof (EQUIVALENT) 130.74/78.40 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz3882, zzz3882))), Succ(zzz3882)), Succ(zzz3882)), Succ(zzz3882)), bc) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.74/78.40 130.74/78.40 (new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc)) 130.74/78.40 130.74/78.40 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (608) 130.74/78.40 Obligation: 130.74/78.40 Q DP problem: 130.74/78.40 The TRS P consists of the following rules: 130.74/78.40 130.74/78.40 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 130.74/78.40 The TRS R consists of the following rules: 130.74/78.40 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.40 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.40 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.40 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.40 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.40 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.40 new_primPlusNat2(Zero) -> Zero 130.74/78.40 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.40 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.40 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.40 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.40 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.40 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.40 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.40 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.40 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.40 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.40 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.40 130.74/78.40 The set Q consists of the following terms: 130.74/78.40 130.74/78.40 new_primPlusNat1(Succ(x0)) 130.74/78.40 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.40 new_primPlusNat1(Zero) 130.74/78.40 new_primPlusNat2(Zero) 130.74/78.40 new_primPlusNat3(Succ(x0)) 130.74/78.40 new_primPlusNat8(Succ(x0), x1) 130.74/78.40 new_primPlusNat6(x0, Succ(x1)) 130.74/78.40 new_primPlusNat0(Succ(x0), Zero) 130.74/78.40 new_primPlusNat6(x0, Zero) 130.74/78.40 new_primPlusNat5(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.40 new_primPlusNat4(Succ(x0)) 130.74/78.40 new_primPlusNat8(Zero, x0) 130.74/78.40 new_primPlusNat3(Zero) 130.74/78.40 new_primPlusNat7(x0, Zero) 130.74/78.40 new_primPlusNat5(Zero) 130.74/78.40 new_primPlusNat7(x0, Succ(x1)) 130.74/78.40 new_primPlusNat4(Zero) 130.74/78.40 new_primPlusNat2(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Zero) 130.74/78.40 130.74/78.40 We have to consider all minimal (P,Q,R)-chains. 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (609) TransformationProof (EQUIVALENT) 130.74/78.40 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) at position [10,0,0] we obtained the following new rules [LPAR04]: 130.74/78.40 130.74/78.40 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb)) 130.74/78.40 130.74/78.40 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (610) 130.74/78.40 Obligation: 130.74/78.40 Q DP problem: 130.74/78.40 The TRS P consists of the following rules: 130.74/78.40 130.74/78.40 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.40 130.74/78.40 The TRS R consists of the following rules: 130.74/78.40 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.40 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.40 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.40 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.40 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.40 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.40 new_primPlusNat2(Zero) -> Zero 130.74/78.40 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.40 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.40 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.40 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.40 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.40 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.40 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.40 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.40 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.40 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.40 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.40 130.74/78.40 The set Q consists of the following terms: 130.74/78.40 130.74/78.40 new_primPlusNat1(Succ(x0)) 130.74/78.40 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.40 new_primPlusNat1(Zero) 130.74/78.40 new_primPlusNat2(Zero) 130.74/78.40 new_primPlusNat3(Succ(x0)) 130.74/78.40 new_primPlusNat8(Succ(x0), x1) 130.74/78.40 new_primPlusNat6(x0, Succ(x1)) 130.74/78.40 new_primPlusNat0(Succ(x0), Zero) 130.74/78.40 new_primPlusNat6(x0, Zero) 130.74/78.40 new_primPlusNat5(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.40 new_primPlusNat4(Succ(x0)) 130.74/78.40 new_primPlusNat8(Zero, x0) 130.74/78.40 new_primPlusNat3(Zero) 130.74/78.40 new_primPlusNat7(x0, Zero) 130.74/78.40 new_primPlusNat5(Zero) 130.74/78.40 new_primPlusNat7(x0, Succ(x1)) 130.74/78.40 new_primPlusNat4(Zero) 130.74/78.40 new_primPlusNat2(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Zero) 130.74/78.40 130.74/78.40 We have to consider all minimal (P,Q,R)-chains. 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (611) TransformationProof (EQUIVALENT) 130.74/78.40 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))), bb) at position [10,0,0] we obtained the following new rules [LPAR04]: 130.74/78.40 130.74/78.40 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb)) 130.74/78.40 130.74/78.40 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (612) 130.74/78.40 Obligation: 130.74/78.40 Q DP problem: 130.74/78.40 The TRS P consists of the following rules: 130.74/78.40 130.74/78.40 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.40 130.74/78.40 The TRS R consists of the following rules: 130.74/78.40 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.40 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.40 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.40 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.40 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.40 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.40 new_primPlusNat2(Zero) -> Zero 130.74/78.40 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.40 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.40 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.40 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.40 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.40 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.40 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.40 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.40 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.40 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.40 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.40 130.74/78.40 The set Q consists of the following terms: 130.74/78.40 130.74/78.40 new_primPlusNat1(Succ(x0)) 130.74/78.40 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.40 new_primPlusNat1(Zero) 130.74/78.40 new_primPlusNat2(Zero) 130.74/78.40 new_primPlusNat3(Succ(x0)) 130.74/78.40 new_primPlusNat8(Succ(x0), x1) 130.74/78.40 new_primPlusNat6(x0, Succ(x1)) 130.74/78.40 new_primPlusNat0(Succ(x0), Zero) 130.74/78.40 new_primPlusNat6(x0, Zero) 130.74/78.40 new_primPlusNat5(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.40 new_primPlusNat4(Succ(x0)) 130.74/78.40 new_primPlusNat8(Zero, x0) 130.74/78.40 new_primPlusNat3(Zero) 130.74/78.40 new_primPlusNat7(x0, Zero) 130.74/78.40 new_primPlusNat5(Zero) 130.74/78.40 new_primPlusNat7(x0, Succ(x1)) 130.74/78.40 new_primPlusNat4(Zero) 130.74/78.40 new_primPlusNat2(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Zero) 130.74/78.40 130.74/78.40 We have to consider all minimal (P,Q,R)-chains. 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (613) TransformationProof (EQUIVALENT) 130.74/78.40 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Succ(Zero))))), bb) at position [10,0] we obtained the following new rules [LPAR04]: 130.74/78.40 130.74/78.40 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), bb)) 130.74/78.40 130.74/78.40 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (614) 130.74/78.40 Obligation: 130.74/78.40 Q DP problem: 130.74/78.40 The TRS P consists of the following rules: 130.74/78.40 130.74/78.40 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.40 130.74/78.40 The TRS R consists of the following rules: 130.74/78.40 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.40 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.40 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.40 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.40 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.40 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.40 new_primPlusNat2(Zero) -> Zero 130.74/78.40 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.40 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.40 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.40 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.40 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.40 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.40 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.40 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.40 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.40 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.40 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.40 130.74/78.40 The set Q consists of the following terms: 130.74/78.40 130.74/78.40 new_primPlusNat1(Succ(x0)) 130.74/78.40 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.40 new_primPlusNat1(Zero) 130.74/78.40 new_primPlusNat2(Zero) 130.74/78.40 new_primPlusNat3(Succ(x0)) 130.74/78.40 new_primPlusNat8(Succ(x0), x1) 130.74/78.40 new_primPlusNat6(x0, Succ(x1)) 130.74/78.40 new_primPlusNat0(Succ(x0), Zero) 130.74/78.40 new_primPlusNat6(x0, Zero) 130.74/78.40 new_primPlusNat5(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.40 new_primPlusNat4(Succ(x0)) 130.74/78.40 new_primPlusNat8(Zero, x0) 130.74/78.40 new_primPlusNat3(Zero) 130.74/78.40 new_primPlusNat7(x0, Zero) 130.74/78.40 new_primPlusNat5(Zero) 130.74/78.40 new_primPlusNat7(x0, Succ(x1)) 130.74/78.40 new_primPlusNat4(Zero) 130.74/78.40 new_primPlusNat2(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Zero) 130.74/78.40 130.74/78.40 We have to consider all minimal (P,Q,R)-chains. 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (615) TransformationProof (EQUIVALENT) 130.74/78.40 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat5(Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) at position [10] we obtained the following new rules [LPAR04]: 130.74/78.40 130.74/78.40 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb)) 130.74/78.40 130.74/78.40 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (616) 130.74/78.40 Obligation: 130.74/78.40 Q DP problem: 130.74/78.40 The TRS P consists of the following rules: 130.74/78.40 130.74/78.40 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.40 130.74/78.40 The TRS R consists of the following rules: 130.74/78.40 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.40 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.40 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.40 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.40 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.40 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.40 new_primPlusNat2(Zero) -> Zero 130.74/78.40 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.40 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.40 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.40 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.40 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.40 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.40 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.40 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.40 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.40 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.40 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.40 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.40 130.74/78.40 The set Q consists of the following terms: 130.74/78.40 130.74/78.40 new_primPlusNat1(Succ(x0)) 130.74/78.40 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.40 new_primPlusNat1(Zero) 130.74/78.40 new_primPlusNat2(Zero) 130.74/78.40 new_primPlusNat3(Succ(x0)) 130.74/78.40 new_primPlusNat8(Succ(x0), x1) 130.74/78.40 new_primPlusNat6(x0, Succ(x1)) 130.74/78.40 new_primPlusNat0(Succ(x0), Zero) 130.74/78.40 new_primPlusNat6(x0, Zero) 130.74/78.40 new_primPlusNat5(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.40 new_primPlusNat4(Succ(x0)) 130.74/78.40 new_primPlusNat8(Zero, x0) 130.74/78.40 new_primPlusNat3(Zero) 130.74/78.40 new_primPlusNat7(x0, Zero) 130.74/78.40 new_primPlusNat5(Zero) 130.74/78.40 new_primPlusNat7(x0, Succ(x1)) 130.74/78.40 new_primPlusNat4(Zero) 130.74/78.40 new_primPlusNat2(Succ(x0)) 130.74/78.40 new_primPlusNat0(Zero, Zero) 130.74/78.40 130.74/78.40 We have to consider all minimal (P,Q,R)-chains. 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (617) DependencyGraphProof (EQUIVALENT) 130.74/78.40 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 130.74/78.40 ---------------------------------------- 130.74/78.40 130.74/78.40 (618) 130.74/78.40 Obligation: 130.74/78.40 Q DP problem: 130.74/78.40 The TRS P consists of the following rules: 130.74/78.40 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.40 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.40 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.40 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.40 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.41 130.74/78.41 The TRS R consists of the following rules: 130.74/78.41 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.41 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.41 new_primPlusNat5(Succ(zzz48250)) -> Succ(Succ(new_primPlusNat4(zzz48250))) 130.74/78.41 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.41 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.41 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.41 new_primPlusNat2(Zero) -> Zero 130.74/78.41 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.41 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.41 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.41 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.41 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.41 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.41 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.41 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.41 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.41 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.41 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.41 130.74/78.41 The set Q consists of the following terms: 130.74/78.41 130.74/78.41 new_primPlusNat1(Succ(x0)) 130.74/78.41 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.41 new_primPlusNat1(Zero) 130.74/78.41 new_primPlusNat2(Zero) 130.74/78.41 new_primPlusNat3(Succ(x0)) 130.74/78.41 new_primPlusNat8(Succ(x0), x1) 130.74/78.41 new_primPlusNat6(x0, Succ(x1)) 130.74/78.41 new_primPlusNat0(Succ(x0), Zero) 130.74/78.41 new_primPlusNat6(x0, Zero) 130.74/78.41 new_primPlusNat5(Succ(x0)) 130.74/78.41 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.41 new_primPlusNat4(Succ(x0)) 130.74/78.41 new_primPlusNat8(Zero, x0) 130.74/78.41 new_primPlusNat3(Zero) 130.74/78.41 new_primPlusNat7(x0, Zero) 130.74/78.41 new_primPlusNat5(Zero) 130.74/78.41 new_primPlusNat7(x0, Succ(x1)) 130.74/78.41 new_primPlusNat4(Zero) 130.74/78.41 new_primPlusNat2(Succ(x0)) 130.74/78.41 new_primPlusNat0(Zero, Zero) 130.74/78.41 130.74/78.41 We have to consider all minimal (P,Q,R)-chains. 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (619) UsableRulesProof (EQUIVALENT) 130.74/78.41 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (620) 130.74/78.41 Obligation: 130.74/78.41 Q DP problem: 130.74/78.41 The TRS P consists of the following rules: 130.74/78.41 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.41 130.74/78.41 The TRS R consists of the following rules: 130.74/78.41 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.41 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.41 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.41 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.41 new_primPlusNat2(Zero) -> Zero 130.74/78.41 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.41 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.41 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.41 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.41 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.41 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.41 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.41 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.41 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.41 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.41 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.41 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.41 130.74/78.41 The set Q consists of the following terms: 130.74/78.41 130.74/78.41 new_primPlusNat1(Succ(x0)) 130.74/78.41 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.41 new_primPlusNat1(Zero) 130.74/78.41 new_primPlusNat2(Zero) 130.74/78.41 new_primPlusNat3(Succ(x0)) 130.74/78.41 new_primPlusNat8(Succ(x0), x1) 130.74/78.41 new_primPlusNat6(x0, Succ(x1)) 130.74/78.41 new_primPlusNat0(Succ(x0), Zero) 130.74/78.41 new_primPlusNat6(x0, Zero) 130.74/78.41 new_primPlusNat5(Succ(x0)) 130.74/78.41 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.41 new_primPlusNat4(Succ(x0)) 130.74/78.41 new_primPlusNat8(Zero, x0) 130.74/78.41 new_primPlusNat3(Zero) 130.74/78.41 new_primPlusNat7(x0, Zero) 130.74/78.41 new_primPlusNat5(Zero) 130.74/78.41 new_primPlusNat7(x0, Succ(x1)) 130.74/78.41 new_primPlusNat4(Zero) 130.74/78.41 new_primPlusNat2(Succ(x0)) 130.74/78.41 new_primPlusNat0(Zero, Zero) 130.74/78.41 130.74/78.41 We have to consider all minimal (P,Q,R)-chains. 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (621) QReductionProof (EQUIVALENT) 130.74/78.41 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.74/78.41 130.74/78.41 new_primPlusNat5(Succ(x0)) 130.74/78.41 new_primPlusNat5(Zero) 130.74/78.41 130.74/78.41 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (622) 130.74/78.41 Obligation: 130.74/78.41 Q DP problem: 130.74/78.41 The TRS P consists of the following rules: 130.74/78.41 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.41 130.74/78.41 The TRS R consists of the following rules: 130.74/78.41 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.41 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.41 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.41 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.41 new_primPlusNat2(Zero) -> Zero 130.74/78.41 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.41 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.41 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.41 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.41 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.41 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.41 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.41 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.41 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.41 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.41 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.41 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.41 130.74/78.41 The set Q consists of the following terms: 130.74/78.41 130.74/78.41 new_primPlusNat1(Succ(x0)) 130.74/78.41 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.41 new_primPlusNat1(Zero) 130.74/78.41 new_primPlusNat2(Zero) 130.74/78.41 new_primPlusNat3(Succ(x0)) 130.74/78.41 new_primPlusNat8(Succ(x0), x1) 130.74/78.41 new_primPlusNat6(x0, Succ(x1)) 130.74/78.41 new_primPlusNat0(Succ(x0), Zero) 130.74/78.41 new_primPlusNat6(x0, Zero) 130.74/78.41 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.41 new_primPlusNat4(Succ(x0)) 130.74/78.41 new_primPlusNat8(Zero, x0) 130.74/78.41 new_primPlusNat3(Zero) 130.74/78.41 new_primPlusNat7(x0, Zero) 130.74/78.41 new_primPlusNat7(x0, Succ(x1)) 130.74/78.41 new_primPlusNat4(Zero) 130.74/78.41 new_primPlusNat2(Succ(x0)) 130.74/78.41 new_primPlusNat0(Zero, Zero) 130.74/78.41 130.74/78.41 We have to consider all minimal (P,Q,R)-chains. 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (623) TransformationProof (EQUIVALENT) 130.74/78.41 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero)))))))), bb) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.41 130.74/78.41 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb)) 130.74/78.41 130.74/78.41 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (624) 130.74/78.41 Obligation: 130.74/78.41 Q DP problem: 130.74/78.41 The TRS P consists of the following rules: 130.74/78.41 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.41 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.74/78.41 130.74/78.41 The TRS R consists of the following rules: 130.74/78.41 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.41 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.41 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.41 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.41 new_primPlusNat2(Zero) -> Zero 130.74/78.41 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.41 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.41 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.41 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.41 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.41 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.41 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.41 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.41 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.41 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.41 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.41 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.41 130.74/78.41 The set Q consists of the following terms: 130.74/78.41 130.74/78.41 new_primPlusNat1(Succ(x0)) 130.74/78.41 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.41 new_primPlusNat1(Zero) 130.74/78.41 new_primPlusNat2(Zero) 130.74/78.41 new_primPlusNat3(Succ(x0)) 130.74/78.41 new_primPlusNat8(Succ(x0), x1) 130.74/78.41 new_primPlusNat6(x0, Succ(x1)) 130.74/78.41 new_primPlusNat0(Succ(x0), Zero) 130.74/78.41 new_primPlusNat6(x0, Zero) 130.74/78.41 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.41 new_primPlusNat4(Succ(x0)) 130.74/78.41 new_primPlusNat8(Zero, x0) 130.74/78.41 new_primPlusNat3(Zero) 130.74/78.41 new_primPlusNat7(x0, Zero) 130.74/78.41 new_primPlusNat7(x0, Succ(x1)) 130.74/78.41 new_primPlusNat4(Zero) 130.74/78.41 new_primPlusNat2(Succ(x0)) 130.74/78.41 new_primPlusNat0(Zero, Zero) 130.74/78.41 130.74/78.41 We have to consider all minimal (P,Q,R)-chains. 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (625) TransformationProof (EQUIVALENT) 130.74/78.41 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) at position [12,0] we obtained the following new rules [LPAR04]: 130.74/78.41 130.74/78.41 (new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h),new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h)) 130.74/78.41 130.74/78.41 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (626) 130.74/78.41 Obligation: 130.74/78.41 Q DP problem: 130.74/78.41 The TRS P consists of the following rules: 130.74/78.41 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.41 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.41 130.74/78.41 The TRS R consists of the following rules: 130.74/78.41 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.41 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.41 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.41 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.41 new_primPlusNat2(Zero) -> Zero 130.74/78.41 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.41 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.41 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.41 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.41 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.41 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.41 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.41 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.41 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.41 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.41 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.41 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.41 130.74/78.41 The set Q consists of the following terms: 130.74/78.41 130.74/78.41 new_primPlusNat1(Succ(x0)) 130.74/78.41 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.41 new_primPlusNat1(Zero) 130.74/78.41 new_primPlusNat2(Zero) 130.74/78.41 new_primPlusNat3(Succ(x0)) 130.74/78.41 new_primPlusNat8(Succ(x0), x1) 130.74/78.41 new_primPlusNat6(x0, Succ(x1)) 130.74/78.41 new_primPlusNat0(Succ(x0), Zero) 130.74/78.41 new_primPlusNat6(x0, Zero) 130.74/78.41 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.41 new_primPlusNat4(Succ(x0)) 130.74/78.41 new_primPlusNat8(Zero, x0) 130.74/78.41 new_primPlusNat3(Zero) 130.74/78.41 new_primPlusNat7(x0, Zero) 130.74/78.41 new_primPlusNat7(x0, Succ(x1)) 130.74/78.41 new_primPlusNat4(Zero) 130.74/78.41 new_primPlusNat2(Succ(x0)) 130.74/78.41 new_primPlusNat0(Zero, Zero) 130.74/78.41 130.74/78.41 We have to consider all minimal (P,Q,R)-chains. 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (627) TransformationProof (EQUIVALENT) 130.74/78.41 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.41 130.74/78.41 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb)) 130.74/78.41 130.74/78.41 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (628) 130.74/78.41 Obligation: 130.74/78.41 Q DP problem: 130.74/78.41 The TRS P consists of the following rules: 130.74/78.41 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.41 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.41 130.74/78.41 The TRS R consists of the following rules: 130.74/78.41 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.41 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.41 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.41 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.41 new_primPlusNat2(Zero) -> Zero 130.74/78.41 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.41 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.41 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.41 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.41 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.41 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.41 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.41 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.41 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.41 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.41 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.41 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.41 130.74/78.41 The set Q consists of the following terms: 130.74/78.41 130.74/78.41 new_primPlusNat1(Succ(x0)) 130.74/78.41 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.41 new_primPlusNat1(Zero) 130.74/78.41 new_primPlusNat2(Zero) 130.74/78.41 new_primPlusNat3(Succ(x0)) 130.74/78.41 new_primPlusNat8(Succ(x0), x1) 130.74/78.41 new_primPlusNat6(x0, Succ(x1)) 130.74/78.41 new_primPlusNat0(Succ(x0), Zero) 130.74/78.41 new_primPlusNat6(x0, Zero) 130.74/78.41 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.41 new_primPlusNat4(Succ(x0)) 130.74/78.41 new_primPlusNat8(Zero, x0) 130.74/78.41 new_primPlusNat3(Zero) 130.74/78.41 new_primPlusNat7(x0, Zero) 130.74/78.41 new_primPlusNat7(x0, Succ(x1)) 130.74/78.41 new_primPlusNat4(Zero) 130.74/78.41 new_primPlusNat2(Succ(x0)) 130.74/78.41 new_primPlusNat0(Zero, Zero) 130.74/78.41 130.74/78.41 We have to consider all minimal (P,Q,R)-chains. 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (629) TransformationProof (EQUIVALENT) 130.74/78.41 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))), bb) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.41 130.74/78.41 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb)) 130.74/78.41 130.74/78.41 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (630) 130.74/78.41 Obligation: 130.74/78.41 Q DP problem: 130.74/78.41 The TRS P consists of the following rules: 130.74/78.41 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.41 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 130.74/78.41 The TRS R consists of the following rules: 130.74/78.41 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.41 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.41 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.41 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.41 new_primPlusNat2(Zero) -> Zero 130.74/78.41 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.41 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.41 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.41 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.41 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.41 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.41 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.41 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.41 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.41 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.41 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.41 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.41 130.74/78.41 The set Q consists of the following terms: 130.74/78.41 130.74/78.41 new_primPlusNat1(Succ(x0)) 130.74/78.41 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.41 new_primPlusNat1(Zero) 130.74/78.41 new_primPlusNat2(Zero) 130.74/78.41 new_primPlusNat3(Succ(x0)) 130.74/78.41 new_primPlusNat8(Succ(x0), x1) 130.74/78.41 new_primPlusNat6(x0, Succ(x1)) 130.74/78.41 new_primPlusNat0(Succ(x0), Zero) 130.74/78.41 new_primPlusNat6(x0, Zero) 130.74/78.41 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.41 new_primPlusNat4(Succ(x0)) 130.74/78.41 new_primPlusNat8(Zero, x0) 130.74/78.41 new_primPlusNat3(Zero) 130.74/78.41 new_primPlusNat7(x0, Zero) 130.74/78.41 new_primPlusNat7(x0, Succ(x1)) 130.74/78.41 new_primPlusNat4(Zero) 130.74/78.41 new_primPlusNat2(Succ(x0)) 130.74/78.41 new_primPlusNat0(Zero, Zero) 130.74/78.41 130.74/78.41 We have to consider all minimal (P,Q,R)-chains. 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (631) TransformationProof (EQUIVALENT) 130.74/78.41 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz4708, zzz4708))), Succ(zzz4708)), Succ(zzz4708)), Succ(zzz4708)), h) at position [12,0,0] we obtained the following new rules [LPAR04]: 130.74/78.41 130.74/78.41 (new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h),new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h)) 130.74/78.41 130.74/78.41 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (632) 130.74/78.41 Obligation: 130.74/78.41 Q DP problem: 130.74/78.41 The TRS P consists of the following rules: 130.74/78.41 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.41 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 130.74/78.41 The TRS R consists of the following rules: 130.74/78.41 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.41 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.41 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.41 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.41 new_primPlusNat2(Zero) -> Zero 130.74/78.41 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.41 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.41 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.41 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.41 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.41 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.41 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.41 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.41 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.41 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.41 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.41 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.41 130.74/78.41 The set Q consists of the following terms: 130.74/78.41 130.74/78.41 new_primPlusNat1(Succ(x0)) 130.74/78.41 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.41 new_primPlusNat1(Zero) 130.74/78.41 new_primPlusNat2(Zero) 130.74/78.41 new_primPlusNat3(Succ(x0)) 130.74/78.41 new_primPlusNat8(Succ(x0), x1) 130.74/78.41 new_primPlusNat6(x0, Succ(x1)) 130.74/78.41 new_primPlusNat0(Succ(x0), Zero) 130.74/78.41 new_primPlusNat6(x0, Zero) 130.74/78.41 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.41 new_primPlusNat4(Succ(x0)) 130.74/78.41 new_primPlusNat8(Zero, x0) 130.74/78.41 new_primPlusNat3(Zero) 130.74/78.41 new_primPlusNat7(x0, Zero) 130.74/78.41 new_primPlusNat7(x0, Succ(x1)) 130.74/78.41 new_primPlusNat4(Zero) 130.74/78.41 new_primPlusNat2(Succ(x0)) 130.74/78.41 new_primPlusNat0(Zero, Zero) 130.74/78.41 130.74/78.41 We have to consider all minimal (P,Q,R)-chains. 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (633) TransformationProof (EQUIVALENT) 130.74/78.41 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) at position [11,0] we obtained the following new rules [LPAR04]: 130.74/78.41 130.74/78.41 (new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc)) 130.74/78.41 130.74/78.41 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (634) 130.74/78.41 Obligation: 130.74/78.41 Q DP problem: 130.74/78.41 The TRS P consists of the following rules: 130.74/78.41 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.41 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 130.74/78.41 The TRS R consists of the following rules: 130.74/78.41 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.41 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.41 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.41 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.41 new_primPlusNat2(Zero) -> Zero 130.74/78.41 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.41 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.41 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.41 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.41 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.41 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.41 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.41 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.41 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.41 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.41 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.41 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.41 130.74/78.41 The set Q consists of the following terms: 130.74/78.41 130.74/78.41 new_primPlusNat1(Succ(x0)) 130.74/78.41 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.41 new_primPlusNat1(Zero) 130.74/78.41 new_primPlusNat2(Zero) 130.74/78.41 new_primPlusNat3(Succ(x0)) 130.74/78.41 new_primPlusNat8(Succ(x0), x1) 130.74/78.41 new_primPlusNat6(x0, Succ(x1)) 130.74/78.41 new_primPlusNat0(Succ(x0), Zero) 130.74/78.41 new_primPlusNat6(x0, Zero) 130.74/78.41 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.41 new_primPlusNat4(Succ(x0)) 130.74/78.41 new_primPlusNat8(Zero, x0) 130.74/78.41 new_primPlusNat3(Zero) 130.74/78.41 new_primPlusNat7(x0, Zero) 130.74/78.41 new_primPlusNat7(x0, Succ(x1)) 130.74/78.41 new_primPlusNat4(Zero) 130.74/78.41 new_primPlusNat2(Succ(x0)) 130.74/78.41 new_primPlusNat0(Zero, Zero) 130.74/78.41 130.74/78.41 We have to consider all minimal (P,Q,R)-chains. 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (635) TransformationProof (EQUIVALENT) 130.74/78.41 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) at position [11,0] we obtained the following new rules [LPAR04]: 130.74/78.41 130.74/78.41 (new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc)) 130.74/78.41 130.74/78.41 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (636) 130.74/78.41 Obligation: 130.74/78.41 Q DP problem: 130.74/78.41 The TRS P consists of the following rules: 130.74/78.41 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.41 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 130.74/78.41 The TRS R consists of the following rules: 130.74/78.41 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.41 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.41 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.41 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.41 new_primPlusNat2(Zero) -> Zero 130.74/78.41 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.41 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.41 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.41 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.41 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.41 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.41 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.41 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.41 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.41 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.41 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.41 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.41 130.74/78.41 The set Q consists of the following terms: 130.74/78.41 130.74/78.41 new_primPlusNat1(Succ(x0)) 130.74/78.41 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.41 new_primPlusNat1(Zero) 130.74/78.41 new_primPlusNat2(Zero) 130.74/78.41 new_primPlusNat3(Succ(x0)) 130.74/78.41 new_primPlusNat8(Succ(x0), x1) 130.74/78.41 new_primPlusNat6(x0, Succ(x1)) 130.74/78.41 new_primPlusNat0(Succ(x0), Zero) 130.74/78.41 new_primPlusNat6(x0, Zero) 130.74/78.41 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.41 new_primPlusNat4(Succ(x0)) 130.74/78.41 new_primPlusNat8(Zero, x0) 130.74/78.41 new_primPlusNat3(Zero) 130.74/78.41 new_primPlusNat7(x0, Zero) 130.74/78.41 new_primPlusNat7(x0, Succ(x1)) 130.74/78.41 new_primPlusNat4(Zero) 130.74/78.41 new_primPlusNat2(Succ(x0)) 130.74/78.41 new_primPlusNat0(Zero, Zero) 130.74/78.41 130.74/78.41 We have to consider all minimal (P,Q,R)-chains. 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (637) TransformationProof (EQUIVALENT) 130.74/78.41 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882))), Succ(zzz3882)), Succ(zzz3882)), bc) at position [11,0] we obtained the following new rules [LPAR04]: 130.74/78.41 130.74/78.41 (new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc),new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc)) 130.74/78.41 130.74/78.41 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (638) 130.74/78.41 Obligation: 130.74/78.41 Q DP problem: 130.74/78.41 The TRS P consists of the following rules: 130.74/78.41 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.41 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 130.74/78.41 The TRS R consists of the following rules: 130.74/78.41 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.41 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.41 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.41 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.41 new_primPlusNat2(Zero) -> Zero 130.74/78.41 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.41 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.41 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.41 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.41 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.41 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.41 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.41 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.41 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.41 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.41 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.41 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.41 130.74/78.41 The set Q consists of the following terms: 130.74/78.41 130.74/78.41 new_primPlusNat1(Succ(x0)) 130.74/78.41 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.41 new_primPlusNat1(Zero) 130.74/78.41 new_primPlusNat2(Zero) 130.74/78.41 new_primPlusNat3(Succ(x0)) 130.74/78.41 new_primPlusNat8(Succ(x0), x1) 130.74/78.41 new_primPlusNat6(x0, Succ(x1)) 130.74/78.41 new_primPlusNat0(Succ(x0), Zero) 130.74/78.41 new_primPlusNat6(x0, Zero) 130.74/78.41 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.41 new_primPlusNat4(Succ(x0)) 130.74/78.41 new_primPlusNat8(Zero, x0) 130.74/78.41 new_primPlusNat3(Zero) 130.74/78.41 new_primPlusNat7(x0, Zero) 130.74/78.41 new_primPlusNat7(x0, Succ(x1)) 130.74/78.41 new_primPlusNat4(Zero) 130.74/78.41 new_primPlusNat2(Succ(x0)) 130.74/78.41 new_primPlusNat0(Zero, Zero) 130.74/78.41 130.74/78.41 We have to consider all minimal (P,Q,R)-chains. 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (639) TransformationProof (EQUIVALENT) 130.74/78.41 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) at position [10,0] we obtained the following new rules [LPAR04]: 130.74/78.41 130.74/78.41 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb)) 130.74/78.41 130.74/78.41 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (640) 130.74/78.41 Obligation: 130.74/78.41 Q DP problem: 130.74/78.41 The TRS P consists of the following rules: 130.74/78.41 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.41 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.41 130.74/78.41 The TRS R consists of the following rules: 130.74/78.41 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.41 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.41 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.41 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.41 new_primPlusNat2(Zero) -> Zero 130.74/78.41 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.41 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.41 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.41 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.41 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.41 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.41 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.41 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.41 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.41 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.41 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.41 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.41 130.74/78.41 The set Q consists of the following terms: 130.74/78.41 130.74/78.41 new_primPlusNat1(Succ(x0)) 130.74/78.41 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.41 new_primPlusNat1(Zero) 130.74/78.41 new_primPlusNat2(Zero) 130.74/78.41 new_primPlusNat3(Succ(x0)) 130.74/78.41 new_primPlusNat8(Succ(x0), x1) 130.74/78.41 new_primPlusNat6(x0, Succ(x1)) 130.74/78.41 new_primPlusNat0(Succ(x0), Zero) 130.74/78.41 new_primPlusNat6(x0, Zero) 130.74/78.41 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.41 new_primPlusNat4(Succ(x0)) 130.74/78.41 new_primPlusNat8(Zero, x0) 130.74/78.41 new_primPlusNat3(Zero) 130.74/78.41 new_primPlusNat7(x0, Zero) 130.74/78.41 new_primPlusNat7(x0, Succ(x1)) 130.74/78.41 new_primPlusNat4(Zero) 130.74/78.41 new_primPlusNat2(Succ(x0)) 130.74/78.41 new_primPlusNat0(Zero, Zero) 130.74/78.41 130.74/78.41 We have to consider all minimal (P,Q,R)-chains. 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (641) TransformationProof (EQUIVALENT) 130.74/78.41 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) at position [10,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.41 130.74/78.41 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb)) 130.74/78.41 130.74/78.41 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (642) 130.74/78.41 Obligation: 130.74/78.41 Q DP problem: 130.74/78.41 The TRS P consists of the following rules: 130.74/78.41 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.41 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.41 130.74/78.41 The TRS R consists of the following rules: 130.74/78.41 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.41 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.41 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.41 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.41 new_primPlusNat2(Zero) -> Zero 130.74/78.41 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.41 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.41 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.41 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.41 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.41 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.41 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.41 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.41 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.41 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.41 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.41 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.41 130.74/78.41 The set Q consists of the following terms: 130.74/78.41 130.74/78.41 new_primPlusNat1(Succ(x0)) 130.74/78.41 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.41 new_primPlusNat1(Zero) 130.74/78.41 new_primPlusNat2(Zero) 130.74/78.41 new_primPlusNat3(Succ(x0)) 130.74/78.41 new_primPlusNat8(Succ(x0), x1) 130.74/78.41 new_primPlusNat6(x0, Succ(x1)) 130.74/78.41 new_primPlusNat0(Succ(x0), Zero) 130.74/78.41 new_primPlusNat6(x0, Zero) 130.74/78.41 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.41 new_primPlusNat4(Succ(x0)) 130.74/78.41 new_primPlusNat8(Zero, x0) 130.74/78.41 new_primPlusNat3(Zero) 130.74/78.41 new_primPlusNat7(x0, Zero) 130.74/78.41 new_primPlusNat7(x0, Succ(x1)) 130.74/78.41 new_primPlusNat4(Zero) 130.74/78.41 new_primPlusNat2(Succ(x0)) 130.74/78.41 new_primPlusNat0(Zero, Zero) 130.74/78.41 130.74/78.41 We have to consider all minimal (P,Q,R)-chains. 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (643) TransformationProof (EQUIVALENT) 130.74/78.41 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), bb) at position [10] we obtained the following new rules [LPAR04]: 130.74/78.41 130.74/78.41 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb)) 130.74/78.41 130.74/78.41 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (644) 130.74/78.41 Obligation: 130.74/78.41 Q DP problem: 130.74/78.41 The TRS P consists of the following rules: 130.74/78.41 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.41 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.41 130.74/78.41 The TRS R consists of the following rules: 130.74/78.41 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.41 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.41 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.41 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.41 new_primPlusNat2(Zero) -> Zero 130.74/78.41 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.41 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.41 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.41 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.41 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.41 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.41 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.41 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.41 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.41 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.41 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.41 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.41 130.74/78.41 The set Q consists of the following terms: 130.74/78.41 130.74/78.41 new_primPlusNat1(Succ(x0)) 130.74/78.41 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.41 new_primPlusNat1(Zero) 130.74/78.41 new_primPlusNat2(Zero) 130.74/78.41 new_primPlusNat3(Succ(x0)) 130.74/78.41 new_primPlusNat8(Succ(x0), x1) 130.74/78.41 new_primPlusNat6(x0, Succ(x1)) 130.74/78.41 new_primPlusNat0(Succ(x0), Zero) 130.74/78.41 new_primPlusNat6(x0, Zero) 130.74/78.41 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.41 new_primPlusNat4(Succ(x0)) 130.74/78.41 new_primPlusNat8(Zero, x0) 130.74/78.41 new_primPlusNat3(Zero) 130.74/78.41 new_primPlusNat7(x0, Zero) 130.74/78.41 new_primPlusNat7(x0, Succ(x1)) 130.74/78.41 new_primPlusNat4(Zero) 130.74/78.41 new_primPlusNat2(Succ(x0)) 130.74/78.41 new_primPlusNat0(Zero, Zero) 130.74/78.41 130.74/78.41 We have to consider all minimal (P,Q,R)-chains. 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (645) DependencyGraphProof (EQUIVALENT) 130.74/78.41 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (646) 130.74/78.41 Obligation: 130.74/78.41 Q DP problem: 130.74/78.41 The TRS P consists of the following rules: 130.74/78.41 130.74/78.41 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.41 130.74/78.41 The TRS R consists of the following rules: 130.74/78.41 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.41 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.41 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.41 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.41 new_primPlusNat2(Zero) -> Zero 130.74/78.41 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.41 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.41 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.41 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.41 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.41 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.41 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.41 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.41 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.41 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.41 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.41 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.41 130.74/78.41 The set Q consists of the following terms: 130.74/78.41 130.74/78.41 new_primPlusNat1(Succ(x0)) 130.74/78.41 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.41 new_primPlusNat1(Zero) 130.74/78.41 new_primPlusNat2(Zero) 130.74/78.41 new_primPlusNat3(Succ(x0)) 130.74/78.41 new_primPlusNat8(Succ(x0), x1) 130.74/78.41 new_primPlusNat6(x0, Succ(x1)) 130.74/78.41 new_primPlusNat0(Succ(x0), Zero) 130.74/78.41 new_primPlusNat6(x0, Zero) 130.74/78.41 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.41 new_primPlusNat4(Succ(x0)) 130.74/78.41 new_primPlusNat8(Zero, x0) 130.74/78.41 new_primPlusNat3(Zero) 130.74/78.41 new_primPlusNat7(x0, Zero) 130.74/78.41 new_primPlusNat7(x0, Succ(x1)) 130.74/78.41 new_primPlusNat4(Zero) 130.74/78.41 new_primPlusNat2(Succ(x0)) 130.74/78.41 new_primPlusNat0(Zero, Zero) 130.74/78.41 130.74/78.41 We have to consider all minimal (P,Q,R)-chains. 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (647) TransformationProof (EQUIVALENT) 130.74/78.41 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) at position [10,0,0] we obtained the following new rules [LPAR04]: 130.74/78.41 130.74/78.41 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb)) 130.74/78.41 130.74/78.41 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (648) 130.74/78.41 Obligation: 130.74/78.41 Q DP problem: 130.74/78.41 The TRS P consists of the following rules: 130.74/78.41 130.74/78.41 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.41 130.74/78.41 The TRS R consists of the following rules: 130.74/78.41 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.41 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.41 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.41 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.41 new_primPlusNat2(Zero) -> Zero 130.74/78.41 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.41 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.41 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.41 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.41 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.41 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.41 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.41 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.41 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.41 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.41 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.41 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.41 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.41 130.74/78.41 The set Q consists of the following terms: 130.74/78.41 130.74/78.41 new_primPlusNat1(Succ(x0)) 130.74/78.41 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.41 new_primPlusNat1(Zero) 130.74/78.41 new_primPlusNat2(Zero) 130.74/78.41 new_primPlusNat3(Succ(x0)) 130.74/78.41 new_primPlusNat8(Succ(x0), x1) 130.74/78.41 new_primPlusNat6(x0, Succ(x1)) 130.74/78.41 new_primPlusNat0(Succ(x0), Zero) 130.74/78.41 new_primPlusNat6(x0, Zero) 130.74/78.41 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.41 new_primPlusNat4(Succ(x0)) 130.74/78.41 new_primPlusNat8(Zero, x0) 130.74/78.41 new_primPlusNat3(Zero) 130.74/78.41 new_primPlusNat7(x0, Zero) 130.74/78.41 new_primPlusNat7(x0, Succ(x1)) 130.74/78.41 new_primPlusNat4(Zero) 130.74/78.41 new_primPlusNat2(Succ(x0)) 130.74/78.41 new_primPlusNat0(Zero, Zero) 130.74/78.41 130.74/78.41 We have to consider all minimal (P,Q,R)-chains. 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (649) TransformationProof (EQUIVALENT) 130.74/78.41 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) at position [12] we obtained the following new rules [LPAR04]: 130.74/78.41 130.74/78.41 (new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h),new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h)) 130.74/78.41 130.74/78.41 130.74/78.41 ---------------------------------------- 130.74/78.41 130.74/78.41 (650) 130.74/78.41 Obligation: 130.74/78.41 Q DP problem: 130.74/78.41 The TRS P consists of the following rules: 130.74/78.41 130.74/78.41 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.41 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.41 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.41 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.42 130.74/78.42 The TRS R consists of the following rules: 130.74/78.42 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.42 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.42 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.42 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.42 new_primPlusNat2(Zero) -> Zero 130.74/78.42 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.42 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.42 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.42 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.42 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.42 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.42 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.42 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.42 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.42 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.42 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.42 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.42 130.74/78.42 The set Q consists of the following terms: 130.74/78.42 130.74/78.42 new_primPlusNat1(Succ(x0)) 130.74/78.42 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.42 new_primPlusNat1(Zero) 130.74/78.42 new_primPlusNat2(Zero) 130.74/78.42 new_primPlusNat3(Succ(x0)) 130.74/78.42 new_primPlusNat8(Succ(x0), x1) 130.74/78.42 new_primPlusNat6(x0, Succ(x1)) 130.74/78.42 new_primPlusNat0(Succ(x0), Zero) 130.74/78.42 new_primPlusNat6(x0, Zero) 130.74/78.42 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.42 new_primPlusNat4(Succ(x0)) 130.74/78.42 new_primPlusNat8(Zero, x0) 130.74/78.42 new_primPlusNat3(Zero) 130.74/78.42 new_primPlusNat7(x0, Zero) 130.74/78.42 new_primPlusNat7(x0, Succ(x1)) 130.74/78.42 new_primPlusNat4(Zero) 130.74/78.42 new_primPlusNat2(Succ(x0)) 130.74/78.42 new_primPlusNat0(Zero, Zero) 130.74/78.42 130.74/78.42 We have to consider all minimal (P,Q,R)-chains. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (651) TransformationProof (EQUIVALENT) 130.74/78.42 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Zero))))))), bb) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.42 130.74/78.42 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb)) 130.74/78.42 130.74/78.42 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (652) 130.74/78.42 Obligation: 130.74/78.42 Q DP problem: 130.74/78.42 The TRS P consists of the following rules: 130.74/78.42 130.74/78.42 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.74/78.42 130.74/78.42 The TRS R consists of the following rules: 130.74/78.42 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.42 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.42 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.42 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.42 new_primPlusNat2(Zero) -> Zero 130.74/78.42 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.42 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.42 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.42 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.42 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.42 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.42 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.42 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.42 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.42 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.42 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.42 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.42 130.74/78.42 The set Q consists of the following terms: 130.74/78.42 130.74/78.42 new_primPlusNat1(Succ(x0)) 130.74/78.42 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.42 new_primPlusNat1(Zero) 130.74/78.42 new_primPlusNat2(Zero) 130.74/78.42 new_primPlusNat3(Succ(x0)) 130.74/78.42 new_primPlusNat8(Succ(x0), x1) 130.74/78.42 new_primPlusNat6(x0, Succ(x1)) 130.74/78.42 new_primPlusNat0(Succ(x0), Zero) 130.74/78.42 new_primPlusNat6(x0, Zero) 130.74/78.42 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.42 new_primPlusNat4(Succ(x0)) 130.74/78.42 new_primPlusNat8(Zero, x0) 130.74/78.42 new_primPlusNat3(Zero) 130.74/78.42 new_primPlusNat7(x0, Zero) 130.74/78.42 new_primPlusNat7(x0, Succ(x1)) 130.74/78.42 new_primPlusNat4(Zero) 130.74/78.42 new_primPlusNat2(Succ(x0)) 130.74/78.42 new_primPlusNat0(Zero, Zero) 130.74/78.42 130.74/78.42 We have to consider all minimal (P,Q,R)-chains. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (653) TransformationProof (EQUIVALENT) 130.74/78.42 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.42 130.74/78.42 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb)) 130.74/78.42 130.74/78.42 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (654) 130.74/78.42 Obligation: 130.74/78.42 Q DP problem: 130.74/78.42 The TRS P consists of the following rules: 130.74/78.42 130.74/78.42 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.42 130.74/78.42 The TRS R consists of the following rules: 130.74/78.42 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.42 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.42 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.42 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.42 new_primPlusNat2(Zero) -> Zero 130.74/78.42 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.42 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.42 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.42 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.42 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.42 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.42 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.42 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.42 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.42 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.42 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.42 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.42 130.74/78.42 The set Q consists of the following terms: 130.74/78.42 130.74/78.42 new_primPlusNat1(Succ(x0)) 130.74/78.42 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.42 new_primPlusNat1(Zero) 130.74/78.42 new_primPlusNat2(Zero) 130.74/78.42 new_primPlusNat3(Succ(x0)) 130.74/78.42 new_primPlusNat8(Succ(x0), x1) 130.74/78.42 new_primPlusNat6(x0, Succ(x1)) 130.74/78.42 new_primPlusNat0(Succ(x0), Zero) 130.74/78.42 new_primPlusNat6(x0, Zero) 130.74/78.42 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.42 new_primPlusNat4(Succ(x0)) 130.74/78.42 new_primPlusNat8(Zero, x0) 130.74/78.42 new_primPlusNat3(Zero) 130.74/78.42 new_primPlusNat7(x0, Zero) 130.74/78.42 new_primPlusNat7(x0, Succ(x1)) 130.74/78.42 new_primPlusNat4(Zero) 130.74/78.42 new_primPlusNat2(Succ(x0)) 130.74/78.42 new_primPlusNat0(Zero, Zero) 130.74/78.42 130.74/78.42 We have to consider all minimal (P,Q,R)-chains. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (655) TransformationProof (EQUIVALENT) 130.74/78.42 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.42 130.74/78.42 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb)) 130.74/78.42 130.74/78.42 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (656) 130.74/78.42 Obligation: 130.74/78.42 Q DP problem: 130.74/78.42 The TRS P consists of the following rules: 130.74/78.42 130.74/78.42 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 130.74/78.42 The TRS R consists of the following rules: 130.74/78.42 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.42 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.42 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.42 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.42 new_primPlusNat2(Zero) -> Zero 130.74/78.42 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.42 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.42 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.42 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.42 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.42 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.42 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.42 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.42 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.42 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.42 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.42 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.42 130.74/78.42 The set Q consists of the following terms: 130.74/78.42 130.74/78.42 new_primPlusNat1(Succ(x0)) 130.74/78.42 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.42 new_primPlusNat1(Zero) 130.74/78.42 new_primPlusNat2(Zero) 130.74/78.42 new_primPlusNat3(Succ(x0)) 130.74/78.42 new_primPlusNat8(Succ(x0), x1) 130.74/78.42 new_primPlusNat6(x0, Succ(x1)) 130.74/78.42 new_primPlusNat0(Succ(x0), Zero) 130.74/78.42 new_primPlusNat6(x0, Zero) 130.74/78.42 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.42 new_primPlusNat4(Succ(x0)) 130.74/78.42 new_primPlusNat8(Zero, x0) 130.74/78.42 new_primPlusNat3(Zero) 130.74/78.42 new_primPlusNat7(x0, Zero) 130.74/78.42 new_primPlusNat7(x0, Succ(x1)) 130.74/78.42 new_primPlusNat4(Zero) 130.74/78.42 new_primPlusNat2(Succ(x0)) 130.74/78.42 new_primPlusNat0(Zero, Zero) 130.74/78.42 130.74/78.42 We have to consider all minimal (P,Q,R)-chains. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (657) TransformationProof (EQUIVALENT) 130.74/78.42 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708))), Succ(zzz4708)), Succ(zzz4708)), h) at position [12,0] we obtained the following new rules [LPAR04]: 130.74/78.42 130.74/78.42 (new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h),new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h)) 130.74/78.42 130.74/78.42 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (658) 130.74/78.42 Obligation: 130.74/78.42 Q DP problem: 130.74/78.42 The TRS P consists of the following rules: 130.74/78.42 130.74/78.42 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.42 130.74/78.42 The TRS R consists of the following rules: 130.74/78.42 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.42 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.42 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.42 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.42 new_primPlusNat2(Zero) -> Zero 130.74/78.42 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.42 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.42 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.42 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.42 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.42 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.42 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.42 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.42 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.42 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.42 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.42 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.42 130.74/78.42 The set Q consists of the following terms: 130.74/78.42 130.74/78.42 new_primPlusNat1(Succ(x0)) 130.74/78.42 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.42 new_primPlusNat1(Zero) 130.74/78.42 new_primPlusNat2(Zero) 130.74/78.42 new_primPlusNat3(Succ(x0)) 130.74/78.42 new_primPlusNat8(Succ(x0), x1) 130.74/78.42 new_primPlusNat6(x0, Succ(x1)) 130.74/78.42 new_primPlusNat0(Succ(x0), Zero) 130.74/78.42 new_primPlusNat6(x0, Zero) 130.74/78.42 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.42 new_primPlusNat4(Succ(x0)) 130.74/78.42 new_primPlusNat8(Zero, x0) 130.74/78.42 new_primPlusNat3(Zero) 130.74/78.42 new_primPlusNat7(x0, Zero) 130.74/78.42 new_primPlusNat7(x0, Succ(x1)) 130.74/78.42 new_primPlusNat4(Zero) 130.74/78.42 new_primPlusNat2(Succ(x0)) 130.74/78.42 new_primPlusNat0(Zero, Zero) 130.74/78.42 130.74/78.42 We have to consider all minimal (P,Q,R)-chains. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (659) TransformationProof (EQUIVALENT) 130.74/78.42 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) at position [11] we obtained the following new rules [LPAR04]: 130.74/78.42 130.74/78.42 (new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc),new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc)) 130.74/78.42 130.74/78.42 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (660) 130.74/78.42 Obligation: 130.74/78.42 Q DP problem: 130.74/78.42 The TRS P consists of the following rules: 130.74/78.42 130.74/78.42 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 130.74/78.42 The TRS R consists of the following rules: 130.74/78.42 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.42 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.42 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.42 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.42 new_primPlusNat2(Zero) -> Zero 130.74/78.42 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.42 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.42 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.42 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.42 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.42 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.42 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.42 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.42 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.42 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.42 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.42 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.42 130.74/78.42 The set Q consists of the following terms: 130.74/78.42 130.74/78.42 new_primPlusNat1(Succ(x0)) 130.74/78.42 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.42 new_primPlusNat1(Zero) 130.74/78.42 new_primPlusNat2(Zero) 130.74/78.42 new_primPlusNat3(Succ(x0)) 130.74/78.42 new_primPlusNat8(Succ(x0), x1) 130.74/78.42 new_primPlusNat6(x0, Succ(x1)) 130.74/78.42 new_primPlusNat0(Succ(x0), Zero) 130.74/78.42 new_primPlusNat6(x0, Zero) 130.74/78.42 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.42 new_primPlusNat4(Succ(x0)) 130.74/78.42 new_primPlusNat8(Zero, x0) 130.74/78.42 new_primPlusNat3(Zero) 130.74/78.42 new_primPlusNat7(x0, Zero) 130.74/78.42 new_primPlusNat7(x0, Succ(x1)) 130.74/78.42 new_primPlusNat4(Zero) 130.74/78.42 new_primPlusNat2(Succ(x0)) 130.74/78.42 new_primPlusNat0(Zero, Zero) 130.74/78.42 130.74/78.42 We have to consider all minimal (P,Q,R)-chains. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (661) TransformationProof (EQUIVALENT) 130.74/78.42 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) at position [11] we obtained the following new rules [LPAR04]: 130.74/78.42 130.74/78.42 (new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc),new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc)) 130.74/78.42 130.74/78.42 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (662) 130.74/78.42 Obligation: 130.74/78.42 Q DP problem: 130.74/78.42 The TRS P consists of the following rules: 130.74/78.42 130.74/78.42 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 130.74/78.42 The TRS R consists of the following rules: 130.74/78.42 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.42 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.42 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.42 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.42 new_primPlusNat2(Zero) -> Zero 130.74/78.42 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.42 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.42 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.42 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.42 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.42 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.42 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.42 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.42 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.42 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.42 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.42 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.42 130.74/78.42 The set Q consists of the following terms: 130.74/78.42 130.74/78.42 new_primPlusNat1(Succ(x0)) 130.74/78.42 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.42 new_primPlusNat1(Zero) 130.74/78.42 new_primPlusNat2(Zero) 130.74/78.42 new_primPlusNat3(Succ(x0)) 130.74/78.42 new_primPlusNat8(Succ(x0), x1) 130.74/78.42 new_primPlusNat6(x0, Succ(x1)) 130.74/78.42 new_primPlusNat0(Succ(x0), Zero) 130.74/78.42 new_primPlusNat6(x0, Zero) 130.74/78.42 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.42 new_primPlusNat4(Succ(x0)) 130.74/78.42 new_primPlusNat8(Zero, x0) 130.74/78.42 new_primPlusNat3(Zero) 130.74/78.42 new_primPlusNat7(x0, Zero) 130.74/78.42 new_primPlusNat7(x0, Succ(x1)) 130.74/78.42 new_primPlusNat4(Zero) 130.74/78.42 new_primPlusNat2(Succ(x0)) 130.74/78.42 new_primPlusNat0(Zero, Zero) 130.74/78.42 130.74/78.42 We have to consider all minimal (P,Q,R)-chains. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (663) TransformationProof (EQUIVALENT) 130.74/78.42 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882))), Succ(zzz3882)), bc) at position [11] we obtained the following new rules [LPAR04]: 130.74/78.42 130.74/78.42 (new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc),new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc)) 130.74/78.42 130.74/78.42 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (664) 130.74/78.42 Obligation: 130.74/78.42 Q DP problem: 130.74/78.42 The TRS P consists of the following rules: 130.74/78.42 130.74/78.42 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 130.74/78.42 The TRS R consists of the following rules: 130.74/78.42 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.42 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.42 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.42 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.42 new_primPlusNat2(Zero) -> Zero 130.74/78.42 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.42 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.42 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.42 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.42 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.42 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.42 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.42 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.42 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.42 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.42 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.42 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.42 130.74/78.42 The set Q consists of the following terms: 130.74/78.42 130.74/78.42 new_primPlusNat1(Succ(x0)) 130.74/78.42 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.42 new_primPlusNat1(Zero) 130.74/78.42 new_primPlusNat2(Zero) 130.74/78.42 new_primPlusNat3(Succ(x0)) 130.74/78.42 new_primPlusNat8(Succ(x0), x1) 130.74/78.42 new_primPlusNat6(x0, Succ(x1)) 130.74/78.42 new_primPlusNat0(Succ(x0), Zero) 130.74/78.42 new_primPlusNat6(x0, Zero) 130.74/78.42 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.42 new_primPlusNat4(Succ(x0)) 130.74/78.42 new_primPlusNat8(Zero, x0) 130.74/78.42 new_primPlusNat3(Zero) 130.74/78.42 new_primPlusNat7(x0, Zero) 130.74/78.42 new_primPlusNat7(x0, Succ(x1)) 130.74/78.42 new_primPlusNat4(Zero) 130.74/78.42 new_primPlusNat2(Succ(x0)) 130.74/78.42 new_primPlusNat0(Zero, Zero) 130.74/78.42 130.74/78.42 We have to consider all minimal (P,Q,R)-chains. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (665) DependencyGraphProof (EQUIVALENT) 130.74/78.42 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (666) 130.74/78.42 Obligation: 130.74/78.42 Q DP problem: 130.74/78.42 The TRS P consists of the following rules: 130.74/78.42 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.42 130.74/78.42 The TRS R consists of the following rules: 130.74/78.42 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.42 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.42 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.42 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.42 new_primPlusNat2(Zero) -> Zero 130.74/78.42 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.42 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.42 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.42 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.42 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.42 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.42 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.42 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.42 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.42 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.42 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.42 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.42 130.74/78.42 The set Q consists of the following terms: 130.74/78.42 130.74/78.42 new_primPlusNat1(Succ(x0)) 130.74/78.42 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.42 new_primPlusNat1(Zero) 130.74/78.42 new_primPlusNat2(Zero) 130.74/78.42 new_primPlusNat3(Succ(x0)) 130.74/78.42 new_primPlusNat8(Succ(x0), x1) 130.74/78.42 new_primPlusNat6(x0, Succ(x1)) 130.74/78.42 new_primPlusNat0(Succ(x0), Zero) 130.74/78.42 new_primPlusNat6(x0, Zero) 130.74/78.42 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.42 new_primPlusNat4(Succ(x0)) 130.74/78.42 new_primPlusNat8(Zero, x0) 130.74/78.42 new_primPlusNat3(Zero) 130.74/78.42 new_primPlusNat7(x0, Zero) 130.74/78.42 new_primPlusNat7(x0, Succ(x1)) 130.74/78.42 new_primPlusNat4(Zero) 130.74/78.42 new_primPlusNat2(Succ(x0)) 130.74/78.42 new_primPlusNat0(Zero, Zero) 130.74/78.42 130.74/78.42 We have to consider all minimal (P,Q,R)-chains. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (667) TransformationProof (EQUIVALENT) 130.74/78.42 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), Succ(Succ(Succ(Succ(Succ(Zero)))))), bb) at position [10] we obtained the following new rules [LPAR04]: 130.74/78.42 130.74/78.42 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb)) 130.74/78.42 130.74/78.42 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (668) 130.74/78.42 Obligation: 130.74/78.42 Q DP problem: 130.74/78.42 The TRS P consists of the following rules: 130.74/78.42 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Zero, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Zero, Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb) 130.74/78.42 130.74/78.42 The TRS R consists of the following rules: 130.74/78.42 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.42 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.42 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.42 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.42 new_primPlusNat2(Zero) -> Zero 130.74/78.42 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.42 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.42 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.42 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.42 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.42 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.42 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.42 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.42 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.42 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.42 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.42 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.42 130.74/78.42 The set Q consists of the following terms: 130.74/78.42 130.74/78.42 new_primPlusNat1(Succ(x0)) 130.74/78.42 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.42 new_primPlusNat1(Zero) 130.74/78.42 new_primPlusNat2(Zero) 130.74/78.42 new_primPlusNat3(Succ(x0)) 130.74/78.42 new_primPlusNat8(Succ(x0), x1) 130.74/78.42 new_primPlusNat6(x0, Succ(x1)) 130.74/78.42 new_primPlusNat0(Succ(x0), Zero) 130.74/78.42 new_primPlusNat6(x0, Zero) 130.74/78.42 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.42 new_primPlusNat4(Succ(x0)) 130.74/78.42 new_primPlusNat8(Zero, x0) 130.74/78.42 new_primPlusNat3(Zero) 130.74/78.42 new_primPlusNat7(x0, Zero) 130.74/78.42 new_primPlusNat7(x0, Succ(x1)) 130.74/78.42 new_primPlusNat4(Zero) 130.74/78.42 new_primPlusNat2(Succ(x0)) 130.74/78.42 new_primPlusNat0(Zero, Zero) 130.74/78.42 130.74/78.42 We have to consider all minimal (P,Q,R)-chains. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (669) DependencyGraphProof (EQUIVALENT) 130.74/78.42 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (670) 130.74/78.42 Obligation: 130.74/78.42 Q DP problem: 130.74/78.42 The TRS P consists of the following rules: 130.74/78.42 130.74/78.42 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.42 130.74/78.42 The TRS R consists of the following rules: 130.74/78.42 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.42 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.42 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.42 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.42 new_primPlusNat2(Zero) -> Zero 130.74/78.42 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.42 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.42 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.42 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.42 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.42 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.42 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.42 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.42 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.42 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.42 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.42 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.42 130.74/78.42 The set Q consists of the following terms: 130.74/78.42 130.74/78.42 new_primPlusNat1(Succ(x0)) 130.74/78.42 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.42 new_primPlusNat1(Zero) 130.74/78.42 new_primPlusNat2(Zero) 130.74/78.42 new_primPlusNat3(Succ(x0)) 130.74/78.42 new_primPlusNat8(Succ(x0), x1) 130.74/78.42 new_primPlusNat6(x0, Succ(x1)) 130.74/78.42 new_primPlusNat0(Succ(x0), Zero) 130.74/78.42 new_primPlusNat6(x0, Zero) 130.74/78.42 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.42 new_primPlusNat4(Succ(x0)) 130.74/78.42 new_primPlusNat8(Zero, x0) 130.74/78.42 new_primPlusNat3(Zero) 130.74/78.42 new_primPlusNat7(x0, Zero) 130.74/78.42 new_primPlusNat7(x0, Succ(x1)) 130.74/78.42 new_primPlusNat4(Zero) 130.74/78.42 new_primPlusNat2(Succ(x0)) 130.74/78.42 new_primPlusNat0(Zero, Zero) 130.74/78.42 130.74/78.42 We have to consider all minimal (P,Q,R)-chains. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (671) TransformationProof (EQUIVALENT) 130.74/78.42 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero)))))))))))), bb) at position [10,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.42 130.74/78.42 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb)) 130.74/78.42 130.74/78.42 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (672) 130.74/78.42 Obligation: 130.74/78.42 Q DP problem: 130.74/78.42 The TRS P consists of the following rules: 130.74/78.42 130.74/78.42 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.42 130.74/78.42 The TRS R consists of the following rules: 130.74/78.42 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.42 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.42 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.42 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.42 new_primPlusNat2(Zero) -> Zero 130.74/78.42 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.42 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.42 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.42 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.42 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.42 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.42 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.42 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.42 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.42 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.42 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.42 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.42 130.74/78.42 The set Q consists of the following terms: 130.74/78.42 130.74/78.42 new_primPlusNat1(Succ(x0)) 130.74/78.42 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.42 new_primPlusNat1(Zero) 130.74/78.42 new_primPlusNat2(Zero) 130.74/78.42 new_primPlusNat3(Succ(x0)) 130.74/78.42 new_primPlusNat8(Succ(x0), x1) 130.74/78.42 new_primPlusNat6(x0, Succ(x1)) 130.74/78.42 new_primPlusNat0(Succ(x0), Zero) 130.74/78.42 new_primPlusNat6(x0, Zero) 130.74/78.42 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.42 new_primPlusNat4(Succ(x0)) 130.74/78.42 new_primPlusNat8(Zero, x0) 130.74/78.42 new_primPlusNat3(Zero) 130.74/78.42 new_primPlusNat7(x0, Zero) 130.74/78.42 new_primPlusNat7(x0, Succ(x1)) 130.74/78.42 new_primPlusNat4(Zero) 130.74/78.42 new_primPlusNat2(Succ(x0)) 130.74/78.42 new_primPlusNat0(Zero, Zero) 130.74/78.42 130.74/78.42 We have to consider all minimal (P,Q,R)-chains. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (673) TransformationProof (EQUIVALENT) 130.74/78.42 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero)))))), bb) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.42 130.74/78.42 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb)) 130.74/78.42 130.74/78.42 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (674) 130.74/78.42 Obligation: 130.74/78.42 Q DP problem: 130.74/78.42 The TRS P consists of the following rules: 130.74/78.42 130.74/78.42 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.42 130.74/78.42 The TRS R consists of the following rules: 130.74/78.42 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.42 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.42 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.42 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.42 new_primPlusNat2(Zero) -> Zero 130.74/78.42 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.42 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.42 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.42 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.42 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.42 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.42 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.42 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.42 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.42 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.42 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.42 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.42 130.74/78.42 The set Q consists of the following terms: 130.74/78.42 130.74/78.42 new_primPlusNat1(Succ(x0)) 130.74/78.42 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.42 new_primPlusNat1(Zero) 130.74/78.42 new_primPlusNat2(Zero) 130.74/78.42 new_primPlusNat3(Succ(x0)) 130.74/78.42 new_primPlusNat8(Succ(x0), x1) 130.74/78.42 new_primPlusNat6(x0, Succ(x1)) 130.74/78.42 new_primPlusNat0(Succ(x0), Zero) 130.74/78.42 new_primPlusNat6(x0, Zero) 130.74/78.42 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.42 new_primPlusNat4(Succ(x0)) 130.74/78.42 new_primPlusNat8(Zero, x0) 130.74/78.42 new_primPlusNat3(Zero) 130.74/78.42 new_primPlusNat7(x0, Zero) 130.74/78.42 new_primPlusNat7(x0, Succ(x1)) 130.74/78.42 new_primPlusNat4(Zero) 130.74/78.42 new_primPlusNat2(Succ(x0)) 130.74/78.42 new_primPlusNat0(Zero, Zero) 130.74/78.42 130.74/78.42 We have to consider all minimal (P,Q,R)-chains. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (675) TransformationProof (EQUIVALENT) 130.74/78.42 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) at position [11,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.42 130.74/78.42 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))))))))), bb)) 130.74/78.42 130.74/78.42 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (676) 130.74/78.42 Obligation: 130.74/78.42 Q DP problem: 130.74/78.42 The TRS P consists of the following rules: 130.74/78.42 130.74/78.42 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.42 130.74/78.42 The TRS R consists of the following rules: 130.74/78.42 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.42 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.42 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.42 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.42 new_primPlusNat2(Zero) -> Zero 130.74/78.42 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.42 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.42 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.42 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.42 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.42 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.42 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.42 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.42 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.42 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.42 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.42 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.42 130.74/78.42 The set Q consists of the following terms: 130.74/78.42 130.74/78.42 new_primPlusNat1(Succ(x0)) 130.74/78.42 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.42 new_primPlusNat1(Zero) 130.74/78.42 new_primPlusNat2(Zero) 130.74/78.42 new_primPlusNat3(Succ(x0)) 130.74/78.42 new_primPlusNat8(Succ(x0), x1) 130.74/78.42 new_primPlusNat6(x0, Succ(x1)) 130.74/78.42 new_primPlusNat0(Succ(x0), Zero) 130.74/78.42 new_primPlusNat6(x0, Zero) 130.74/78.42 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.42 new_primPlusNat4(Succ(x0)) 130.74/78.42 new_primPlusNat8(Zero, x0) 130.74/78.42 new_primPlusNat3(Zero) 130.74/78.42 new_primPlusNat7(x0, Zero) 130.74/78.42 new_primPlusNat7(x0, Succ(x1)) 130.74/78.42 new_primPlusNat4(Zero) 130.74/78.42 new_primPlusNat2(Succ(x0)) 130.74/78.42 new_primPlusNat0(Zero, Zero) 130.74/78.42 130.74/78.42 We have to consider all minimal (P,Q,R)-chains. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (677) TransformationProof (EQUIVALENT) 130.74/78.42 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) at position [11,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.42 130.74/78.42 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb)) 130.74/78.42 130.74/78.42 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (678) 130.74/78.42 Obligation: 130.74/78.42 Q DP problem: 130.74/78.42 The TRS P consists of the following rules: 130.74/78.42 130.74/78.42 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.42 130.74/78.42 The TRS R consists of the following rules: 130.74/78.42 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.42 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.42 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.42 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.42 new_primPlusNat2(Zero) -> Zero 130.74/78.42 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.42 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.42 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.42 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.42 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.42 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.42 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.42 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.42 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.42 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.42 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.42 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.42 130.74/78.42 The set Q consists of the following terms: 130.74/78.42 130.74/78.42 new_primPlusNat1(Succ(x0)) 130.74/78.42 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.42 new_primPlusNat1(Zero) 130.74/78.42 new_primPlusNat2(Zero) 130.74/78.42 new_primPlusNat3(Succ(x0)) 130.74/78.42 new_primPlusNat8(Succ(x0), x1) 130.74/78.42 new_primPlusNat6(x0, Succ(x1)) 130.74/78.42 new_primPlusNat0(Succ(x0), Zero) 130.74/78.42 new_primPlusNat6(x0, Zero) 130.74/78.42 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.42 new_primPlusNat4(Succ(x0)) 130.74/78.42 new_primPlusNat8(Zero, x0) 130.74/78.42 new_primPlusNat3(Zero) 130.74/78.42 new_primPlusNat7(x0, Zero) 130.74/78.42 new_primPlusNat7(x0, Succ(x1)) 130.74/78.42 new_primPlusNat4(Zero) 130.74/78.42 new_primPlusNat2(Succ(x0)) 130.74/78.42 new_primPlusNat0(Zero, Zero) 130.74/78.42 130.74/78.42 We have to consider all minimal (P,Q,R)-chains. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (679) TransformationProof (EQUIVALENT) 130.74/78.42 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708))), Succ(zzz4708)), h) at position [12] we obtained the following new rules [LPAR04]: 130.74/78.42 130.74/78.42 (new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h),new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h)) 130.74/78.42 130.74/78.42 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (680) 130.74/78.42 Obligation: 130.74/78.42 Q DP problem: 130.74/78.42 The TRS P consists of the following rules: 130.74/78.42 130.74/78.42 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.42 130.74/78.42 The TRS R consists of the following rules: 130.74/78.42 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.42 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.42 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.42 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.42 new_primPlusNat2(Zero) -> Zero 130.74/78.42 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.42 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.42 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.42 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.42 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.42 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.42 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.42 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.42 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.42 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.42 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.42 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.42 130.74/78.42 The set Q consists of the following terms: 130.74/78.42 130.74/78.42 new_primPlusNat1(Succ(x0)) 130.74/78.42 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.42 new_primPlusNat1(Zero) 130.74/78.42 new_primPlusNat2(Zero) 130.74/78.42 new_primPlusNat3(Succ(x0)) 130.74/78.42 new_primPlusNat8(Succ(x0), x1) 130.74/78.42 new_primPlusNat6(x0, Succ(x1)) 130.74/78.42 new_primPlusNat0(Succ(x0), Zero) 130.74/78.42 new_primPlusNat6(x0, Zero) 130.74/78.42 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.42 new_primPlusNat4(Succ(x0)) 130.74/78.42 new_primPlusNat8(Zero, x0) 130.74/78.42 new_primPlusNat3(Zero) 130.74/78.42 new_primPlusNat7(x0, Zero) 130.74/78.42 new_primPlusNat7(x0, Succ(x1)) 130.74/78.42 new_primPlusNat4(Zero) 130.74/78.42 new_primPlusNat2(Succ(x0)) 130.74/78.42 new_primPlusNat0(Zero, Zero) 130.74/78.42 130.74/78.42 We have to consider all minimal (P,Q,R)-chains. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (681) DependencyGraphProof (EQUIVALENT) 130.74/78.42 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (682) 130.74/78.42 Obligation: 130.74/78.42 Q DP problem: 130.74/78.42 The TRS P consists of the following rules: 130.74/78.42 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.42 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.42 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.42 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.42 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.42 130.74/78.42 The TRS R consists of the following rules: 130.74/78.42 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.42 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.42 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.42 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.42 new_primPlusNat2(Zero) -> Zero 130.74/78.42 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.42 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.42 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.42 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.42 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.42 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.42 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.42 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.42 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.42 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.42 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.42 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.42 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.42 130.74/78.42 The set Q consists of the following terms: 130.74/78.42 130.74/78.42 new_primPlusNat1(Succ(x0)) 130.74/78.42 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.42 new_primPlusNat1(Zero) 130.74/78.42 new_primPlusNat2(Zero) 130.74/78.42 new_primPlusNat3(Succ(x0)) 130.74/78.42 new_primPlusNat8(Succ(x0), x1) 130.74/78.42 new_primPlusNat6(x0, Succ(x1)) 130.74/78.42 new_primPlusNat0(Succ(x0), Zero) 130.74/78.42 new_primPlusNat6(x0, Zero) 130.74/78.42 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.42 new_primPlusNat4(Succ(x0)) 130.74/78.42 new_primPlusNat8(Zero, x0) 130.74/78.42 new_primPlusNat3(Zero) 130.74/78.42 new_primPlusNat7(x0, Zero) 130.74/78.42 new_primPlusNat7(x0, Succ(x1)) 130.74/78.42 new_primPlusNat4(Zero) 130.74/78.42 new_primPlusNat2(Succ(x0)) 130.74/78.42 new_primPlusNat0(Zero, Zero) 130.74/78.42 130.74/78.42 We have to consider all minimal (P,Q,R)-chains. 130.74/78.42 ---------------------------------------- 130.74/78.42 130.74/78.42 (683) TransformationProof (EQUIVALENT) 130.74/78.42 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), bb) at position [10,0,0] we obtained the following new rules [LPAR04]: 130.74/78.42 130.74/78.42 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))))), bb)) 130.74/78.43 130.74/78.43 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (684) 130.74/78.43 Obligation: 130.74/78.43 Q DP problem: 130.74/78.43 The TRS P consists of the following rules: 130.74/78.43 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.43 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))))), bb) 130.74/78.43 130.74/78.43 The TRS R consists of the following rules: 130.74/78.43 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.43 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.43 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.43 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.43 new_primPlusNat2(Zero) -> Zero 130.74/78.43 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.43 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.43 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.43 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.43 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.43 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.43 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.43 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.43 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.43 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.43 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.43 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.43 130.74/78.43 The set Q consists of the following terms: 130.74/78.43 130.74/78.43 new_primPlusNat1(Succ(x0)) 130.74/78.43 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.43 new_primPlusNat1(Zero) 130.74/78.43 new_primPlusNat2(Zero) 130.74/78.43 new_primPlusNat3(Succ(x0)) 130.74/78.43 new_primPlusNat8(Succ(x0), x1) 130.74/78.43 new_primPlusNat6(x0, Succ(x1)) 130.74/78.43 new_primPlusNat0(Succ(x0), Zero) 130.74/78.43 new_primPlusNat6(x0, Zero) 130.74/78.43 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.43 new_primPlusNat4(Succ(x0)) 130.74/78.43 new_primPlusNat8(Zero, x0) 130.74/78.43 new_primPlusNat3(Zero) 130.74/78.43 new_primPlusNat7(x0, Zero) 130.74/78.43 new_primPlusNat7(x0, Succ(x1)) 130.74/78.43 new_primPlusNat4(Zero) 130.74/78.43 new_primPlusNat2(Succ(x0)) 130.74/78.43 new_primPlusNat0(Zero, Zero) 130.74/78.43 130.74/78.43 We have to consider all minimal (P,Q,R)-chains. 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (685) TransformationProof (EQUIVALENT) 130.74/78.43 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))))))))), bb) at position [11,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.43 130.74/78.43 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))))))), bb)) 130.74/78.43 130.74/78.43 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (686) 130.74/78.43 Obligation: 130.74/78.43 Q DP problem: 130.74/78.43 The TRS P consists of the following rules: 130.74/78.43 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.43 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.43 130.74/78.43 The TRS R consists of the following rules: 130.74/78.43 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.43 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.43 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.43 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.43 new_primPlusNat2(Zero) -> Zero 130.74/78.43 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.43 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.43 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.43 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.43 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.43 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.43 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.43 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.43 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.43 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.43 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.43 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.43 130.74/78.43 The set Q consists of the following terms: 130.74/78.43 130.74/78.43 new_primPlusNat1(Succ(x0)) 130.74/78.43 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.43 new_primPlusNat1(Zero) 130.74/78.43 new_primPlusNat2(Zero) 130.74/78.43 new_primPlusNat3(Succ(x0)) 130.74/78.43 new_primPlusNat8(Succ(x0), x1) 130.74/78.43 new_primPlusNat6(x0, Succ(x1)) 130.74/78.43 new_primPlusNat0(Succ(x0), Zero) 130.74/78.43 new_primPlusNat6(x0, Zero) 130.74/78.43 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.43 new_primPlusNat4(Succ(x0)) 130.74/78.43 new_primPlusNat8(Zero, x0) 130.74/78.43 new_primPlusNat3(Zero) 130.74/78.43 new_primPlusNat7(x0, Zero) 130.74/78.43 new_primPlusNat7(x0, Succ(x1)) 130.74/78.43 new_primPlusNat4(Zero) 130.74/78.43 new_primPlusNat2(Succ(x0)) 130.74/78.43 new_primPlusNat0(Zero, Zero) 130.74/78.43 130.74/78.43 We have to consider all minimal (P,Q,R)-chains. 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (687) TransformationProof (EQUIVALENT) 130.74/78.43 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))), bb) at position [11,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.43 130.74/78.43 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))), bb)) 130.74/78.43 130.74/78.43 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (688) 130.74/78.43 Obligation: 130.74/78.43 Q DP problem: 130.74/78.43 The TRS P consists of the following rules: 130.74/78.43 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.43 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))), bb) 130.74/78.43 130.74/78.43 The TRS R consists of the following rules: 130.74/78.43 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.43 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.43 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.43 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.43 new_primPlusNat2(Zero) -> Zero 130.74/78.43 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.43 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.43 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.43 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.43 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.43 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.43 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.43 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.43 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.43 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.43 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.43 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.43 130.74/78.43 The set Q consists of the following terms: 130.74/78.43 130.74/78.43 new_primPlusNat1(Succ(x0)) 130.74/78.43 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.43 new_primPlusNat1(Zero) 130.74/78.43 new_primPlusNat2(Zero) 130.74/78.43 new_primPlusNat3(Succ(x0)) 130.74/78.43 new_primPlusNat8(Succ(x0), x1) 130.74/78.43 new_primPlusNat6(x0, Succ(x1)) 130.74/78.43 new_primPlusNat0(Succ(x0), Zero) 130.74/78.43 new_primPlusNat6(x0, Zero) 130.74/78.43 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.43 new_primPlusNat4(Succ(x0)) 130.74/78.43 new_primPlusNat8(Zero, x0) 130.74/78.43 new_primPlusNat3(Zero) 130.74/78.43 new_primPlusNat7(x0, Zero) 130.74/78.43 new_primPlusNat7(x0, Succ(x1)) 130.74/78.43 new_primPlusNat4(Zero) 130.74/78.43 new_primPlusNat2(Succ(x0)) 130.74/78.43 new_primPlusNat0(Zero, Zero) 130.74/78.43 130.74/78.43 We have to consider all minimal (P,Q,R)-chains. 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (689) TransformationProof (EQUIVALENT) 130.74/78.43 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))), bb) at position [10,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.43 130.74/78.43 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))), bb)) 130.74/78.43 130.74/78.43 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (690) 130.74/78.43 Obligation: 130.74/78.43 Q DP problem: 130.74/78.43 The TRS P consists of the following rules: 130.74/78.43 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.43 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))), bb) 130.74/78.43 130.74/78.43 The TRS R consists of the following rules: 130.74/78.43 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.43 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.43 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.43 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.43 new_primPlusNat2(Zero) -> Zero 130.74/78.43 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.43 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.43 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.43 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.43 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.43 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.43 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.43 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.43 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.43 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.43 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.43 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.43 130.74/78.43 The set Q consists of the following terms: 130.74/78.43 130.74/78.43 new_primPlusNat1(Succ(x0)) 130.74/78.43 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.43 new_primPlusNat1(Zero) 130.74/78.43 new_primPlusNat2(Zero) 130.74/78.43 new_primPlusNat3(Succ(x0)) 130.74/78.43 new_primPlusNat8(Succ(x0), x1) 130.74/78.43 new_primPlusNat6(x0, Succ(x1)) 130.74/78.43 new_primPlusNat0(Succ(x0), Zero) 130.74/78.43 new_primPlusNat6(x0, Zero) 130.74/78.43 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.43 new_primPlusNat4(Succ(x0)) 130.74/78.43 new_primPlusNat8(Zero, x0) 130.74/78.43 new_primPlusNat3(Zero) 130.74/78.43 new_primPlusNat7(x0, Zero) 130.74/78.43 new_primPlusNat7(x0, Succ(x1)) 130.74/78.43 new_primPlusNat4(Zero) 130.74/78.43 new_primPlusNat2(Succ(x0)) 130.74/78.43 new_primPlusNat0(Zero, Zero) 130.74/78.43 130.74/78.43 We have to consider all minimal (P,Q,R)-chains. 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (691) TransformationProof (EQUIVALENT) 130.74/78.43 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))))), bb) at position [10,0,0] we obtained the following new rules [LPAR04]: 130.74/78.43 130.74/78.43 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))))), bb)) 130.74/78.43 130.74/78.43 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (692) 130.74/78.43 Obligation: 130.74/78.43 Q DP problem: 130.74/78.43 The TRS P consists of the following rules: 130.74/78.43 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.43 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))))), bb) 130.74/78.43 130.74/78.43 The TRS R consists of the following rules: 130.74/78.43 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.43 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.43 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.43 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.43 new_primPlusNat2(Zero) -> Zero 130.74/78.43 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.43 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.43 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.43 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.43 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.43 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.43 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.43 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.43 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.43 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.43 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.43 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.43 130.74/78.43 The set Q consists of the following terms: 130.74/78.43 130.74/78.43 new_primPlusNat1(Succ(x0)) 130.74/78.43 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.43 new_primPlusNat1(Zero) 130.74/78.43 new_primPlusNat2(Zero) 130.74/78.43 new_primPlusNat3(Succ(x0)) 130.74/78.43 new_primPlusNat8(Succ(x0), x1) 130.74/78.43 new_primPlusNat6(x0, Succ(x1)) 130.74/78.43 new_primPlusNat0(Succ(x0), Zero) 130.74/78.43 new_primPlusNat6(x0, Zero) 130.74/78.43 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.43 new_primPlusNat4(Succ(x0)) 130.74/78.43 new_primPlusNat8(Zero, x0) 130.74/78.43 new_primPlusNat3(Zero) 130.74/78.43 new_primPlusNat7(x0, Zero) 130.74/78.43 new_primPlusNat7(x0, Succ(x1)) 130.74/78.43 new_primPlusNat4(Zero) 130.74/78.43 new_primPlusNat2(Succ(x0)) 130.74/78.43 new_primPlusNat0(Zero, Zero) 130.74/78.43 130.74/78.43 We have to consider all minimal (P,Q,R)-chains. 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (693) TransformationProof (EQUIVALENT) 130.74/78.43 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(Succ(Zero))))))))))), bb) at position [10,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.43 130.74/78.43 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))))))))), bb)) 130.74/78.43 130.74/78.43 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (694) 130.74/78.43 Obligation: 130.74/78.43 Q DP problem: 130.74/78.43 The TRS P consists of the following rules: 130.74/78.43 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.43 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.43 130.74/78.43 The TRS R consists of the following rules: 130.74/78.43 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.43 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.43 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.43 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.43 new_primPlusNat2(Zero) -> Zero 130.74/78.43 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.43 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.43 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.43 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.43 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.43 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.43 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.43 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.43 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.43 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.43 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.43 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.43 130.74/78.43 The set Q consists of the following terms: 130.74/78.43 130.74/78.43 new_primPlusNat1(Succ(x0)) 130.74/78.43 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.43 new_primPlusNat1(Zero) 130.74/78.43 new_primPlusNat2(Zero) 130.74/78.43 new_primPlusNat3(Succ(x0)) 130.74/78.43 new_primPlusNat8(Succ(x0), x1) 130.74/78.43 new_primPlusNat6(x0, Succ(x1)) 130.74/78.43 new_primPlusNat0(Succ(x0), Zero) 130.74/78.43 new_primPlusNat6(x0, Zero) 130.74/78.43 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.43 new_primPlusNat4(Succ(x0)) 130.74/78.43 new_primPlusNat8(Zero, x0) 130.74/78.43 new_primPlusNat3(Zero) 130.74/78.43 new_primPlusNat7(x0, Zero) 130.74/78.43 new_primPlusNat7(x0, Succ(x1)) 130.74/78.43 new_primPlusNat4(Zero) 130.74/78.43 new_primPlusNat2(Succ(x0)) 130.74/78.43 new_primPlusNat0(Zero, Zero) 130.74/78.43 130.74/78.43 We have to consider all minimal (P,Q,R)-chains. 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (695) TransformationProof (EQUIVALENT) 130.74/78.43 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))))), bb) at position [10,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.43 130.74/78.43 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))))))), bb)) 130.74/78.43 130.74/78.43 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (696) 130.74/78.43 Obligation: 130.74/78.43 Q DP problem: 130.74/78.43 The TRS P consists of the following rules: 130.74/78.43 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.43 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))))))), bb) 130.74/78.43 130.74/78.43 The TRS R consists of the following rules: 130.74/78.43 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.43 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.43 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.43 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.43 new_primPlusNat2(Zero) -> Zero 130.74/78.43 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.43 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.43 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.43 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.43 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.43 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.43 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.43 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.43 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.43 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.43 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.43 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.43 130.74/78.43 The set Q consists of the following terms: 130.74/78.43 130.74/78.43 new_primPlusNat1(Succ(x0)) 130.74/78.43 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.43 new_primPlusNat1(Zero) 130.74/78.43 new_primPlusNat2(Zero) 130.74/78.43 new_primPlusNat3(Succ(x0)) 130.74/78.43 new_primPlusNat8(Succ(x0), x1) 130.74/78.43 new_primPlusNat6(x0, Succ(x1)) 130.74/78.43 new_primPlusNat0(Succ(x0), Zero) 130.74/78.43 new_primPlusNat6(x0, Zero) 130.74/78.43 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.43 new_primPlusNat4(Succ(x0)) 130.74/78.43 new_primPlusNat8(Zero, x0) 130.74/78.43 new_primPlusNat3(Zero) 130.74/78.43 new_primPlusNat7(x0, Zero) 130.74/78.43 new_primPlusNat7(x0, Succ(x1)) 130.74/78.43 new_primPlusNat4(Zero) 130.74/78.43 new_primPlusNat2(Succ(x0)) 130.74/78.43 new_primPlusNat0(Zero, Zero) 130.74/78.43 130.74/78.43 We have to consider all minimal (P,Q,R)-chains. 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (697) TransformationProof (EQUIVALENT) 130.74/78.43 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.43 130.74/78.43 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero)))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero)))))))))))), bb)) 130.74/78.43 130.74/78.43 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (698) 130.74/78.43 Obligation: 130.74/78.43 Q DP problem: 130.74/78.43 The TRS P consists of the following rules: 130.74/78.43 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.43 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero)))))))))))), bb) 130.74/78.43 130.74/78.43 The TRS R consists of the following rules: 130.74/78.43 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.43 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.43 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.43 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.43 new_primPlusNat2(Zero) -> Zero 130.74/78.43 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.43 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.43 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.43 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.43 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.43 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.43 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.43 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.43 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.43 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.43 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.43 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.43 130.74/78.43 The set Q consists of the following terms: 130.74/78.43 130.74/78.43 new_primPlusNat1(Succ(x0)) 130.74/78.43 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.43 new_primPlusNat1(Zero) 130.74/78.43 new_primPlusNat2(Zero) 130.74/78.43 new_primPlusNat3(Succ(x0)) 130.74/78.43 new_primPlusNat8(Succ(x0), x1) 130.74/78.43 new_primPlusNat6(x0, Succ(x1)) 130.74/78.43 new_primPlusNat0(Succ(x0), Zero) 130.74/78.43 new_primPlusNat6(x0, Zero) 130.74/78.43 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.43 new_primPlusNat4(Succ(x0)) 130.74/78.43 new_primPlusNat8(Zero, x0) 130.74/78.43 new_primPlusNat3(Zero) 130.74/78.43 new_primPlusNat7(x0, Zero) 130.74/78.43 new_primPlusNat7(x0, Succ(x1)) 130.74/78.43 new_primPlusNat4(Zero) 130.74/78.43 new_primPlusNat2(Succ(x0)) 130.74/78.43 new_primPlusNat0(Zero, Zero) 130.74/78.43 130.74/78.43 We have to consider all minimal (P,Q,R)-chains. 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (699) TransformationProof (EQUIVALENT) 130.74/78.43 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))), bb) at position [11,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.43 130.74/78.43 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))), bb)) 130.74/78.43 130.74/78.43 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (700) 130.74/78.43 Obligation: 130.74/78.43 Q DP problem: 130.74/78.43 The TRS P consists of the following rules: 130.74/78.43 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.43 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))), bb) 130.74/78.43 130.74/78.43 The TRS R consists of the following rules: 130.74/78.43 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.43 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.43 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.43 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.43 new_primPlusNat2(Zero) -> Zero 130.74/78.43 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.43 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.43 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.43 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.43 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.43 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.43 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.43 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.43 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.43 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.43 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.43 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.43 130.74/78.43 The set Q consists of the following terms: 130.74/78.43 130.74/78.43 new_primPlusNat1(Succ(x0)) 130.74/78.43 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.43 new_primPlusNat1(Zero) 130.74/78.43 new_primPlusNat2(Zero) 130.74/78.43 new_primPlusNat3(Succ(x0)) 130.74/78.43 new_primPlusNat8(Succ(x0), x1) 130.74/78.43 new_primPlusNat6(x0, Succ(x1)) 130.74/78.43 new_primPlusNat0(Succ(x0), Zero) 130.74/78.43 new_primPlusNat6(x0, Zero) 130.74/78.43 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.43 new_primPlusNat4(Succ(x0)) 130.74/78.43 new_primPlusNat8(Zero, x0) 130.74/78.43 new_primPlusNat3(Zero) 130.74/78.43 new_primPlusNat7(x0, Zero) 130.74/78.43 new_primPlusNat7(x0, Succ(x1)) 130.74/78.43 new_primPlusNat4(Zero) 130.74/78.43 new_primPlusNat2(Succ(x0)) 130.74/78.43 new_primPlusNat0(Zero, Zero) 130.74/78.43 130.74/78.43 We have to consider all minimal (P,Q,R)-chains. 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (701) TransformationProof (EQUIVALENT) 130.74/78.43 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))), bb) at position [10,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.43 130.74/78.43 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb)) 130.74/78.43 130.74/78.43 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (702) 130.74/78.43 Obligation: 130.74/78.43 Q DP problem: 130.74/78.43 The TRS P consists of the following rules: 130.74/78.43 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.43 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb) 130.74/78.43 130.74/78.43 The TRS R consists of the following rules: 130.74/78.43 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.43 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.43 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.43 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.43 new_primPlusNat2(Zero) -> Zero 130.74/78.43 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.43 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.43 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.43 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.43 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.43 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.43 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.43 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.43 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.43 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.43 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.43 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.43 130.74/78.43 The set Q consists of the following terms: 130.74/78.43 130.74/78.43 new_primPlusNat1(Succ(x0)) 130.74/78.43 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.43 new_primPlusNat1(Zero) 130.74/78.43 new_primPlusNat2(Zero) 130.74/78.43 new_primPlusNat3(Succ(x0)) 130.74/78.43 new_primPlusNat8(Succ(x0), x1) 130.74/78.43 new_primPlusNat6(x0, Succ(x1)) 130.74/78.43 new_primPlusNat0(Succ(x0), Zero) 130.74/78.43 new_primPlusNat6(x0, Zero) 130.74/78.43 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.43 new_primPlusNat4(Succ(x0)) 130.74/78.43 new_primPlusNat8(Zero, x0) 130.74/78.43 new_primPlusNat3(Zero) 130.74/78.43 new_primPlusNat7(x0, Zero) 130.74/78.43 new_primPlusNat7(x0, Succ(x1)) 130.74/78.43 new_primPlusNat4(Zero) 130.74/78.43 new_primPlusNat2(Succ(x0)) 130.74/78.43 new_primPlusNat0(Zero, Zero) 130.74/78.43 130.74/78.43 We have to consider all minimal (P,Q,R)-chains. 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (703) TransformationProof (EQUIVALENT) 130.74/78.43 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))))), bb) at position [10,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.43 130.74/78.43 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))))))), bb)) 130.74/78.43 130.74/78.43 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (704) 130.74/78.43 Obligation: 130.74/78.43 Q DP problem: 130.74/78.43 The TRS P consists of the following rules: 130.74/78.43 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.43 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))))))), bb) 130.74/78.43 130.74/78.43 The TRS R consists of the following rules: 130.74/78.43 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.43 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.43 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.43 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.43 new_primPlusNat2(Zero) -> Zero 130.74/78.43 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.43 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.43 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.43 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.43 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.43 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.43 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.43 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.43 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.43 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.43 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.43 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.43 130.74/78.43 The set Q consists of the following terms: 130.74/78.43 130.74/78.43 new_primPlusNat1(Succ(x0)) 130.74/78.43 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.43 new_primPlusNat1(Zero) 130.74/78.43 new_primPlusNat2(Zero) 130.74/78.43 new_primPlusNat3(Succ(x0)) 130.74/78.43 new_primPlusNat8(Succ(x0), x1) 130.74/78.43 new_primPlusNat6(x0, Succ(x1)) 130.74/78.43 new_primPlusNat0(Succ(x0), Zero) 130.74/78.43 new_primPlusNat6(x0, Zero) 130.74/78.43 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.43 new_primPlusNat4(Succ(x0)) 130.74/78.43 new_primPlusNat8(Zero, x0) 130.74/78.43 new_primPlusNat3(Zero) 130.74/78.43 new_primPlusNat7(x0, Zero) 130.74/78.43 new_primPlusNat7(x0, Succ(x1)) 130.74/78.43 new_primPlusNat4(Zero) 130.74/78.43 new_primPlusNat2(Succ(x0)) 130.74/78.43 new_primPlusNat0(Zero, Zero) 130.74/78.43 130.74/78.43 We have to consider all minimal (P,Q,R)-chains. 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (705) TransformationProof (EQUIVALENT) 130.74/78.43 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero)))))))))))), bb) at position [10,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.43 130.74/78.43 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))))))), bb)) 130.74/78.43 130.74/78.43 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (706) 130.74/78.43 Obligation: 130.74/78.43 Q DP problem: 130.74/78.43 The TRS P consists of the following rules: 130.74/78.43 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.43 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.43 130.74/78.43 The TRS R consists of the following rules: 130.74/78.43 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.43 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.43 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.43 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.43 new_primPlusNat2(Zero) -> Zero 130.74/78.43 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.43 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.43 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.43 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.43 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.43 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.43 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.43 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.43 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.43 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.43 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.43 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.43 130.74/78.43 The set Q consists of the following terms: 130.74/78.43 130.74/78.43 new_primPlusNat1(Succ(x0)) 130.74/78.43 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.43 new_primPlusNat1(Zero) 130.74/78.43 new_primPlusNat2(Zero) 130.74/78.43 new_primPlusNat3(Succ(x0)) 130.74/78.43 new_primPlusNat8(Succ(x0), x1) 130.74/78.43 new_primPlusNat6(x0, Succ(x1)) 130.74/78.43 new_primPlusNat0(Succ(x0), Zero) 130.74/78.43 new_primPlusNat6(x0, Zero) 130.74/78.43 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.43 new_primPlusNat4(Succ(x0)) 130.74/78.43 new_primPlusNat8(Zero, x0) 130.74/78.43 new_primPlusNat3(Zero) 130.74/78.43 new_primPlusNat7(x0, Zero) 130.74/78.43 new_primPlusNat7(x0, Succ(x1)) 130.74/78.43 new_primPlusNat4(Zero) 130.74/78.43 new_primPlusNat2(Succ(x0)) 130.74/78.43 new_primPlusNat0(Zero, Zero) 130.74/78.43 130.74/78.43 We have to consider all minimal (P,Q,R)-chains. 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (707) TransformationProof (EQUIVALENT) 130.74/78.43 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))))))), bb) at position [10,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.43 130.74/78.43 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))), bb)) 130.74/78.43 130.74/78.43 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (708) 130.74/78.43 Obligation: 130.74/78.43 Q DP problem: 130.74/78.43 The TRS P consists of the following rules: 130.74/78.43 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.43 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))), bb) 130.74/78.43 130.74/78.43 The TRS R consists of the following rules: 130.74/78.43 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.43 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.43 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.43 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.43 new_primPlusNat2(Zero) -> Zero 130.74/78.43 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.43 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.43 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.43 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.43 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.43 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.43 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.43 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.43 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.43 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.43 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.43 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.43 130.74/78.43 The set Q consists of the following terms: 130.74/78.43 130.74/78.43 new_primPlusNat1(Succ(x0)) 130.74/78.43 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.43 new_primPlusNat1(Zero) 130.74/78.43 new_primPlusNat2(Zero) 130.74/78.43 new_primPlusNat3(Succ(x0)) 130.74/78.43 new_primPlusNat8(Succ(x0), x1) 130.74/78.43 new_primPlusNat6(x0, Succ(x1)) 130.74/78.43 new_primPlusNat0(Succ(x0), Zero) 130.74/78.43 new_primPlusNat6(x0, Zero) 130.74/78.43 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.43 new_primPlusNat4(Succ(x0)) 130.74/78.43 new_primPlusNat8(Zero, x0) 130.74/78.43 new_primPlusNat3(Zero) 130.74/78.43 new_primPlusNat7(x0, Zero) 130.74/78.43 new_primPlusNat7(x0, Succ(x1)) 130.74/78.43 new_primPlusNat4(Zero) 130.74/78.43 new_primPlusNat2(Succ(x0)) 130.74/78.43 new_primPlusNat0(Zero, Zero) 130.74/78.43 130.74/78.43 We have to consider all minimal (P,Q,R)-chains. 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (709) TransformationProof (EQUIVALENT) 130.74/78.43 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero)))))))))))), bb) at position [11,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.43 130.74/78.43 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero))))))))))), bb)) 130.74/78.43 130.74/78.43 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (710) 130.74/78.43 Obligation: 130.74/78.43 Q DP problem: 130.74/78.43 The TRS P consists of the following rules: 130.74/78.43 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.43 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero))))))))))), bb) 130.74/78.43 130.74/78.43 The TRS R consists of the following rules: 130.74/78.43 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.43 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.43 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.43 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.43 new_primPlusNat2(Zero) -> Zero 130.74/78.43 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.43 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.43 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.43 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.43 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.43 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.43 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.43 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.43 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.43 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.43 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.43 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.43 130.74/78.43 The set Q consists of the following terms: 130.74/78.43 130.74/78.43 new_primPlusNat1(Succ(x0)) 130.74/78.43 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.43 new_primPlusNat1(Zero) 130.74/78.43 new_primPlusNat2(Zero) 130.74/78.43 new_primPlusNat3(Succ(x0)) 130.74/78.43 new_primPlusNat8(Succ(x0), x1) 130.74/78.43 new_primPlusNat6(x0, Succ(x1)) 130.74/78.43 new_primPlusNat0(Succ(x0), Zero) 130.74/78.43 new_primPlusNat6(x0, Zero) 130.74/78.43 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.43 new_primPlusNat4(Succ(x0)) 130.74/78.43 new_primPlusNat8(Zero, x0) 130.74/78.43 new_primPlusNat3(Zero) 130.74/78.43 new_primPlusNat7(x0, Zero) 130.74/78.43 new_primPlusNat7(x0, Succ(x1)) 130.74/78.43 new_primPlusNat4(Zero) 130.74/78.43 new_primPlusNat2(Succ(x0)) 130.74/78.43 new_primPlusNat0(Zero, Zero) 130.74/78.43 130.74/78.43 We have to consider all minimal (P,Q,R)-chains. 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (711) TransformationProof (EQUIVALENT) 130.74/78.43 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.43 130.74/78.43 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))), bb)) 130.74/78.43 130.74/78.43 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (712) 130.74/78.43 Obligation: 130.74/78.43 Q DP problem: 130.74/78.43 The TRS P consists of the following rules: 130.74/78.43 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.43 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))), bb) 130.74/78.43 130.74/78.43 The TRS R consists of the following rules: 130.74/78.43 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.43 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.43 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.43 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.43 new_primPlusNat2(Zero) -> Zero 130.74/78.43 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.43 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.43 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.43 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.43 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.43 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.43 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.43 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.43 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.43 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.43 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.43 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.43 130.74/78.43 The set Q consists of the following terms: 130.74/78.43 130.74/78.43 new_primPlusNat1(Succ(x0)) 130.74/78.43 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.43 new_primPlusNat1(Zero) 130.74/78.43 new_primPlusNat2(Zero) 130.74/78.43 new_primPlusNat3(Succ(x0)) 130.74/78.43 new_primPlusNat8(Succ(x0), x1) 130.74/78.43 new_primPlusNat6(x0, Succ(x1)) 130.74/78.43 new_primPlusNat0(Succ(x0), Zero) 130.74/78.43 new_primPlusNat6(x0, Zero) 130.74/78.43 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.43 new_primPlusNat4(Succ(x0)) 130.74/78.43 new_primPlusNat8(Zero, x0) 130.74/78.43 new_primPlusNat3(Zero) 130.74/78.43 new_primPlusNat7(x0, Zero) 130.74/78.43 new_primPlusNat7(x0, Succ(x1)) 130.74/78.43 new_primPlusNat4(Zero) 130.74/78.43 new_primPlusNat2(Succ(x0)) 130.74/78.43 new_primPlusNat0(Zero, Zero) 130.74/78.43 130.74/78.43 We have to consider all minimal (P,Q,R)-chains. 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (713) TransformationProof (EQUIVALENT) 130.74/78.43 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb) at position [10,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.43 130.74/78.43 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))), bb)) 130.74/78.43 130.74/78.43 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (714) 130.74/78.43 Obligation: 130.74/78.43 Q DP problem: 130.74/78.43 The TRS P consists of the following rules: 130.74/78.43 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.43 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.43 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))), bb) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))), bb) 130.74/78.43 130.74/78.43 The TRS R consists of the following rules: 130.74/78.43 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.43 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.43 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.43 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.43 new_primPlusNat2(Zero) -> Zero 130.74/78.43 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.43 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.43 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.43 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.43 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.43 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.43 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.43 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.43 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.43 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.43 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.43 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.43 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.43 130.74/78.43 The set Q consists of the following terms: 130.74/78.43 130.74/78.43 new_primPlusNat1(Succ(x0)) 130.74/78.43 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.43 new_primPlusNat1(Zero) 130.74/78.43 new_primPlusNat2(Zero) 130.74/78.43 new_primPlusNat3(Succ(x0)) 130.74/78.43 new_primPlusNat8(Succ(x0), x1) 130.74/78.43 new_primPlusNat6(x0, Succ(x1)) 130.74/78.43 new_primPlusNat0(Succ(x0), Zero) 130.74/78.43 new_primPlusNat6(x0, Zero) 130.74/78.43 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.43 new_primPlusNat4(Succ(x0)) 130.74/78.43 new_primPlusNat8(Zero, x0) 130.74/78.43 new_primPlusNat3(Zero) 130.74/78.43 new_primPlusNat7(x0, Zero) 130.74/78.43 new_primPlusNat7(x0, Succ(x1)) 130.74/78.43 new_primPlusNat4(Zero) 130.74/78.43 new_primPlusNat2(Succ(x0)) 130.74/78.43 new_primPlusNat0(Zero, Zero) 130.74/78.43 130.74/78.43 We have to consider all minimal (P,Q,R)-chains. 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (715) TransformationProof (EQUIVALENT) 130.74/78.43 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))))))), bb) at position [10,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.43 130.74/78.43 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))), bb)) 130.74/78.43 130.74/78.43 130.74/78.43 ---------------------------------------- 130.74/78.43 130.74/78.43 (716) 130.74/78.43 Obligation: 130.74/78.43 Q DP problem: 130.74/78.43 The TRS P consists of the following rules: 130.74/78.43 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.43 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.43 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.43 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))), bb) 130.74/78.44 130.74/78.44 The TRS R consists of the following rules: 130.74/78.44 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.44 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.44 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.44 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.44 new_primPlusNat2(Zero) -> Zero 130.74/78.44 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.44 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.44 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.44 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.44 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.44 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.44 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.44 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.44 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.44 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.44 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.44 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.44 130.74/78.44 The set Q consists of the following terms: 130.74/78.44 130.74/78.44 new_primPlusNat1(Succ(x0)) 130.74/78.44 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.44 new_primPlusNat1(Zero) 130.74/78.44 new_primPlusNat2(Zero) 130.74/78.44 new_primPlusNat3(Succ(x0)) 130.74/78.44 new_primPlusNat8(Succ(x0), x1) 130.74/78.44 new_primPlusNat6(x0, Succ(x1)) 130.74/78.44 new_primPlusNat0(Succ(x0), Zero) 130.74/78.44 new_primPlusNat6(x0, Zero) 130.74/78.44 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.44 new_primPlusNat4(Succ(x0)) 130.74/78.44 new_primPlusNat8(Zero, x0) 130.74/78.44 new_primPlusNat3(Zero) 130.74/78.44 new_primPlusNat7(x0, Zero) 130.74/78.44 new_primPlusNat7(x0, Succ(x1)) 130.74/78.44 new_primPlusNat4(Zero) 130.74/78.44 new_primPlusNat2(Succ(x0)) 130.74/78.44 new_primPlusNat0(Zero, Zero) 130.74/78.44 130.74/78.44 We have to consider all minimal (P,Q,R)-chains. 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (717) TransformationProof (EQUIVALENT) 130.74/78.44 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(new_primPlusNat3(Succ(Zero))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.44 130.74/78.44 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero)))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero)))))))))))), bb)) 130.74/78.44 130.74/78.44 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (718) 130.74/78.44 Obligation: 130.74/78.44 Q DP problem: 130.74/78.44 The TRS P consists of the following rules: 130.74/78.44 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.44 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero)))))))))))), bb) 130.74/78.44 130.74/78.44 The TRS R consists of the following rules: 130.74/78.44 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.44 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.44 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.44 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.44 new_primPlusNat2(Zero) -> Zero 130.74/78.44 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.44 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.44 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.44 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.44 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.44 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.44 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.44 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.44 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.44 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.44 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.44 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.44 130.74/78.44 The set Q consists of the following terms: 130.74/78.44 130.74/78.44 new_primPlusNat1(Succ(x0)) 130.74/78.44 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.44 new_primPlusNat1(Zero) 130.74/78.44 new_primPlusNat2(Zero) 130.74/78.44 new_primPlusNat3(Succ(x0)) 130.74/78.44 new_primPlusNat8(Succ(x0), x1) 130.74/78.44 new_primPlusNat6(x0, Succ(x1)) 130.74/78.44 new_primPlusNat0(Succ(x0), Zero) 130.74/78.44 new_primPlusNat6(x0, Zero) 130.74/78.44 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.44 new_primPlusNat4(Succ(x0)) 130.74/78.44 new_primPlusNat8(Zero, x0) 130.74/78.44 new_primPlusNat3(Zero) 130.74/78.44 new_primPlusNat7(x0, Zero) 130.74/78.44 new_primPlusNat7(x0, Succ(x1)) 130.74/78.44 new_primPlusNat4(Zero) 130.74/78.44 new_primPlusNat2(Succ(x0)) 130.74/78.44 new_primPlusNat0(Zero, Zero) 130.74/78.44 130.74/78.44 We have to consider all minimal (P,Q,R)-chains. 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (719) TransformationProof (EQUIVALENT) 130.74/78.44 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))), bb) at position [10,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.44 130.74/78.44 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))), bb)) 130.74/78.44 130.74/78.44 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (720) 130.74/78.44 Obligation: 130.74/78.44 Q DP problem: 130.74/78.44 The TRS P consists of the following rules: 130.74/78.44 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.44 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero)))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))), bb) 130.74/78.44 130.74/78.44 The TRS R consists of the following rules: 130.74/78.44 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.44 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.44 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.44 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.44 new_primPlusNat2(Zero) -> Zero 130.74/78.44 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.44 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.44 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.44 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.44 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.44 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.44 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.44 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.44 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.44 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.44 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.44 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.44 130.74/78.44 The set Q consists of the following terms: 130.74/78.44 130.74/78.44 new_primPlusNat1(Succ(x0)) 130.74/78.44 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.44 new_primPlusNat1(Zero) 130.74/78.44 new_primPlusNat2(Zero) 130.74/78.44 new_primPlusNat3(Succ(x0)) 130.74/78.44 new_primPlusNat8(Succ(x0), x1) 130.74/78.44 new_primPlusNat6(x0, Succ(x1)) 130.74/78.44 new_primPlusNat0(Succ(x0), Zero) 130.74/78.44 new_primPlusNat6(x0, Zero) 130.74/78.44 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.44 new_primPlusNat4(Succ(x0)) 130.74/78.44 new_primPlusNat8(Zero, x0) 130.74/78.44 new_primPlusNat3(Zero) 130.74/78.44 new_primPlusNat7(x0, Zero) 130.74/78.44 new_primPlusNat7(x0, Succ(x1)) 130.74/78.44 new_primPlusNat4(Zero) 130.74/78.44 new_primPlusNat2(Succ(x0)) 130.74/78.44 new_primPlusNat0(Zero, Zero) 130.74/78.44 130.74/78.44 We have to consider all minimal (P,Q,R)-chains. 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (721) TransformationProof (EQUIVALENT) 130.74/78.44 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero))))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.44 130.74/78.44 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb)) 130.74/78.44 130.74/78.44 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (722) 130.74/78.44 Obligation: 130.74/78.44 Q DP problem: 130.74/78.44 The TRS P consists of the following rules: 130.74/78.44 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.44 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero)))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.44 130.74/78.44 The TRS R consists of the following rules: 130.74/78.44 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.44 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.44 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.44 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.44 new_primPlusNat2(Zero) -> Zero 130.74/78.44 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.44 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.44 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.44 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.44 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.44 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.44 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.44 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.44 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.44 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.44 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.44 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.44 130.74/78.44 The set Q consists of the following terms: 130.74/78.44 130.74/78.44 new_primPlusNat1(Succ(x0)) 130.74/78.44 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.44 new_primPlusNat1(Zero) 130.74/78.44 new_primPlusNat2(Zero) 130.74/78.44 new_primPlusNat3(Succ(x0)) 130.74/78.44 new_primPlusNat8(Succ(x0), x1) 130.74/78.44 new_primPlusNat6(x0, Succ(x1)) 130.74/78.44 new_primPlusNat0(Succ(x0), Zero) 130.74/78.44 new_primPlusNat6(x0, Zero) 130.74/78.44 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.44 new_primPlusNat4(Succ(x0)) 130.74/78.44 new_primPlusNat8(Zero, x0) 130.74/78.44 new_primPlusNat3(Zero) 130.74/78.44 new_primPlusNat7(x0, Zero) 130.74/78.44 new_primPlusNat7(x0, Succ(x1)) 130.74/78.44 new_primPlusNat4(Zero) 130.74/78.44 new_primPlusNat2(Succ(x0)) 130.74/78.44 new_primPlusNat0(Zero, Zero) 130.74/78.44 130.74/78.44 We have to consider all minimal (P,Q,R)-chains. 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (723) TransformationProof (EQUIVALENT) 130.74/78.44 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.44 130.74/78.44 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero))))))))))))), bb)) 130.74/78.44 130.74/78.44 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (724) 130.74/78.44 Obligation: 130.74/78.44 Q DP problem: 130.74/78.44 The TRS P consists of the following rules: 130.74/78.44 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.44 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero)))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero))))))))))))), bb) 130.74/78.44 130.74/78.44 The TRS R consists of the following rules: 130.74/78.44 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.44 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.44 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.44 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.44 new_primPlusNat2(Zero) -> Zero 130.74/78.44 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.44 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.44 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.44 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.44 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.44 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.44 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.44 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.44 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.44 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.44 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.44 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.44 130.74/78.44 The set Q consists of the following terms: 130.74/78.44 130.74/78.44 new_primPlusNat1(Succ(x0)) 130.74/78.44 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.44 new_primPlusNat1(Zero) 130.74/78.44 new_primPlusNat2(Zero) 130.74/78.44 new_primPlusNat3(Succ(x0)) 130.74/78.44 new_primPlusNat8(Succ(x0), x1) 130.74/78.44 new_primPlusNat6(x0, Succ(x1)) 130.74/78.44 new_primPlusNat0(Succ(x0), Zero) 130.74/78.44 new_primPlusNat6(x0, Zero) 130.74/78.44 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.44 new_primPlusNat4(Succ(x0)) 130.74/78.44 new_primPlusNat8(Zero, x0) 130.74/78.44 new_primPlusNat3(Zero) 130.74/78.44 new_primPlusNat7(x0, Zero) 130.74/78.44 new_primPlusNat7(x0, Succ(x1)) 130.74/78.44 new_primPlusNat4(Zero) 130.74/78.44 new_primPlusNat2(Succ(x0)) 130.74/78.44 new_primPlusNat0(Zero, Zero) 130.74/78.44 130.74/78.44 We have to consider all minimal (P,Q,R)-chains. 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (725) TransformationProof (EQUIVALENT) 130.74/78.44 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat4(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.44 130.74/78.44 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb)) 130.74/78.44 130.74/78.44 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (726) 130.74/78.44 Obligation: 130.74/78.44 Q DP problem: 130.74/78.44 The TRS P consists of the following rules: 130.74/78.44 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.44 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero)))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero))))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb) 130.74/78.44 130.74/78.44 The TRS R consists of the following rules: 130.74/78.44 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.44 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.44 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.44 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.44 new_primPlusNat2(Zero) -> Zero 130.74/78.44 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.44 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.44 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.44 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.44 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.44 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.44 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.44 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.44 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.44 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.44 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.44 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.44 130.74/78.44 The set Q consists of the following terms: 130.74/78.44 130.74/78.44 new_primPlusNat1(Succ(x0)) 130.74/78.44 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.44 new_primPlusNat1(Zero) 130.74/78.44 new_primPlusNat2(Zero) 130.74/78.44 new_primPlusNat3(Succ(x0)) 130.74/78.44 new_primPlusNat8(Succ(x0), x1) 130.74/78.44 new_primPlusNat6(x0, Succ(x1)) 130.74/78.44 new_primPlusNat0(Succ(x0), Zero) 130.74/78.44 new_primPlusNat6(x0, Zero) 130.74/78.44 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.44 new_primPlusNat4(Succ(x0)) 130.74/78.44 new_primPlusNat8(Zero, x0) 130.74/78.44 new_primPlusNat3(Zero) 130.74/78.44 new_primPlusNat7(x0, Zero) 130.74/78.44 new_primPlusNat7(x0, Succ(x1)) 130.74/78.44 new_primPlusNat4(Zero) 130.74/78.44 new_primPlusNat2(Succ(x0)) 130.74/78.44 new_primPlusNat0(Zero, Zero) 130.74/78.44 130.74/78.44 We have to consider all minimal (P,Q,R)-chains. 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (727) TransformationProof (EQUIVALENT) 130.74/78.44 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))), bb) at position [10,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.44 130.74/78.44 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb)) 130.74/78.44 130.74/78.44 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (728) 130.74/78.44 Obligation: 130.74/78.44 Q DP problem: 130.74/78.44 The TRS P consists of the following rules: 130.74/78.44 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.44 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero)))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero))))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb) 130.74/78.44 130.74/78.44 The TRS R consists of the following rules: 130.74/78.44 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.44 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.44 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.44 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.44 new_primPlusNat2(Zero) -> Zero 130.74/78.44 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.44 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.44 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.44 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.44 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.44 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.44 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.44 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.44 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.44 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.44 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.44 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.44 130.74/78.44 The set Q consists of the following terms: 130.74/78.44 130.74/78.44 new_primPlusNat1(Succ(x0)) 130.74/78.44 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.44 new_primPlusNat1(Zero) 130.74/78.44 new_primPlusNat2(Zero) 130.74/78.44 new_primPlusNat3(Succ(x0)) 130.74/78.44 new_primPlusNat8(Succ(x0), x1) 130.74/78.44 new_primPlusNat6(x0, Succ(x1)) 130.74/78.44 new_primPlusNat0(Succ(x0), Zero) 130.74/78.44 new_primPlusNat6(x0, Zero) 130.74/78.44 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.44 new_primPlusNat4(Succ(x0)) 130.74/78.44 new_primPlusNat8(Zero, x0) 130.74/78.44 new_primPlusNat3(Zero) 130.74/78.44 new_primPlusNat7(x0, Zero) 130.74/78.44 new_primPlusNat7(x0, Succ(x1)) 130.74/78.44 new_primPlusNat4(Zero) 130.74/78.44 new_primPlusNat2(Succ(x0)) 130.74/78.44 new_primPlusNat0(Zero, Zero) 130.74/78.44 130.74/78.44 We have to consider all minimal (P,Q,R)-chains. 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (729) TransformationProof (EQUIVALENT) 130.74/78.44 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(new_primPlusNat2(Zero)))))))))))), bb) at position [10,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.44 130.74/78.44 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero))))))))))), bb)) 130.74/78.44 130.74/78.44 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (730) 130.74/78.44 Obligation: 130.74/78.44 Q DP problem: 130.74/78.44 The TRS P consists of the following rules: 130.74/78.44 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.44 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero))))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero))))))))))), bb) 130.74/78.44 130.74/78.44 The TRS R consists of the following rules: 130.74/78.44 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.44 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.44 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.44 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.44 new_primPlusNat2(Zero) -> Zero 130.74/78.44 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.44 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.44 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.44 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.44 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.44 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.44 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.44 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.44 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.44 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.44 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.44 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.44 130.74/78.44 The set Q consists of the following terms: 130.74/78.44 130.74/78.44 new_primPlusNat1(Succ(x0)) 130.74/78.44 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.44 new_primPlusNat1(Zero) 130.74/78.44 new_primPlusNat2(Zero) 130.74/78.44 new_primPlusNat3(Succ(x0)) 130.74/78.44 new_primPlusNat8(Succ(x0), x1) 130.74/78.44 new_primPlusNat6(x0, Succ(x1)) 130.74/78.44 new_primPlusNat0(Succ(x0), Zero) 130.74/78.44 new_primPlusNat6(x0, Zero) 130.74/78.44 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.44 new_primPlusNat4(Succ(x0)) 130.74/78.44 new_primPlusNat8(Zero, x0) 130.74/78.44 new_primPlusNat3(Zero) 130.74/78.44 new_primPlusNat7(x0, Zero) 130.74/78.44 new_primPlusNat7(x0, Succ(x1)) 130.74/78.44 new_primPlusNat4(Zero) 130.74/78.44 new_primPlusNat2(Succ(x0)) 130.74/78.44 new_primPlusNat0(Zero, Zero) 130.74/78.44 130.74/78.44 We have to consider all minimal (P,Q,R)-chains. 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (731) TransformationProof (EQUIVALENT) 130.74/78.44 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.44 130.74/78.44 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))), bb)) 130.74/78.44 130.74/78.44 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (732) 130.74/78.44 Obligation: 130.74/78.44 Q DP problem: 130.74/78.44 The TRS P consists of the following rules: 130.74/78.44 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.44 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero))))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))), bb) 130.74/78.44 130.74/78.44 The TRS R consists of the following rules: 130.74/78.44 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.44 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.44 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.44 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.44 new_primPlusNat2(Zero) -> Zero 130.74/78.44 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.44 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.44 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.44 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.44 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.44 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.44 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.44 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.44 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.44 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.44 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.44 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.44 130.74/78.44 The set Q consists of the following terms: 130.74/78.44 130.74/78.44 new_primPlusNat1(Succ(x0)) 130.74/78.44 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.44 new_primPlusNat1(Zero) 130.74/78.44 new_primPlusNat2(Zero) 130.74/78.44 new_primPlusNat3(Succ(x0)) 130.74/78.44 new_primPlusNat8(Succ(x0), x1) 130.74/78.44 new_primPlusNat6(x0, Succ(x1)) 130.74/78.44 new_primPlusNat0(Succ(x0), Zero) 130.74/78.44 new_primPlusNat6(x0, Zero) 130.74/78.44 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.44 new_primPlusNat4(Succ(x0)) 130.74/78.44 new_primPlusNat8(Zero, x0) 130.74/78.44 new_primPlusNat3(Zero) 130.74/78.44 new_primPlusNat7(x0, Zero) 130.74/78.44 new_primPlusNat7(x0, Succ(x1)) 130.74/78.44 new_primPlusNat4(Zero) 130.74/78.44 new_primPlusNat2(Succ(x0)) 130.74/78.44 new_primPlusNat0(Zero, Zero) 130.74/78.44 130.74/78.44 We have to consider all minimal (P,Q,R)-chains. 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (733) TransformationProof (EQUIVALENT) 130.74/78.44 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero))))))))))))), bb) at position [11,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.44 130.74/78.44 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb)) 130.74/78.44 130.74/78.44 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (734) 130.74/78.44 Obligation: 130.74/78.44 Q DP problem: 130.74/78.44 The TRS P consists of the following rules: 130.74/78.44 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.44 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.44 130.74/78.44 The TRS R consists of the following rules: 130.74/78.44 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.44 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.44 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.44 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.44 new_primPlusNat2(Zero) -> Zero 130.74/78.44 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.44 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.44 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.44 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.44 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.44 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.44 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.44 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.44 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.44 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.44 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.44 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.44 130.74/78.44 The set Q consists of the following terms: 130.74/78.44 130.74/78.44 new_primPlusNat1(Succ(x0)) 130.74/78.44 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.44 new_primPlusNat1(Zero) 130.74/78.44 new_primPlusNat2(Zero) 130.74/78.44 new_primPlusNat3(Succ(x0)) 130.74/78.44 new_primPlusNat8(Succ(x0), x1) 130.74/78.44 new_primPlusNat6(x0, Succ(x1)) 130.74/78.44 new_primPlusNat0(Succ(x0), Zero) 130.74/78.44 new_primPlusNat6(x0, Zero) 130.74/78.44 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.44 new_primPlusNat4(Succ(x0)) 130.74/78.44 new_primPlusNat8(Zero, x0) 130.74/78.44 new_primPlusNat3(Zero) 130.74/78.44 new_primPlusNat7(x0, Zero) 130.74/78.44 new_primPlusNat7(x0, Succ(x1)) 130.74/78.44 new_primPlusNat4(Zero) 130.74/78.44 new_primPlusNat2(Succ(x0)) 130.74/78.44 new_primPlusNat0(Zero, Zero) 130.74/78.44 130.74/78.44 We have to consider all minimal (P,Q,R)-chains. 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (735) TransformationProof (EQUIVALENT) 130.74/78.44 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb) at position [10,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.44 130.74/78.44 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))))), bb)) 130.74/78.44 130.74/78.44 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (736) 130.74/78.44 Obligation: 130.74/78.44 Q DP problem: 130.74/78.44 The TRS P consists of the following rules: 130.74/78.44 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.44 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))))), bb) 130.74/78.44 130.74/78.44 The TRS R consists of the following rules: 130.74/78.44 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.44 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.44 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.44 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.44 new_primPlusNat2(Zero) -> Zero 130.74/78.44 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.44 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.44 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.44 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.44 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.44 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.44 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.44 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.44 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.44 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.44 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.44 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.44 130.74/78.44 The set Q consists of the following terms: 130.74/78.44 130.74/78.44 new_primPlusNat1(Succ(x0)) 130.74/78.44 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.44 new_primPlusNat1(Zero) 130.74/78.44 new_primPlusNat2(Zero) 130.74/78.44 new_primPlusNat3(Succ(x0)) 130.74/78.44 new_primPlusNat8(Succ(x0), x1) 130.74/78.44 new_primPlusNat6(x0, Succ(x1)) 130.74/78.44 new_primPlusNat0(Succ(x0), Zero) 130.74/78.44 new_primPlusNat6(x0, Zero) 130.74/78.44 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.44 new_primPlusNat4(Succ(x0)) 130.74/78.44 new_primPlusNat8(Zero, x0) 130.74/78.44 new_primPlusNat3(Zero) 130.74/78.44 new_primPlusNat7(x0, Zero) 130.74/78.44 new_primPlusNat7(x0, Succ(x1)) 130.74/78.44 new_primPlusNat4(Zero) 130.74/78.44 new_primPlusNat2(Succ(x0)) 130.74/78.44 new_primPlusNat0(Zero, Zero) 130.74/78.44 130.74/78.44 We have to consider all minimal (P,Q,R)-chains. 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (737) TransformationProof (EQUIVALENT) 130.74/78.44 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.44 130.74/78.44 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb)) 130.74/78.44 130.74/78.44 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (738) 130.74/78.44 Obligation: 130.74/78.44 Q DP problem: 130.74/78.44 The TRS P consists of the following rules: 130.74/78.44 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.44 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb) 130.74/78.44 130.74/78.44 The TRS R consists of the following rules: 130.74/78.44 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.44 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.44 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.44 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.44 new_primPlusNat2(Zero) -> Zero 130.74/78.44 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.44 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.44 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.44 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.44 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.44 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.44 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.44 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.44 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.44 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.44 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.44 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.44 130.74/78.44 The set Q consists of the following terms: 130.74/78.44 130.74/78.44 new_primPlusNat1(Succ(x0)) 130.74/78.44 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.44 new_primPlusNat1(Zero) 130.74/78.44 new_primPlusNat2(Zero) 130.74/78.44 new_primPlusNat3(Succ(x0)) 130.74/78.44 new_primPlusNat8(Succ(x0), x1) 130.74/78.44 new_primPlusNat6(x0, Succ(x1)) 130.74/78.44 new_primPlusNat0(Succ(x0), Zero) 130.74/78.44 new_primPlusNat6(x0, Zero) 130.74/78.44 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.44 new_primPlusNat4(Succ(x0)) 130.74/78.44 new_primPlusNat8(Zero, x0) 130.74/78.44 new_primPlusNat3(Zero) 130.74/78.44 new_primPlusNat7(x0, Zero) 130.74/78.44 new_primPlusNat7(x0, Succ(x1)) 130.74/78.44 new_primPlusNat4(Zero) 130.74/78.44 new_primPlusNat2(Succ(x0)) 130.74/78.44 new_primPlusNat0(Zero, Zero) 130.74/78.44 130.74/78.44 We have to consider all minimal (P,Q,R)-chains. 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (739) TransformationProof (EQUIVALENT) 130.74/78.44 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Zero))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.44 130.74/78.44 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb)) 130.74/78.44 130.74/78.44 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (740) 130.74/78.44 Obligation: 130.74/78.44 Q DP problem: 130.74/78.44 The TRS P consists of the following rules: 130.74/78.44 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.44 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.44 130.74/78.44 The TRS R consists of the following rules: 130.74/78.44 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.44 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.44 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.44 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.44 new_primPlusNat2(Zero) -> Zero 130.74/78.44 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.44 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.44 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.44 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.44 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.44 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.44 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.44 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.44 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.44 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.44 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.44 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.44 130.74/78.44 The set Q consists of the following terms: 130.74/78.44 130.74/78.44 new_primPlusNat1(Succ(x0)) 130.74/78.44 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.44 new_primPlusNat1(Zero) 130.74/78.44 new_primPlusNat2(Zero) 130.74/78.44 new_primPlusNat3(Succ(x0)) 130.74/78.44 new_primPlusNat8(Succ(x0), x1) 130.74/78.44 new_primPlusNat6(x0, Succ(x1)) 130.74/78.44 new_primPlusNat0(Succ(x0), Zero) 130.74/78.44 new_primPlusNat6(x0, Zero) 130.74/78.44 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.44 new_primPlusNat4(Succ(x0)) 130.74/78.44 new_primPlusNat8(Zero, x0) 130.74/78.44 new_primPlusNat3(Zero) 130.74/78.44 new_primPlusNat7(x0, Zero) 130.74/78.44 new_primPlusNat7(x0, Succ(x1)) 130.74/78.44 new_primPlusNat4(Zero) 130.74/78.44 new_primPlusNat2(Succ(x0)) 130.74/78.44 new_primPlusNat0(Zero, Zero) 130.74/78.44 130.74/78.44 We have to consider all minimal (P,Q,R)-chains. 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (741) TransformationProof (EQUIVALENT) 130.74/78.44 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.44 130.74/78.44 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))), bb)) 130.74/78.44 130.74/78.44 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (742) 130.74/78.44 Obligation: 130.74/78.44 Q DP problem: 130.74/78.44 The TRS P consists of the following rules: 130.74/78.44 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.44 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))), bb) 130.74/78.44 130.74/78.44 The TRS R consists of the following rules: 130.74/78.44 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.44 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.44 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.44 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.44 new_primPlusNat2(Zero) -> Zero 130.74/78.44 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.44 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.44 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.44 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.44 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.44 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.44 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.44 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.44 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.44 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.44 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.44 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.44 130.74/78.44 The set Q consists of the following terms: 130.74/78.44 130.74/78.44 new_primPlusNat1(Succ(x0)) 130.74/78.44 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.44 new_primPlusNat1(Zero) 130.74/78.44 new_primPlusNat2(Zero) 130.74/78.44 new_primPlusNat3(Succ(x0)) 130.74/78.44 new_primPlusNat8(Succ(x0), x1) 130.74/78.44 new_primPlusNat6(x0, Succ(x1)) 130.74/78.44 new_primPlusNat0(Succ(x0), Zero) 130.74/78.44 new_primPlusNat6(x0, Zero) 130.74/78.44 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.44 new_primPlusNat4(Succ(x0)) 130.74/78.44 new_primPlusNat8(Zero, x0) 130.74/78.44 new_primPlusNat3(Zero) 130.74/78.44 new_primPlusNat7(x0, Zero) 130.74/78.44 new_primPlusNat7(x0, Succ(x1)) 130.74/78.44 new_primPlusNat4(Zero) 130.74/78.44 new_primPlusNat2(Succ(x0)) 130.74/78.44 new_primPlusNat0(Zero, Zero) 130.74/78.44 130.74/78.44 We have to consider all minimal (P,Q,R)-chains. 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (743) TransformationProof (EQUIVALENT) 130.74/78.44 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.44 130.74/78.44 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb)) 130.74/78.44 130.74/78.44 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (744) 130.74/78.44 Obligation: 130.74/78.44 Q DP problem: 130.74/78.44 The TRS P consists of the following rules: 130.74/78.44 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.44 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb) 130.74/78.44 130.74/78.44 The TRS R consists of the following rules: 130.74/78.44 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.44 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.44 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.44 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.44 new_primPlusNat2(Zero) -> Zero 130.74/78.44 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.44 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.44 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.44 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.44 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.44 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.44 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.44 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.44 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.44 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.44 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.44 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.44 130.74/78.44 The set Q consists of the following terms: 130.74/78.44 130.74/78.44 new_primPlusNat1(Succ(x0)) 130.74/78.44 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.44 new_primPlusNat1(Zero) 130.74/78.44 new_primPlusNat2(Zero) 130.74/78.44 new_primPlusNat3(Succ(x0)) 130.74/78.44 new_primPlusNat8(Succ(x0), x1) 130.74/78.44 new_primPlusNat6(x0, Succ(x1)) 130.74/78.44 new_primPlusNat0(Succ(x0), Zero) 130.74/78.44 new_primPlusNat6(x0, Zero) 130.74/78.44 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.44 new_primPlusNat4(Succ(x0)) 130.74/78.44 new_primPlusNat8(Zero, x0) 130.74/78.44 new_primPlusNat3(Zero) 130.74/78.44 new_primPlusNat7(x0, Zero) 130.74/78.44 new_primPlusNat7(x0, Succ(x1)) 130.74/78.44 new_primPlusNat4(Zero) 130.74/78.44 new_primPlusNat2(Succ(x0)) 130.74/78.44 new_primPlusNat0(Zero, Zero) 130.74/78.44 130.74/78.44 We have to consider all minimal (P,Q,R)-chains. 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (745) TransformationProof (EQUIVALENT) 130.74/78.44 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.44 130.74/78.44 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))), Succ(Zero)))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))), Succ(Zero)))))))))), bb)) 130.74/78.44 130.74/78.44 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (746) 130.74/78.44 Obligation: 130.74/78.44 Q DP problem: 130.74/78.44 The TRS P consists of the following rules: 130.74/78.44 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.44 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))), Succ(Zero)))))))))), bb) 130.74/78.44 130.74/78.44 The TRS R consists of the following rules: 130.74/78.44 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.44 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.44 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.44 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.44 new_primPlusNat2(Zero) -> Zero 130.74/78.44 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.44 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.44 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.44 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.44 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.44 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.44 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.44 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.44 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.44 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.44 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.44 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.44 130.74/78.44 The set Q consists of the following terms: 130.74/78.44 130.74/78.44 new_primPlusNat1(Succ(x0)) 130.74/78.44 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.44 new_primPlusNat1(Zero) 130.74/78.44 new_primPlusNat2(Zero) 130.74/78.44 new_primPlusNat3(Succ(x0)) 130.74/78.44 new_primPlusNat8(Succ(x0), x1) 130.74/78.44 new_primPlusNat6(x0, Succ(x1)) 130.74/78.44 new_primPlusNat0(Succ(x0), Zero) 130.74/78.44 new_primPlusNat6(x0, Zero) 130.74/78.44 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.44 new_primPlusNat4(Succ(x0)) 130.74/78.44 new_primPlusNat8(Zero, x0) 130.74/78.44 new_primPlusNat3(Zero) 130.74/78.44 new_primPlusNat7(x0, Zero) 130.74/78.44 new_primPlusNat7(x0, Succ(x1)) 130.74/78.44 new_primPlusNat4(Zero) 130.74/78.44 new_primPlusNat2(Succ(x0)) 130.74/78.44 new_primPlusNat0(Zero, Zero) 130.74/78.44 130.74/78.44 We have to consider all minimal (P,Q,R)-chains. 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (747) TransformationProof (EQUIVALENT) 130.74/78.44 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))), bb) at position [10,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.44 130.74/78.44 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))))))), bb)) 130.74/78.44 130.74/78.44 130.74/78.44 ---------------------------------------- 130.74/78.44 130.74/78.44 (748) 130.74/78.44 Obligation: 130.74/78.44 Q DP problem: 130.74/78.44 The TRS P consists of the following rules: 130.74/78.44 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.44 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.44 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.44 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))), Succ(Zero)))))))))), bb) 130.74/78.44 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))))))), bb) 130.74/78.44 130.74/78.44 The TRS R consists of the following rules: 130.74/78.44 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.44 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.44 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.44 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.44 new_primPlusNat2(Zero) -> Zero 130.74/78.44 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.44 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.44 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.44 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.44 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.44 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.44 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.44 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.44 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.44 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.44 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.44 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.44 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.44 130.74/78.44 The set Q consists of the following terms: 130.74/78.44 130.74/78.44 new_primPlusNat1(Succ(x0)) 130.74/78.44 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.44 new_primPlusNat1(Zero) 130.74/78.44 new_primPlusNat2(Zero) 130.74/78.44 new_primPlusNat3(Succ(x0)) 130.74/78.44 new_primPlusNat8(Succ(x0), x1) 130.74/78.44 new_primPlusNat6(x0, Succ(x1)) 130.74/78.44 new_primPlusNat0(Succ(x0), Zero) 130.74/78.44 new_primPlusNat6(x0, Zero) 130.74/78.44 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.44 new_primPlusNat4(Succ(x0)) 130.74/78.44 new_primPlusNat8(Zero, x0) 130.74/78.44 new_primPlusNat3(Zero) 130.74/78.44 new_primPlusNat7(x0, Zero) 130.74/78.44 new_primPlusNat7(x0, Succ(x1)) 130.74/78.45 new_primPlusNat4(Zero) 130.74/78.45 new_primPlusNat2(Succ(x0)) 130.74/78.45 new_primPlusNat0(Zero, Zero) 130.74/78.45 130.74/78.45 We have to consider all minimal (P,Q,R)-chains. 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (749) TransformationProof (EQUIVALENT) 130.74/78.45 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.45 130.74/78.45 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))), bb)) 130.74/78.45 130.74/78.45 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (750) 130.74/78.45 Obligation: 130.74/78.45 Q DP problem: 130.74/78.45 The TRS P consists of the following rules: 130.74/78.45 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.45 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))), Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))), bb) 130.74/78.45 130.74/78.45 The TRS R consists of the following rules: 130.74/78.45 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.45 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.45 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.45 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.45 new_primPlusNat2(Zero) -> Zero 130.74/78.45 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.45 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.45 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.45 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.45 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.45 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.45 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.45 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.45 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.45 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.45 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.45 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.45 130.74/78.45 The set Q consists of the following terms: 130.74/78.45 130.74/78.45 new_primPlusNat1(Succ(x0)) 130.74/78.45 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.45 new_primPlusNat1(Zero) 130.74/78.45 new_primPlusNat2(Zero) 130.74/78.45 new_primPlusNat3(Succ(x0)) 130.74/78.45 new_primPlusNat8(Succ(x0), x1) 130.74/78.45 new_primPlusNat6(x0, Succ(x1)) 130.74/78.45 new_primPlusNat0(Succ(x0), Zero) 130.74/78.45 new_primPlusNat6(x0, Zero) 130.74/78.45 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.45 new_primPlusNat4(Succ(x0)) 130.74/78.45 new_primPlusNat8(Zero, x0) 130.74/78.45 new_primPlusNat3(Zero) 130.74/78.45 new_primPlusNat7(x0, Zero) 130.74/78.45 new_primPlusNat7(x0, Succ(x1)) 130.74/78.45 new_primPlusNat4(Zero) 130.74/78.45 new_primPlusNat2(Succ(x0)) 130.74/78.45 new_primPlusNat0(Zero, Zero) 130.74/78.45 130.74/78.45 We have to consider all minimal (P,Q,R)-chains. 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (751) TransformationProof (EQUIVALENT) 130.74/78.45 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))), Succ(Zero)))))))))), bb) at position [10,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.45 130.74/78.45 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))), Zero))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))), Zero))))))))))), bb)) 130.74/78.45 130.74/78.45 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (752) 130.74/78.45 Obligation: 130.74/78.45 Q DP problem: 130.74/78.45 The TRS P consists of the following rules: 130.74/78.45 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.45 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))), Zero))))))))))), bb) 130.74/78.45 130.74/78.45 The TRS R consists of the following rules: 130.74/78.45 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.45 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.45 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.45 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.45 new_primPlusNat2(Zero) -> Zero 130.74/78.45 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.45 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.45 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.45 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.45 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.45 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.45 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.45 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.45 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.45 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.45 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.45 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.45 130.74/78.45 The set Q consists of the following terms: 130.74/78.45 130.74/78.45 new_primPlusNat1(Succ(x0)) 130.74/78.45 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.45 new_primPlusNat1(Zero) 130.74/78.45 new_primPlusNat2(Zero) 130.74/78.45 new_primPlusNat3(Succ(x0)) 130.74/78.45 new_primPlusNat8(Succ(x0), x1) 130.74/78.45 new_primPlusNat6(x0, Succ(x1)) 130.74/78.45 new_primPlusNat0(Succ(x0), Zero) 130.74/78.45 new_primPlusNat6(x0, Zero) 130.74/78.45 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.45 new_primPlusNat4(Succ(x0)) 130.74/78.45 new_primPlusNat8(Zero, x0) 130.74/78.45 new_primPlusNat3(Zero) 130.74/78.45 new_primPlusNat7(x0, Zero) 130.74/78.45 new_primPlusNat7(x0, Succ(x1)) 130.74/78.45 new_primPlusNat4(Zero) 130.74/78.45 new_primPlusNat2(Succ(x0)) 130.74/78.45 new_primPlusNat0(Zero, Zero) 130.74/78.45 130.74/78.45 We have to consider all minimal (P,Q,R)-chains. 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (753) TransformationProof (EQUIVALENT) 130.74/78.45 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.45 130.74/78.45 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))))))), bb)) 130.74/78.45 130.74/78.45 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (754) 130.74/78.45 Obligation: 130.74/78.45 Q DP problem: 130.74/78.45 The TRS P consists of the following rules: 130.74/78.45 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.45 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))), Zero))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))))))), bb) 130.74/78.45 130.74/78.45 The TRS R consists of the following rules: 130.74/78.45 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.45 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.45 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.45 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.45 new_primPlusNat2(Zero) -> Zero 130.74/78.45 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.45 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.45 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.45 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.45 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.45 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.45 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.45 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.45 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.45 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.45 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.45 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.45 130.74/78.45 The set Q consists of the following terms: 130.74/78.45 130.74/78.45 new_primPlusNat1(Succ(x0)) 130.74/78.45 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.45 new_primPlusNat1(Zero) 130.74/78.45 new_primPlusNat2(Zero) 130.74/78.45 new_primPlusNat3(Succ(x0)) 130.74/78.45 new_primPlusNat8(Succ(x0), x1) 130.74/78.45 new_primPlusNat6(x0, Succ(x1)) 130.74/78.45 new_primPlusNat0(Succ(x0), Zero) 130.74/78.45 new_primPlusNat6(x0, Zero) 130.74/78.45 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.45 new_primPlusNat4(Succ(x0)) 130.74/78.45 new_primPlusNat8(Zero, x0) 130.74/78.45 new_primPlusNat3(Zero) 130.74/78.45 new_primPlusNat7(x0, Zero) 130.74/78.45 new_primPlusNat7(x0, Succ(x1)) 130.74/78.45 new_primPlusNat4(Zero) 130.74/78.45 new_primPlusNat2(Succ(x0)) 130.74/78.45 new_primPlusNat0(Zero, Zero) 130.74/78.45 130.74/78.45 We have to consider all minimal (P,Q,R)-chains. 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (755) TransformationProof (EQUIVALENT) 130.74/78.45 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.45 130.74/78.45 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))))))), bb)) 130.74/78.45 130.74/78.45 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (756) 130.74/78.45 Obligation: 130.74/78.45 Q DP problem: 130.74/78.45 The TRS P consists of the following rules: 130.74/78.45 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.45 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))), Zero))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))))))), bb) 130.74/78.45 130.74/78.45 The TRS R consists of the following rules: 130.74/78.45 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.45 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.45 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.45 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.45 new_primPlusNat2(Zero) -> Zero 130.74/78.45 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.45 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.45 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.45 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.45 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.45 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.45 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.45 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.45 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.45 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.45 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.45 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.45 130.74/78.45 The set Q consists of the following terms: 130.74/78.45 130.74/78.45 new_primPlusNat1(Succ(x0)) 130.74/78.45 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.45 new_primPlusNat1(Zero) 130.74/78.45 new_primPlusNat2(Zero) 130.74/78.45 new_primPlusNat3(Succ(x0)) 130.74/78.45 new_primPlusNat8(Succ(x0), x1) 130.74/78.45 new_primPlusNat6(x0, Succ(x1)) 130.74/78.45 new_primPlusNat0(Succ(x0), Zero) 130.74/78.45 new_primPlusNat6(x0, Zero) 130.74/78.45 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.45 new_primPlusNat4(Succ(x0)) 130.74/78.45 new_primPlusNat8(Zero, x0) 130.74/78.45 new_primPlusNat3(Zero) 130.74/78.45 new_primPlusNat7(x0, Zero) 130.74/78.45 new_primPlusNat7(x0, Succ(x1)) 130.74/78.45 new_primPlusNat4(Zero) 130.74/78.45 new_primPlusNat2(Succ(x0)) 130.74/78.45 new_primPlusNat0(Zero, Zero) 130.74/78.45 130.74/78.45 We have to consider all minimal (P,Q,R)-chains. 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (757) TransformationProof (EQUIVALENT) 130.74/78.45 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))), Zero))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.45 130.74/78.45 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))))))))))))), bb)) 130.74/78.45 130.74/78.45 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (758) 130.74/78.45 Obligation: 130.74/78.45 Q DP problem: 130.74/78.45 The TRS P consists of the following rules: 130.74/78.45 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.45 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))))))))))))), bb) 130.74/78.45 130.74/78.45 The TRS R consists of the following rules: 130.74/78.45 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.45 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.45 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.45 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.45 new_primPlusNat2(Zero) -> Zero 130.74/78.45 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.45 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.45 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.45 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.45 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.45 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.45 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.45 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.45 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.45 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.45 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.45 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.45 130.74/78.45 The set Q consists of the following terms: 130.74/78.45 130.74/78.45 new_primPlusNat1(Succ(x0)) 130.74/78.45 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.45 new_primPlusNat1(Zero) 130.74/78.45 new_primPlusNat2(Zero) 130.74/78.45 new_primPlusNat3(Succ(x0)) 130.74/78.45 new_primPlusNat8(Succ(x0), x1) 130.74/78.45 new_primPlusNat6(x0, Succ(x1)) 130.74/78.45 new_primPlusNat0(Succ(x0), Zero) 130.74/78.45 new_primPlusNat6(x0, Zero) 130.74/78.45 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.45 new_primPlusNat4(Succ(x0)) 130.74/78.45 new_primPlusNat8(Zero, x0) 130.74/78.45 new_primPlusNat3(Zero) 130.74/78.45 new_primPlusNat7(x0, Zero) 130.74/78.45 new_primPlusNat7(x0, Succ(x1)) 130.74/78.45 new_primPlusNat4(Zero) 130.74/78.45 new_primPlusNat2(Succ(x0)) 130.74/78.45 new_primPlusNat0(Zero, Zero) 130.74/78.45 130.74/78.45 We have to consider all minimal (P,Q,R)-chains. 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (759) TransformationProof (EQUIVALENT) 130.74/78.45 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.45 130.74/78.45 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))))))), bb)) 130.74/78.45 130.74/78.45 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (760) 130.74/78.45 Obligation: 130.74/78.45 Q DP problem: 130.74/78.45 The TRS P consists of the following rules: 130.74/78.45 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.45 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))))))), bb) 130.74/78.45 130.74/78.45 The TRS R consists of the following rules: 130.74/78.45 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.45 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.45 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.45 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.45 new_primPlusNat2(Zero) -> Zero 130.74/78.45 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.45 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.45 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.45 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.45 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.45 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.45 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.45 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.45 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.45 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.45 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.45 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.45 130.74/78.45 The set Q consists of the following terms: 130.74/78.45 130.74/78.45 new_primPlusNat1(Succ(x0)) 130.74/78.45 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.45 new_primPlusNat1(Zero) 130.74/78.45 new_primPlusNat2(Zero) 130.74/78.45 new_primPlusNat3(Succ(x0)) 130.74/78.45 new_primPlusNat8(Succ(x0), x1) 130.74/78.45 new_primPlusNat6(x0, Succ(x1)) 130.74/78.45 new_primPlusNat0(Succ(x0), Zero) 130.74/78.45 new_primPlusNat6(x0, Zero) 130.74/78.45 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.45 new_primPlusNat4(Succ(x0)) 130.74/78.45 new_primPlusNat8(Zero, x0) 130.74/78.45 new_primPlusNat3(Zero) 130.74/78.45 new_primPlusNat7(x0, Zero) 130.74/78.45 new_primPlusNat7(x0, Succ(x1)) 130.74/78.45 new_primPlusNat4(Zero) 130.74/78.45 new_primPlusNat2(Succ(x0)) 130.74/78.45 new_primPlusNat0(Zero, Zero) 130.74/78.45 130.74/78.45 We have to consider all minimal (P,Q,R)-chains. 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (761) TransformationProof (EQUIVALENT) 130.74/78.45 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.45 130.74/78.45 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))), bb)) 130.74/78.45 130.74/78.45 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (762) 130.74/78.45 Obligation: 130.74/78.45 Q DP problem: 130.74/78.45 The TRS P consists of the following rules: 130.74/78.45 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.45 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))), bb) 130.74/78.45 130.74/78.45 The TRS R consists of the following rules: 130.74/78.45 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.45 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.45 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.45 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.45 new_primPlusNat2(Zero) -> Zero 130.74/78.45 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.45 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.45 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.45 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.45 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.45 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.45 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.45 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.45 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.45 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.45 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.45 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.45 130.74/78.45 The set Q consists of the following terms: 130.74/78.45 130.74/78.45 new_primPlusNat1(Succ(x0)) 130.74/78.45 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.45 new_primPlusNat1(Zero) 130.74/78.45 new_primPlusNat2(Zero) 130.74/78.45 new_primPlusNat3(Succ(x0)) 130.74/78.45 new_primPlusNat8(Succ(x0), x1) 130.74/78.45 new_primPlusNat6(x0, Succ(x1)) 130.74/78.45 new_primPlusNat0(Succ(x0), Zero) 130.74/78.45 new_primPlusNat6(x0, Zero) 130.74/78.45 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.45 new_primPlusNat4(Succ(x0)) 130.74/78.45 new_primPlusNat8(Zero, x0) 130.74/78.45 new_primPlusNat3(Zero) 130.74/78.45 new_primPlusNat7(x0, Zero) 130.74/78.45 new_primPlusNat7(x0, Succ(x1)) 130.74/78.45 new_primPlusNat4(Zero) 130.74/78.45 new_primPlusNat2(Succ(x0)) 130.74/78.45 new_primPlusNat0(Zero, Zero) 130.74/78.45 130.74/78.45 We have to consider all minimal (P,Q,R)-chains. 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (763) TransformationProof (EQUIVALENT) 130.74/78.45 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.45 130.74/78.45 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb)) 130.74/78.45 130.74/78.45 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (764) 130.74/78.45 Obligation: 130.74/78.45 Q DP problem: 130.74/78.45 The TRS P consists of the following rules: 130.74/78.45 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.45 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb) 130.74/78.45 130.74/78.45 The TRS R consists of the following rules: 130.74/78.45 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.45 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.45 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.45 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.45 new_primPlusNat2(Zero) -> Zero 130.74/78.45 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.45 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.45 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.45 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.45 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.45 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.45 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.45 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.45 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.45 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.45 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.45 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.45 130.74/78.45 The set Q consists of the following terms: 130.74/78.45 130.74/78.45 new_primPlusNat1(Succ(x0)) 130.74/78.45 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.45 new_primPlusNat1(Zero) 130.74/78.45 new_primPlusNat2(Zero) 130.74/78.45 new_primPlusNat3(Succ(x0)) 130.74/78.45 new_primPlusNat8(Succ(x0), x1) 130.74/78.45 new_primPlusNat6(x0, Succ(x1)) 130.74/78.45 new_primPlusNat0(Succ(x0), Zero) 130.74/78.45 new_primPlusNat6(x0, Zero) 130.74/78.45 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.45 new_primPlusNat4(Succ(x0)) 130.74/78.45 new_primPlusNat8(Zero, x0) 130.74/78.45 new_primPlusNat3(Zero) 130.74/78.45 new_primPlusNat7(x0, Zero) 130.74/78.45 new_primPlusNat7(x0, Succ(x1)) 130.74/78.45 new_primPlusNat4(Zero) 130.74/78.45 new_primPlusNat2(Succ(x0)) 130.74/78.45 new_primPlusNat0(Zero, Zero) 130.74/78.45 130.74/78.45 We have to consider all minimal (P,Q,R)-chains. 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (765) TransformationProof (EQUIVALENT) 130.74/78.45 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.45 130.74/78.45 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))))))), bb)) 130.74/78.45 130.74/78.45 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (766) 130.74/78.45 Obligation: 130.74/78.45 Q DP problem: 130.74/78.45 The TRS P consists of the following rules: 130.74/78.45 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.45 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))))))), bb) 130.74/78.45 130.74/78.45 The TRS R consists of the following rules: 130.74/78.45 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.45 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.45 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.45 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.45 new_primPlusNat2(Zero) -> Zero 130.74/78.45 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.45 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.45 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.45 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.45 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.45 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.45 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.45 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.45 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.45 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.45 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.45 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.45 130.74/78.45 The set Q consists of the following terms: 130.74/78.45 130.74/78.45 new_primPlusNat1(Succ(x0)) 130.74/78.45 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.45 new_primPlusNat1(Zero) 130.74/78.45 new_primPlusNat2(Zero) 130.74/78.45 new_primPlusNat3(Succ(x0)) 130.74/78.45 new_primPlusNat8(Succ(x0), x1) 130.74/78.45 new_primPlusNat6(x0, Succ(x1)) 130.74/78.45 new_primPlusNat0(Succ(x0), Zero) 130.74/78.45 new_primPlusNat6(x0, Zero) 130.74/78.45 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.45 new_primPlusNat4(Succ(x0)) 130.74/78.45 new_primPlusNat8(Zero, x0) 130.74/78.45 new_primPlusNat3(Zero) 130.74/78.45 new_primPlusNat7(x0, Zero) 130.74/78.45 new_primPlusNat7(x0, Succ(x1)) 130.74/78.45 new_primPlusNat4(Zero) 130.74/78.45 new_primPlusNat2(Succ(x0)) 130.74/78.45 new_primPlusNat0(Zero, Zero) 130.74/78.45 130.74/78.45 We have to consider all minimal (P,Q,R)-chains. 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (767) TransformationProof (EQUIVALENT) 130.74/78.45 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.45 130.74/78.45 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))))))))))))), bb)) 130.74/78.45 130.74/78.45 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (768) 130.74/78.45 Obligation: 130.74/78.45 Q DP problem: 130.74/78.45 The TRS P consists of the following rules: 130.74/78.45 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.45 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))))))))))))), bb) 130.74/78.45 130.74/78.45 The TRS R consists of the following rules: 130.74/78.45 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.45 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.45 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.45 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.45 new_primPlusNat2(Zero) -> Zero 130.74/78.45 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.45 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.45 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.45 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.45 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.45 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.45 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.45 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.45 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.45 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.45 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.45 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.45 130.74/78.45 The set Q consists of the following terms: 130.74/78.45 130.74/78.45 new_primPlusNat1(Succ(x0)) 130.74/78.45 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.45 new_primPlusNat1(Zero) 130.74/78.45 new_primPlusNat2(Zero) 130.74/78.45 new_primPlusNat3(Succ(x0)) 130.74/78.45 new_primPlusNat8(Succ(x0), x1) 130.74/78.45 new_primPlusNat6(x0, Succ(x1)) 130.74/78.45 new_primPlusNat0(Succ(x0), Zero) 130.74/78.45 new_primPlusNat6(x0, Zero) 130.74/78.45 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.45 new_primPlusNat4(Succ(x0)) 130.74/78.45 new_primPlusNat8(Zero, x0) 130.74/78.45 new_primPlusNat3(Zero) 130.74/78.45 new_primPlusNat7(x0, Zero) 130.74/78.45 new_primPlusNat7(x0, Succ(x1)) 130.74/78.45 new_primPlusNat4(Zero) 130.74/78.45 new_primPlusNat2(Succ(x0)) 130.74/78.45 new_primPlusNat0(Zero, Zero) 130.74/78.45 130.74/78.45 We have to consider all minimal (P,Q,R)-chains. 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (769) TransformationProof (EQUIVALENT) 130.74/78.45 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.45 130.74/78.45 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb)) 130.74/78.45 130.74/78.45 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (770) 130.74/78.45 Obligation: 130.74/78.45 Q DP problem: 130.74/78.45 The TRS P consists of the following rules: 130.74/78.45 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.45 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb) 130.74/78.45 130.74/78.45 The TRS R consists of the following rules: 130.74/78.45 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.45 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.45 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.45 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.45 new_primPlusNat2(Zero) -> Zero 130.74/78.45 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.45 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.45 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.45 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.45 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.45 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.45 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.45 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.45 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.45 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.45 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.45 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.45 130.74/78.45 The set Q consists of the following terms: 130.74/78.45 130.74/78.45 new_primPlusNat1(Succ(x0)) 130.74/78.45 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.45 new_primPlusNat1(Zero) 130.74/78.45 new_primPlusNat2(Zero) 130.74/78.45 new_primPlusNat3(Succ(x0)) 130.74/78.45 new_primPlusNat8(Succ(x0), x1) 130.74/78.45 new_primPlusNat6(x0, Succ(x1)) 130.74/78.45 new_primPlusNat0(Succ(x0), Zero) 130.74/78.45 new_primPlusNat6(x0, Zero) 130.74/78.45 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.45 new_primPlusNat4(Succ(x0)) 130.74/78.45 new_primPlusNat8(Zero, x0) 130.74/78.45 new_primPlusNat3(Zero) 130.74/78.45 new_primPlusNat7(x0, Zero) 130.74/78.45 new_primPlusNat7(x0, Succ(x1)) 130.74/78.45 new_primPlusNat4(Zero) 130.74/78.45 new_primPlusNat2(Succ(x0)) 130.74/78.45 new_primPlusNat0(Zero, Zero) 130.74/78.45 130.74/78.45 We have to consider all minimal (P,Q,R)-chains. 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (771) TransformationProof (EQUIVALENT) 130.74/78.45 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.45 130.74/78.45 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))))))))))))))), bb)) 130.74/78.45 130.74/78.45 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (772) 130.74/78.45 Obligation: 130.74/78.45 Q DP problem: 130.74/78.45 The TRS P consists of the following rules: 130.74/78.45 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.45 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))))))))))))))), bb) 130.74/78.45 130.74/78.45 The TRS R consists of the following rules: 130.74/78.45 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.45 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.45 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.45 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.45 new_primPlusNat2(Zero) -> Zero 130.74/78.45 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.45 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.45 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.45 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.45 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.45 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.45 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.45 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.45 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.45 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.45 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.45 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.45 130.74/78.45 The set Q consists of the following terms: 130.74/78.45 130.74/78.45 new_primPlusNat1(Succ(x0)) 130.74/78.45 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.45 new_primPlusNat1(Zero) 130.74/78.45 new_primPlusNat2(Zero) 130.74/78.45 new_primPlusNat3(Succ(x0)) 130.74/78.45 new_primPlusNat8(Succ(x0), x1) 130.74/78.45 new_primPlusNat6(x0, Succ(x1)) 130.74/78.45 new_primPlusNat0(Succ(x0), Zero) 130.74/78.45 new_primPlusNat6(x0, Zero) 130.74/78.45 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.45 new_primPlusNat4(Succ(x0)) 130.74/78.45 new_primPlusNat8(Zero, x0) 130.74/78.45 new_primPlusNat3(Zero) 130.74/78.45 new_primPlusNat7(x0, Zero) 130.74/78.45 new_primPlusNat7(x0, Succ(x1)) 130.74/78.45 new_primPlusNat4(Zero) 130.74/78.45 new_primPlusNat2(Succ(x0)) 130.74/78.45 new_primPlusNat0(Zero, Zero) 130.74/78.45 130.74/78.45 We have to consider all minimal (P,Q,R)-chains. 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (773) TransformationProof (EQUIVALENT) 130.74/78.45 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.45 130.74/78.45 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb)) 130.74/78.45 130.74/78.45 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (774) 130.74/78.45 Obligation: 130.74/78.45 Q DP problem: 130.74/78.45 The TRS P consists of the following rules: 130.74/78.45 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.45 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.45 130.74/78.45 The TRS R consists of the following rules: 130.74/78.45 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.45 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.45 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.45 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.45 new_primPlusNat2(Zero) -> Zero 130.74/78.45 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.45 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.45 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.45 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.45 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.45 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.45 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.45 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.45 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.45 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.45 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.45 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.45 130.74/78.45 The set Q consists of the following terms: 130.74/78.45 130.74/78.45 new_primPlusNat1(Succ(x0)) 130.74/78.45 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.45 new_primPlusNat1(Zero) 130.74/78.45 new_primPlusNat2(Zero) 130.74/78.45 new_primPlusNat3(Succ(x0)) 130.74/78.45 new_primPlusNat8(Succ(x0), x1) 130.74/78.45 new_primPlusNat6(x0, Succ(x1)) 130.74/78.45 new_primPlusNat0(Succ(x0), Zero) 130.74/78.45 new_primPlusNat6(x0, Zero) 130.74/78.45 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.45 new_primPlusNat4(Succ(x0)) 130.74/78.45 new_primPlusNat8(Zero, x0) 130.74/78.45 new_primPlusNat3(Zero) 130.74/78.45 new_primPlusNat7(x0, Zero) 130.74/78.45 new_primPlusNat7(x0, Succ(x1)) 130.74/78.45 new_primPlusNat4(Zero) 130.74/78.45 new_primPlusNat2(Succ(x0)) 130.74/78.45 new_primPlusNat0(Zero, Zero) 130.74/78.45 130.74/78.45 We have to consider all minimal (P,Q,R)-chains. 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (775) TransformationProof (EQUIVALENT) 130.74/78.45 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))))), Succ(Succ(Succ(Zero)))), Succ(Zero))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.45 130.74/78.45 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))), Succ(Zero))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))), Succ(Zero))))))))))))))), bb)) 130.74/78.45 130.74/78.45 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (776) 130.74/78.45 Obligation: 130.74/78.45 Q DP problem: 130.74/78.45 The TRS P consists of the following rules: 130.74/78.45 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.45 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))), Succ(Zero))))))))))))))), bb) 130.74/78.45 130.74/78.45 The TRS R consists of the following rules: 130.74/78.45 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.45 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.45 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.45 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.45 new_primPlusNat2(Zero) -> Zero 130.74/78.45 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.45 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.45 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.45 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.45 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.45 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.45 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.45 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.45 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.45 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.45 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.45 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.45 130.74/78.45 The set Q consists of the following terms: 130.74/78.45 130.74/78.45 new_primPlusNat1(Succ(x0)) 130.74/78.45 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.45 new_primPlusNat1(Zero) 130.74/78.45 new_primPlusNat2(Zero) 130.74/78.45 new_primPlusNat3(Succ(x0)) 130.74/78.45 new_primPlusNat8(Succ(x0), x1) 130.74/78.45 new_primPlusNat6(x0, Succ(x1)) 130.74/78.45 new_primPlusNat0(Succ(x0), Zero) 130.74/78.45 new_primPlusNat6(x0, Zero) 130.74/78.45 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.45 new_primPlusNat4(Succ(x0)) 130.74/78.45 new_primPlusNat8(Zero, x0) 130.74/78.45 new_primPlusNat3(Zero) 130.74/78.45 new_primPlusNat7(x0, Zero) 130.74/78.45 new_primPlusNat7(x0, Succ(x1)) 130.74/78.45 new_primPlusNat4(Zero) 130.74/78.45 new_primPlusNat2(Succ(x0)) 130.74/78.45 new_primPlusNat0(Zero, Zero) 130.74/78.45 130.74/78.45 We have to consider all minimal (P,Q,R)-chains. 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (777) TransformationProof (EQUIVALENT) 130.74/78.45 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.45 130.74/78.45 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))), Zero))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))), Zero))))))))))))))))), bb)) 130.74/78.45 130.74/78.45 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (778) 130.74/78.45 Obligation: 130.74/78.45 Q DP problem: 130.74/78.45 The TRS P consists of the following rules: 130.74/78.45 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.45 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))), Succ(Zero))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))), Zero))))))))))))))))), bb) 130.74/78.45 130.74/78.45 The TRS R consists of the following rules: 130.74/78.45 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.45 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.45 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.45 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.45 new_primPlusNat2(Zero) -> Zero 130.74/78.45 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.45 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.45 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.45 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.45 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.45 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.45 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.45 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.45 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.45 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.45 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.45 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.45 130.74/78.45 The set Q consists of the following terms: 130.74/78.45 130.74/78.45 new_primPlusNat1(Succ(x0)) 130.74/78.45 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.45 new_primPlusNat1(Zero) 130.74/78.45 new_primPlusNat2(Zero) 130.74/78.45 new_primPlusNat3(Succ(x0)) 130.74/78.45 new_primPlusNat8(Succ(x0), x1) 130.74/78.45 new_primPlusNat6(x0, Succ(x1)) 130.74/78.45 new_primPlusNat0(Succ(x0), Zero) 130.74/78.45 new_primPlusNat6(x0, Zero) 130.74/78.45 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.45 new_primPlusNat4(Succ(x0)) 130.74/78.45 new_primPlusNat8(Zero, x0) 130.74/78.45 new_primPlusNat3(Zero) 130.74/78.45 new_primPlusNat7(x0, Zero) 130.74/78.45 new_primPlusNat7(x0, Succ(x1)) 130.74/78.45 new_primPlusNat4(Zero) 130.74/78.45 new_primPlusNat2(Succ(x0)) 130.74/78.45 new_primPlusNat0(Zero, Zero) 130.74/78.45 130.74/78.45 We have to consider all minimal (P,Q,R)-chains. 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (779) TransformationProof (EQUIVALENT) 130.74/78.45 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))), Succ(Zero))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.45 130.74/78.45 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))), Zero)))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))), Zero)))))))))))))))), bb)) 130.74/78.45 130.74/78.45 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (780) 130.74/78.45 Obligation: 130.74/78.45 Q DP problem: 130.74/78.45 The TRS P consists of the following rules: 130.74/78.45 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.45 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))), Zero))))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))), Zero)))))))))))))))), bb) 130.74/78.45 130.74/78.45 The TRS R consists of the following rules: 130.74/78.45 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.45 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.45 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.45 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.45 new_primPlusNat2(Zero) -> Zero 130.74/78.45 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.45 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.45 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.45 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.45 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.45 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.45 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.45 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.45 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.45 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.45 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.45 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.45 130.74/78.45 The set Q consists of the following terms: 130.74/78.45 130.74/78.45 new_primPlusNat1(Succ(x0)) 130.74/78.45 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.45 new_primPlusNat1(Zero) 130.74/78.45 new_primPlusNat2(Zero) 130.74/78.45 new_primPlusNat3(Succ(x0)) 130.74/78.45 new_primPlusNat8(Succ(x0), x1) 130.74/78.45 new_primPlusNat6(x0, Succ(x1)) 130.74/78.45 new_primPlusNat0(Succ(x0), Zero) 130.74/78.45 new_primPlusNat6(x0, Zero) 130.74/78.45 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.45 new_primPlusNat4(Succ(x0)) 130.74/78.45 new_primPlusNat8(Zero, x0) 130.74/78.45 new_primPlusNat3(Zero) 130.74/78.45 new_primPlusNat7(x0, Zero) 130.74/78.45 new_primPlusNat7(x0, Succ(x1)) 130.74/78.45 new_primPlusNat4(Zero) 130.74/78.45 new_primPlusNat2(Succ(x0)) 130.74/78.45 new_primPlusNat0(Zero, Zero) 130.74/78.45 130.74/78.45 We have to consider all minimal (P,Q,R)-chains. 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (781) TransformationProof (EQUIVALENT) 130.74/78.45 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))), Zero))))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.45 130.74/78.45 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))), Zero))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))), Zero))))))))))))))))), bb)) 130.74/78.45 130.74/78.45 130.74/78.45 ---------------------------------------- 130.74/78.45 130.74/78.45 (782) 130.74/78.45 Obligation: 130.74/78.45 Q DP problem: 130.74/78.45 The TRS P consists of the following rules: 130.74/78.45 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.45 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.45 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.45 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))), Zero)))))))))))))))), bb) 130.74/78.45 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))), Zero))))))))))))))))), bb) 130.74/78.45 130.74/78.45 The TRS R consists of the following rules: 130.74/78.45 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.45 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.45 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.45 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.45 new_primPlusNat2(Zero) -> Zero 130.74/78.45 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.45 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.45 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.45 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.45 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.45 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.46 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.46 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.46 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.46 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.46 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.46 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.46 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.46 130.74/78.46 The set Q consists of the following terms: 130.74/78.46 130.74/78.46 new_primPlusNat1(Succ(x0)) 130.74/78.46 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.46 new_primPlusNat1(Zero) 130.74/78.46 new_primPlusNat2(Zero) 130.74/78.46 new_primPlusNat3(Succ(x0)) 130.74/78.46 new_primPlusNat8(Succ(x0), x1) 130.74/78.46 new_primPlusNat6(x0, Succ(x1)) 130.74/78.46 new_primPlusNat0(Succ(x0), Zero) 130.74/78.46 new_primPlusNat6(x0, Zero) 130.74/78.46 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.46 new_primPlusNat4(Succ(x0)) 130.74/78.46 new_primPlusNat8(Zero, x0) 130.74/78.46 new_primPlusNat3(Zero) 130.74/78.46 new_primPlusNat7(x0, Zero) 130.74/78.46 new_primPlusNat7(x0, Succ(x1)) 130.74/78.46 new_primPlusNat4(Zero) 130.74/78.46 new_primPlusNat2(Succ(x0)) 130.74/78.46 new_primPlusNat0(Zero, Zero) 130.74/78.46 130.74/78.46 We have to consider all minimal (P,Q,R)-chains. 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (783) TransformationProof (EQUIVALENT) 130.74/78.46 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero)))), Zero)))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.46 130.74/78.46 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))))))))))))), bb)) 130.74/78.46 130.74/78.46 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (784) 130.74/78.46 Obligation: 130.74/78.46 Q DP problem: 130.74/78.46 The TRS P consists of the following rules: 130.74/78.46 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.46 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))), Zero))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))))))))))))), bb) 130.74/78.46 130.74/78.46 The TRS R consists of the following rules: 130.74/78.46 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.46 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.46 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.46 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.46 new_primPlusNat2(Zero) -> Zero 130.74/78.46 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.46 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.46 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.46 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.46 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.46 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.46 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.46 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.46 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.46 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.46 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.46 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.46 130.74/78.46 The set Q consists of the following terms: 130.74/78.46 130.74/78.46 new_primPlusNat1(Succ(x0)) 130.74/78.46 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.46 new_primPlusNat1(Zero) 130.74/78.46 new_primPlusNat2(Zero) 130.74/78.46 new_primPlusNat3(Succ(x0)) 130.74/78.46 new_primPlusNat8(Succ(x0), x1) 130.74/78.46 new_primPlusNat6(x0, Succ(x1)) 130.74/78.46 new_primPlusNat0(Succ(x0), Zero) 130.74/78.46 new_primPlusNat6(x0, Zero) 130.74/78.46 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.46 new_primPlusNat4(Succ(x0)) 130.74/78.46 new_primPlusNat8(Zero, x0) 130.74/78.46 new_primPlusNat3(Zero) 130.74/78.46 new_primPlusNat7(x0, Zero) 130.74/78.46 new_primPlusNat7(x0, Succ(x1)) 130.74/78.46 new_primPlusNat4(Zero) 130.74/78.46 new_primPlusNat2(Succ(x0)) 130.74/78.46 new_primPlusNat0(Zero, Zero) 130.74/78.46 130.74/78.46 We have to consider all minimal (P,Q,R)-chains. 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (785) TransformationProof (EQUIVALENT) 130.74/78.46 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))), Zero))))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.46 130.74/78.46 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))))))))))), bb)) 130.74/78.46 130.74/78.46 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (786) 130.74/78.46 Obligation: 130.74/78.46 Q DP problem: 130.74/78.46 The TRS P consists of the following rules: 130.74/78.46 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.46 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))))))))))), bb) 130.74/78.46 130.74/78.46 The TRS R consists of the following rules: 130.74/78.46 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.46 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.46 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.46 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.46 new_primPlusNat2(Zero) -> Zero 130.74/78.46 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.46 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.46 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.46 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.46 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.46 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.46 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.46 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.46 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.46 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.46 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.46 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.46 130.74/78.46 The set Q consists of the following terms: 130.74/78.46 130.74/78.46 new_primPlusNat1(Succ(x0)) 130.74/78.46 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.46 new_primPlusNat1(Zero) 130.74/78.46 new_primPlusNat2(Zero) 130.74/78.46 new_primPlusNat3(Succ(x0)) 130.74/78.46 new_primPlusNat8(Succ(x0), x1) 130.74/78.46 new_primPlusNat6(x0, Succ(x1)) 130.74/78.46 new_primPlusNat0(Succ(x0), Zero) 130.74/78.46 new_primPlusNat6(x0, Zero) 130.74/78.46 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.46 new_primPlusNat4(Succ(x0)) 130.74/78.46 new_primPlusNat8(Zero, x0) 130.74/78.46 new_primPlusNat3(Zero) 130.74/78.46 new_primPlusNat7(x0, Zero) 130.74/78.46 new_primPlusNat7(x0, Succ(x1)) 130.74/78.46 new_primPlusNat4(Zero) 130.74/78.46 new_primPlusNat2(Succ(x0)) 130.74/78.46 new_primPlusNat0(Zero, Zero) 130.74/78.46 130.74/78.46 We have to consider all minimal (P,Q,R)-chains. 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (787) TransformationProof (EQUIVALENT) 130.74/78.46 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Zero))))))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.46 130.74/78.46 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))))))))))))), bb)) 130.74/78.46 130.74/78.46 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (788) 130.74/78.46 Obligation: 130.74/78.46 Q DP problem: 130.74/78.46 The TRS P consists of the following rules: 130.74/78.46 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.46 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))))))))))))), bb) 130.74/78.46 130.74/78.46 The TRS R consists of the following rules: 130.74/78.46 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.46 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.46 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.46 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.46 new_primPlusNat2(Zero) -> Zero 130.74/78.46 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.46 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.46 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.46 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.46 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.46 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.46 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.46 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.46 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.46 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.46 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.46 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.46 130.74/78.46 The set Q consists of the following terms: 130.74/78.46 130.74/78.46 new_primPlusNat1(Succ(x0)) 130.74/78.46 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.46 new_primPlusNat1(Zero) 130.74/78.46 new_primPlusNat2(Zero) 130.74/78.46 new_primPlusNat3(Succ(x0)) 130.74/78.46 new_primPlusNat8(Succ(x0), x1) 130.74/78.46 new_primPlusNat6(x0, Succ(x1)) 130.74/78.46 new_primPlusNat0(Succ(x0), Zero) 130.74/78.46 new_primPlusNat6(x0, Zero) 130.74/78.46 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.46 new_primPlusNat4(Succ(x0)) 130.74/78.46 new_primPlusNat8(Zero, x0) 130.74/78.46 new_primPlusNat3(Zero) 130.74/78.46 new_primPlusNat7(x0, Zero) 130.74/78.46 new_primPlusNat7(x0, Succ(x1)) 130.74/78.46 new_primPlusNat4(Zero) 130.74/78.46 new_primPlusNat2(Succ(x0)) 130.74/78.46 new_primPlusNat0(Zero, Zero) 130.74/78.46 130.74/78.46 We have to consider all minimal (P,Q,R)-chains. 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (789) TransformationProof (EQUIVALENT) 130.74/78.46 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.46 130.74/78.46 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero))))))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero))))))))))))))))))))), bb)) 130.74/78.46 130.74/78.46 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (790) 130.74/78.46 Obligation: 130.74/78.46 Q DP problem: 130.74/78.46 The TRS P consists of the following rules: 130.74/78.46 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.46 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero))))))))))))))))))))), bb) 130.74/78.46 130.74/78.46 The TRS R consists of the following rules: 130.74/78.46 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.46 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.46 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.46 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.46 new_primPlusNat2(Zero) -> Zero 130.74/78.46 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.46 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.46 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.46 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.46 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.46 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.46 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.46 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.46 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.46 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.46 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.46 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.46 130.74/78.46 The set Q consists of the following terms: 130.74/78.46 130.74/78.46 new_primPlusNat1(Succ(x0)) 130.74/78.46 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.46 new_primPlusNat1(Zero) 130.74/78.46 new_primPlusNat2(Zero) 130.74/78.46 new_primPlusNat3(Succ(x0)) 130.74/78.46 new_primPlusNat8(Succ(x0), x1) 130.74/78.46 new_primPlusNat6(x0, Succ(x1)) 130.74/78.46 new_primPlusNat0(Succ(x0), Zero) 130.74/78.46 new_primPlusNat6(x0, Zero) 130.74/78.46 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.46 new_primPlusNat4(Succ(x0)) 130.74/78.46 new_primPlusNat8(Zero, x0) 130.74/78.46 new_primPlusNat3(Zero) 130.74/78.46 new_primPlusNat7(x0, Zero) 130.74/78.46 new_primPlusNat7(x0, Succ(x1)) 130.74/78.46 new_primPlusNat4(Zero) 130.74/78.46 new_primPlusNat2(Succ(x0)) 130.74/78.46 new_primPlusNat0(Zero, Zero) 130.74/78.46 130.74/78.46 We have to consider all minimal (P,Q,R)-chains. 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (791) TransformationProof (EQUIVALENT) 130.74/78.46 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Zero)))))))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.46 130.74/78.46 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))), Succ(Zero)))))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))), Succ(Zero)))))))))))))))))))), bb)) 130.74/78.46 130.74/78.46 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (792) 130.74/78.46 Obligation: 130.74/78.46 Q DP problem: 130.74/78.46 The TRS P consists of the following rules: 130.74/78.46 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.46 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero))))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))), Succ(Zero)))))))))))))))))))), bb) 130.74/78.46 130.74/78.46 The TRS R consists of the following rules: 130.74/78.46 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.46 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.46 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.46 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.46 new_primPlusNat2(Zero) -> Zero 130.74/78.46 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.46 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.46 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.46 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.46 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.46 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.46 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.46 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.46 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.46 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.46 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.46 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.46 130.74/78.46 The set Q consists of the following terms: 130.74/78.46 130.74/78.46 new_primPlusNat1(Succ(x0)) 130.74/78.46 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.46 new_primPlusNat1(Zero) 130.74/78.46 new_primPlusNat2(Zero) 130.74/78.46 new_primPlusNat3(Succ(x0)) 130.74/78.46 new_primPlusNat8(Succ(x0), x1) 130.74/78.46 new_primPlusNat6(x0, Succ(x1)) 130.74/78.46 new_primPlusNat0(Succ(x0), Zero) 130.74/78.46 new_primPlusNat6(x0, Zero) 130.74/78.46 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.46 new_primPlusNat4(Succ(x0)) 130.74/78.46 new_primPlusNat8(Zero, x0) 130.74/78.46 new_primPlusNat3(Zero) 130.74/78.46 new_primPlusNat7(x0, Zero) 130.74/78.46 new_primPlusNat7(x0, Succ(x1)) 130.74/78.46 new_primPlusNat4(Zero) 130.74/78.46 new_primPlusNat2(Succ(x0)) 130.74/78.46 new_primPlusNat0(Zero, Zero) 130.74/78.46 130.74/78.46 We have to consider all minimal (P,Q,R)-chains. 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (793) TransformationProof (EQUIVALENT) 130.74/78.46 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero))))))))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.46 130.74/78.46 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb)) 130.74/78.46 130.74/78.46 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (794) 130.74/78.46 Obligation: 130.74/78.46 Q DP problem: 130.74/78.46 The TRS P consists of the following rules: 130.74/78.46 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.46 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))), Succ(Zero)))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.46 130.74/78.46 The TRS R consists of the following rules: 130.74/78.46 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.46 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.46 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.46 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.46 new_primPlusNat2(Zero) -> Zero 130.74/78.46 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.46 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.46 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.46 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.46 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.46 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.46 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.46 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.46 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.46 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.46 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.46 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.46 130.74/78.46 The set Q consists of the following terms: 130.74/78.46 130.74/78.46 new_primPlusNat1(Succ(x0)) 130.74/78.46 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.46 new_primPlusNat1(Zero) 130.74/78.46 new_primPlusNat2(Zero) 130.74/78.46 new_primPlusNat3(Succ(x0)) 130.74/78.46 new_primPlusNat8(Succ(x0), x1) 130.74/78.46 new_primPlusNat6(x0, Succ(x1)) 130.74/78.46 new_primPlusNat0(Succ(x0), Zero) 130.74/78.46 new_primPlusNat6(x0, Zero) 130.74/78.46 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.46 new_primPlusNat4(Succ(x0)) 130.74/78.46 new_primPlusNat8(Zero, x0) 130.74/78.46 new_primPlusNat3(Zero) 130.74/78.46 new_primPlusNat7(x0, Zero) 130.74/78.46 new_primPlusNat7(x0, Succ(x1)) 130.74/78.46 new_primPlusNat4(Zero) 130.74/78.46 new_primPlusNat2(Succ(x0)) 130.74/78.46 new_primPlusNat0(Zero, Zero) 130.74/78.46 130.74/78.46 We have to consider all minimal (P,Q,R)-chains. 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (795) TransformationProof (EQUIVALENT) 130.74/78.46 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))), Succ(Zero)))))))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.46 130.74/78.46 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Zero))))))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Zero))))))))))))))))))))), bb)) 130.74/78.46 130.74/78.46 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (796) 130.74/78.46 Obligation: 130.74/78.46 Q DP problem: 130.74/78.46 The TRS P consists of the following rules: 130.74/78.46 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.46 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Zero))))))))))))))))))))), bb) 130.74/78.46 130.74/78.46 The TRS R consists of the following rules: 130.74/78.46 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.46 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.46 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.46 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.46 new_primPlusNat2(Zero) -> Zero 130.74/78.46 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.46 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.46 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.46 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.46 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.46 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.46 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.46 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.46 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.46 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.46 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.46 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.46 130.74/78.46 The set Q consists of the following terms: 130.74/78.46 130.74/78.46 new_primPlusNat1(Succ(x0)) 130.74/78.46 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.46 new_primPlusNat1(Zero) 130.74/78.46 new_primPlusNat2(Zero) 130.74/78.46 new_primPlusNat3(Succ(x0)) 130.74/78.46 new_primPlusNat8(Succ(x0), x1) 130.74/78.46 new_primPlusNat6(x0, Succ(x1)) 130.74/78.46 new_primPlusNat0(Succ(x0), Zero) 130.74/78.46 new_primPlusNat6(x0, Zero) 130.74/78.46 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.46 new_primPlusNat4(Succ(x0)) 130.74/78.46 new_primPlusNat8(Zero, x0) 130.74/78.46 new_primPlusNat3(Zero) 130.74/78.46 new_primPlusNat7(x0, Zero) 130.74/78.46 new_primPlusNat7(x0, Succ(x1)) 130.74/78.46 new_primPlusNat4(Zero) 130.74/78.46 new_primPlusNat2(Succ(x0)) 130.74/78.46 new_primPlusNat0(Zero, Zero) 130.74/78.46 130.74/78.46 We have to consider all minimal (P,Q,R)-chains. 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (797) TransformationProof (EQUIVALENT) 130.74/78.46 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Zero))))))))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.46 130.74/78.46 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))))))))))))), bb)) 130.74/78.46 130.74/78.46 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (798) 130.74/78.46 Obligation: 130.74/78.46 Q DP problem: 130.74/78.46 The TRS P consists of the following rules: 130.74/78.46 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.46 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))))))))))))), bb) 130.74/78.46 130.74/78.46 The TRS R consists of the following rules: 130.74/78.46 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.46 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.46 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.46 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.46 new_primPlusNat2(Zero) -> Zero 130.74/78.46 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.46 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.46 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.46 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.46 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.46 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.46 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.46 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.46 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.46 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.46 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.46 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.46 130.74/78.46 The set Q consists of the following terms: 130.74/78.46 130.74/78.46 new_primPlusNat1(Succ(x0)) 130.74/78.46 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.46 new_primPlusNat1(Zero) 130.74/78.46 new_primPlusNat2(Zero) 130.74/78.46 new_primPlusNat3(Succ(x0)) 130.74/78.46 new_primPlusNat8(Succ(x0), x1) 130.74/78.46 new_primPlusNat6(x0, Succ(x1)) 130.74/78.46 new_primPlusNat0(Succ(x0), Zero) 130.74/78.46 new_primPlusNat6(x0, Zero) 130.74/78.46 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.46 new_primPlusNat4(Succ(x0)) 130.74/78.46 new_primPlusNat8(Zero, x0) 130.74/78.46 new_primPlusNat3(Zero) 130.74/78.46 new_primPlusNat7(x0, Zero) 130.74/78.46 new_primPlusNat7(x0, Succ(x1)) 130.74/78.46 new_primPlusNat4(Zero) 130.74/78.46 new_primPlusNat2(Succ(x0)) 130.74/78.46 new_primPlusNat0(Zero, Zero) 130.74/78.46 130.74/78.46 We have to consider all minimal (P,Q,R)-chains. 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (799) TransformationProof (EQUIVALENT) 130.74/78.46 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))))))))))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.46 130.74/78.46 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))))))))))))), bb)) 130.74/78.46 130.74/78.46 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (800) 130.74/78.46 Obligation: 130.74/78.46 Q DP problem: 130.74/78.46 The TRS P consists of the following rules: 130.74/78.46 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.46 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.46 130.74/78.46 The TRS R consists of the following rules: 130.74/78.46 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.46 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.46 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.46 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.46 new_primPlusNat2(Zero) -> Zero 130.74/78.46 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.46 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.46 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.46 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.46 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.46 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.46 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.46 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.46 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.46 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.46 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.46 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.46 130.74/78.46 The set Q consists of the following terms: 130.74/78.46 130.74/78.46 new_primPlusNat1(Succ(x0)) 130.74/78.46 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.46 new_primPlusNat1(Zero) 130.74/78.46 new_primPlusNat2(Zero) 130.74/78.46 new_primPlusNat3(Succ(x0)) 130.74/78.46 new_primPlusNat8(Succ(x0), x1) 130.74/78.46 new_primPlusNat6(x0, Succ(x1)) 130.74/78.46 new_primPlusNat0(Succ(x0), Zero) 130.74/78.46 new_primPlusNat6(x0, Zero) 130.74/78.46 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.46 new_primPlusNat4(Succ(x0)) 130.74/78.46 new_primPlusNat8(Zero, x0) 130.74/78.46 new_primPlusNat3(Zero) 130.74/78.46 new_primPlusNat7(x0, Zero) 130.74/78.46 new_primPlusNat7(x0, Succ(x1)) 130.74/78.46 new_primPlusNat4(Zero) 130.74/78.46 new_primPlusNat2(Succ(x0)) 130.74/78.46 new_primPlusNat0(Zero, Zero) 130.74/78.46 130.74/78.46 We have to consider all minimal (P,Q,R)-chains. 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (801) TransformationProof (EQUIVALENT) 130.74/78.46 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero))))))))))))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.46 130.74/78.46 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))))))))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))))))))))))))))))))))), bb)) 130.74/78.46 130.74/78.46 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (802) 130.74/78.46 Obligation: 130.74/78.46 Q DP problem: 130.74/78.46 The TRS P consists of the following rules: 130.74/78.46 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.46 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))))))))))))))))))))))), bb) 130.74/78.46 130.74/78.46 The TRS R consists of the following rules: 130.74/78.46 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.46 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.46 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.46 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.46 new_primPlusNat2(Zero) -> Zero 130.74/78.46 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.46 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.46 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.46 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.46 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.46 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.46 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.46 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.46 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.46 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.46 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.46 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.46 130.74/78.46 The set Q consists of the following terms: 130.74/78.46 130.74/78.46 new_primPlusNat1(Succ(x0)) 130.74/78.46 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.46 new_primPlusNat1(Zero) 130.74/78.46 new_primPlusNat2(Zero) 130.74/78.46 new_primPlusNat3(Succ(x0)) 130.74/78.46 new_primPlusNat8(Succ(x0), x1) 130.74/78.46 new_primPlusNat6(x0, Succ(x1)) 130.74/78.46 new_primPlusNat0(Succ(x0), Zero) 130.74/78.46 new_primPlusNat6(x0, Zero) 130.74/78.46 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.46 new_primPlusNat4(Succ(x0)) 130.74/78.46 new_primPlusNat8(Zero, x0) 130.74/78.46 new_primPlusNat3(Zero) 130.74/78.46 new_primPlusNat7(x0, Zero) 130.74/78.46 new_primPlusNat7(x0, Succ(x1)) 130.74/78.46 new_primPlusNat4(Zero) 130.74/78.46 new_primPlusNat2(Succ(x0)) 130.74/78.46 new_primPlusNat0(Zero, Zero) 130.74/78.46 130.74/78.46 We have to consider all minimal (P,Q,R)-chains. 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (803) TransformationProof (EQUIVALENT) 130.74/78.46 By rewriting [LPAR04] the rule new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))))))))))))))))))))))), bb) at position [10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.46 130.74/78.46 (new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb),new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb)) 130.74/78.46 130.74/78.46 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (804) 130.74/78.46 Obligation: 130.74/78.46 Q DP problem: 130.74/78.46 The TRS P consists of the following rules: 130.74/78.46 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.46 new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.46 130.74/78.46 The TRS R consists of the following rules: 130.74/78.46 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.46 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.46 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.46 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.46 new_primPlusNat2(Zero) -> Zero 130.74/78.46 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.46 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.46 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.46 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.46 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.46 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.46 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.46 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.46 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.46 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.46 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.46 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.46 130.74/78.46 The set Q consists of the following terms: 130.74/78.46 130.74/78.46 new_primPlusNat1(Succ(x0)) 130.74/78.46 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.46 new_primPlusNat1(Zero) 130.74/78.46 new_primPlusNat2(Zero) 130.74/78.46 new_primPlusNat3(Succ(x0)) 130.74/78.46 new_primPlusNat8(Succ(x0), x1) 130.74/78.46 new_primPlusNat6(x0, Succ(x1)) 130.74/78.46 new_primPlusNat0(Succ(x0), Zero) 130.74/78.46 new_primPlusNat6(x0, Zero) 130.74/78.46 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.46 new_primPlusNat4(Succ(x0)) 130.74/78.46 new_primPlusNat8(Zero, x0) 130.74/78.46 new_primPlusNat3(Zero) 130.74/78.46 new_primPlusNat7(x0, Zero) 130.74/78.46 new_primPlusNat7(x0, Succ(x1)) 130.74/78.46 new_primPlusNat4(Zero) 130.74/78.46 new_primPlusNat2(Succ(x0)) 130.74/78.46 new_primPlusNat0(Zero, Zero) 130.74/78.46 130.74/78.46 We have to consider all minimal (P,Q,R)-chains. 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (805) TransformationProof (EQUIVALENT) 130.74/78.46 By instantiating [LPAR04] the rule new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Zero))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49630), Succ(Zero), bb) we obtained the following new rules [LPAR04]: 130.74/78.46 130.74/78.46 (new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10),new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10)) 130.74/78.46 130.74/78.46 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (806) 130.74/78.46 Obligation: 130.74/78.46 Q DP problem: 130.74/78.46 The TRS P consists of the following rules: 130.74/78.46 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.46 130.74/78.46 The TRS R consists of the following rules: 130.74/78.46 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.46 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.46 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.46 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.46 new_primPlusNat2(Zero) -> Zero 130.74/78.46 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.46 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.46 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.46 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.46 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.46 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.46 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.46 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.46 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.46 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.46 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.46 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.46 130.74/78.46 The set Q consists of the following terms: 130.74/78.46 130.74/78.46 new_primPlusNat1(Succ(x0)) 130.74/78.46 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.46 new_primPlusNat1(Zero) 130.74/78.46 new_primPlusNat2(Zero) 130.74/78.46 new_primPlusNat3(Succ(x0)) 130.74/78.46 new_primPlusNat8(Succ(x0), x1) 130.74/78.46 new_primPlusNat6(x0, Succ(x1)) 130.74/78.46 new_primPlusNat0(Succ(x0), Zero) 130.74/78.46 new_primPlusNat6(x0, Zero) 130.74/78.46 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.46 new_primPlusNat4(Succ(x0)) 130.74/78.46 new_primPlusNat8(Zero, x0) 130.74/78.46 new_primPlusNat3(Zero) 130.74/78.46 new_primPlusNat7(x0, Zero) 130.74/78.46 new_primPlusNat7(x0, Succ(x1)) 130.74/78.46 new_primPlusNat4(Zero) 130.74/78.46 new_primPlusNat2(Succ(x0)) 130.74/78.46 new_primPlusNat0(Zero, Zero) 130.74/78.46 130.74/78.46 We have to consider all minimal (P,Q,R)-chains. 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (807) TransformationProof (EQUIVALENT) 130.74/78.46 By instantiating [LPAR04] the rule new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, Zero, zzz343, zzz344, zzz300, zzz31, Succ(zzz44380), Succ(zzz250200), bb) we obtained the following new rules [LPAR04]: 130.74/78.46 130.74/78.46 (new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11),new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11)) 130.74/78.46 130.74/78.46 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (808) 130.74/78.46 Obligation: 130.74/78.46 Q DP problem: 130.74/78.46 The TRS P consists of the following rules: 130.74/78.46 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.46 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.46 130.74/78.46 The TRS R consists of the following rules: 130.74/78.46 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.46 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.46 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.46 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.46 new_primPlusNat2(Zero) -> Zero 130.74/78.46 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.46 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.46 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.46 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.46 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.46 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.46 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.46 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.46 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.46 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.46 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.46 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.46 130.74/78.46 The set Q consists of the following terms: 130.74/78.46 130.74/78.46 new_primPlusNat1(Succ(x0)) 130.74/78.46 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.46 new_primPlusNat1(Zero) 130.74/78.46 new_primPlusNat2(Zero) 130.74/78.46 new_primPlusNat3(Succ(x0)) 130.74/78.46 new_primPlusNat8(Succ(x0), x1) 130.74/78.46 new_primPlusNat6(x0, Succ(x1)) 130.74/78.46 new_primPlusNat0(Succ(x0), Zero) 130.74/78.46 new_primPlusNat6(x0, Zero) 130.74/78.46 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.46 new_primPlusNat4(Succ(x0)) 130.74/78.46 new_primPlusNat8(Zero, x0) 130.74/78.46 new_primPlusNat3(Zero) 130.74/78.46 new_primPlusNat7(x0, Zero) 130.74/78.46 new_primPlusNat7(x0, Succ(x1)) 130.74/78.46 new_primPlusNat4(Zero) 130.74/78.46 new_primPlusNat2(Succ(x0)) 130.74/78.46 new_primPlusNat0(Zero, Zero) 130.74/78.46 130.74/78.46 We have to consider all minimal (P,Q,R)-chains. 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (809) TransformationProof (EQUIVALENT) 130.74/78.46 By instantiating [LPAR04] the rule new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47150), Succ(Succ(zzz2502000)), bb) we obtained the following new rules [LPAR04]: 130.74/78.46 130.74/78.46 (new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11),new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11)) 130.74/78.46 130.74/78.46 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (810) 130.74/78.46 Obligation: 130.74/78.46 Q DP problem: 130.74/78.46 The TRS P consists of the following rules: 130.74/78.46 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.46 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.46 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.46 130.74/78.46 The TRS R consists of the following rules: 130.74/78.46 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.46 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.46 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.46 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.46 new_primPlusNat2(Zero) -> Zero 130.74/78.46 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.46 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.46 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.46 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.46 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.46 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.46 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.46 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.46 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.46 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.46 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.46 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.46 130.74/78.46 The set Q consists of the following terms: 130.74/78.46 130.74/78.46 new_primPlusNat1(Succ(x0)) 130.74/78.46 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.46 new_primPlusNat1(Zero) 130.74/78.46 new_primPlusNat2(Zero) 130.74/78.46 new_primPlusNat3(Succ(x0)) 130.74/78.46 new_primPlusNat8(Succ(x0), x1) 130.74/78.46 new_primPlusNat6(x0, Succ(x1)) 130.74/78.46 new_primPlusNat0(Succ(x0), Zero) 130.74/78.46 new_primPlusNat6(x0, Zero) 130.74/78.46 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.46 new_primPlusNat4(Succ(x0)) 130.74/78.46 new_primPlusNat8(Zero, x0) 130.74/78.46 new_primPlusNat3(Zero) 130.74/78.46 new_primPlusNat7(x0, Zero) 130.74/78.46 new_primPlusNat7(x0, Succ(x1)) 130.74/78.46 new_primPlusNat4(Zero) 130.74/78.46 new_primPlusNat2(Succ(x0)) 130.74/78.46 new_primPlusNat0(Zero, Zero) 130.74/78.46 130.74/78.46 We have to consider all minimal (P,Q,R)-chains. 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (811) TransformationProof (EQUIVALENT) 130.74/78.46 By instantiating [LPAR04] the rule new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48110), bb) -> new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, new_primPlusNat4(zzz48110), bb) we obtained the following new rules [LPAR04]: 130.74/78.46 130.74/78.46 (new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, new_primPlusNat4(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11),new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, new_primPlusNat4(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11)) 130.74/78.46 130.74/78.46 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (812) 130.74/78.46 Obligation: 130.74/78.46 Q DP problem: 130.74/78.46 The TRS P consists of the following rules: 130.74/78.46 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.46 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.46 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.46 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, new_primPlusNat4(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) 130.74/78.46 130.74/78.46 The TRS R consists of the following rules: 130.74/78.46 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.46 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.46 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.46 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.46 new_primPlusNat2(Zero) -> Zero 130.74/78.46 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.46 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.46 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.46 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.46 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.46 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.46 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.46 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.46 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.46 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.46 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.46 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.46 130.74/78.46 The set Q consists of the following terms: 130.74/78.46 130.74/78.46 new_primPlusNat1(Succ(x0)) 130.74/78.46 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.46 new_primPlusNat1(Zero) 130.74/78.46 new_primPlusNat2(Zero) 130.74/78.46 new_primPlusNat3(Succ(x0)) 130.74/78.46 new_primPlusNat8(Succ(x0), x1) 130.74/78.46 new_primPlusNat6(x0, Succ(x1)) 130.74/78.46 new_primPlusNat0(Succ(x0), Zero) 130.74/78.46 new_primPlusNat6(x0, Zero) 130.74/78.46 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.46 new_primPlusNat4(Succ(x0)) 130.74/78.46 new_primPlusNat8(Zero, x0) 130.74/78.46 new_primPlusNat3(Zero) 130.74/78.46 new_primPlusNat7(x0, Zero) 130.74/78.46 new_primPlusNat7(x0, Succ(x1)) 130.74/78.46 new_primPlusNat4(Zero) 130.74/78.46 new_primPlusNat2(Succ(x0)) 130.74/78.46 new_primPlusNat0(Zero, Zero) 130.74/78.46 130.74/78.46 We have to consider all minimal (P,Q,R)-chains. 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (813) TransformationProof (EQUIVALENT) 130.74/78.46 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, new_primPlusNat4(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) at position [11] we obtained the following new rules [LPAR04]: 130.74/78.46 130.74/78.46 (new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(new_primPlusNat3(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11),new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(new_primPlusNat3(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11)) 130.74/78.46 130.74/78.46 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (814) 130.74/78.46 Obligation: 130.74/78.46 Q DP problem: 130.74/78.46 The TRS P consists of the following rules: 130.74/78.46 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.46 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.46 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.46 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(new_primPlusNat3(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.46 130.74/78.46 The TRS R consists of the following rules: 130.74/78.46 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.46 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.46 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.46 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.46 new_primPlusNat2(Zero) -> Zero 130.74/78.46 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.46 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.46 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.46 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.46 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.46 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.46 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.46 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.46 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.46 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.46 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.46 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.46 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.46 130.74/78.46 The set Q consists of the following terms: 130.74/78.46 130.74/78.46 new_primPlusNat1(Succ(x0)) 130.74/78.46 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.46 new_primPlusNat1(Zero) 130.74/78.46 new_primPlusNat2(Zero) 130.74/78.46 new_primPlusNat3(Succ(x0)) 130.74/78.46 new_primPlusNat8(Succ(x0), x1) 130.74/78.46 new_primPlusNat6(x0, Succ(x1)) 130.74/78.46 new_primPlusNat0(Succ(x0), Zero) 130.74/78.46 new_primPlusNat6(x0, Zero) 130.74/78.46 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.46 new_primPlusNat4(Succ(x0)) 130.74/78.46 new_primPlusNat8(Zero, x0) 130.74/78.46 new_primPlusNat3(Zero) 130.74/78.46 new_primPlusNat7(x0, Zero) 130.74/78.46 new_primPlusNat7(x0, Succ(x1)) 130.74/78.46 new_primPlusNat4(Zero) 130.74/78.46 new_primPlusNat2(Succ(x0)) 130.74/78.46 new_primPlusNat0(Zero, Zero) 130.74/78.46 130.74/78.46 We have to consider all minimal (P,Q,R)-chains. 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (815) TransformationProof (EQUIVALENT) 130.74/78.46 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(new_primPlusNat3(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.74/78.46 130.74/78.46 (new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))), z11),new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))), z11)) 130.74/78.46 130.74/78.46 130.74/78.46 ---------------------------------------- 130.74/78.46 130.74/78.46 (816) 130.74/78.46 Obligation: 130.74/78.46 Q DP problem: 130.74/78.46 The TRS P consists of the following rules: 130.74/78.46 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.46 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.46 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.46 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.46 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.46 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.46 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))), z11) 130.74/78.47 130.74/78.47 The TRS R consists of the following rules: 130.74/78.47 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.47 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.47 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.47 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.47 new_primPlusNat2(Zero) -> Zero 130.74/78.47 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.47 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.47 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.47 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.47 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.47 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.47 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.47 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.47 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.47 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.47 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.47 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.47 130.74/78.47 The set Q consists of the following terms: 130.74/78.47 130.74/78.47 new_primPlusNat1(Succ(x0)) 130.74/78.47 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.47 new_primPlusNat1(Zero) 130.74/78.47 new_primPlusNat2(Zero) 130.74/78.47 new_primPlusNat3(Succ(x0)) 130.74/78.47 new_primPlusNat8(Succ(x0), x1) 130.74/78.47 new_primPlusNat6(x0, Succ(x1)) 130.74/78.47 new_primPlusNat0(Succ(x0), Zero) 130.74/78.47 new_primPlusNat6(x0, Zero) 130.74/78.47 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.47 new_primPlusNat4(Succ(x0)) 130.74/78.47 new_primPlusNat8(Zero, x0) 130.74/78.47 new_primPlusNat3(Zero) 130.74/78.47 new_primPlusNat7(x0, Zero) 130.74/78.47 new_primPlusNat7(x0, Succ(x1)) 130.74/78.47 new_primPlusNat4(Zero) 130.74/78.47 new_primPlusNat2(Succ(x0)) 130.74/78.47 new_primPlusNat0(Zero, Zero) 130.74/78.47 130.74/78.47 We have to consider all minimal (P,Q,R)-chains. 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (817) TransformationProof (EQUIVALENT) 130.74/78.47 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat2(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))), z11) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.47 130.74/78.47 (new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11),new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11)) 130.74/78.47 130.74/78.47 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (818) 130.74/78.47 Obligation: 130.74/78.47 Q DP problem: 130.74/78.47 The TRS P consists of the following rules: 130.74/78.47 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.47 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.47 130.74/78.47 The TRS R consists of the following rules: 130.74/78.47 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.47 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.47 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.47 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.47 new_primPlusNat2(Zero) -> Zero 130.74/78.47 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.47 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.47 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.47 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.47 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.47 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.47 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.47 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.47 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.47 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.47 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.47 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.47 130.74/78.47 The set Q consists of the following terms: 130.74/78.47 130.74/78.47 new_primPlusNat1(Succ(x0)) 130.74/78.47 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.47 new_primPlusNat1(Zero) 130.74/78.47 new_primPlusNat2(Zero) 130.74/78.47 new_primPlusNat3(Succ(x0)) 130.74/78.47 new_primPlusNat8(Succ(x0), x1) 130.74/78.47 new_primPlusNat6(x0, Succ(x1)) 130.74/78.47 new_primPlusNat0(Succ(x0), Zero) 130.74/78.47 new_primPlusNat6(x0, Zero) 130.74/78.47 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.47 new_primPlusNat4(Succ(x0)) 130.74/78.47 new_primPlusNat8(Zero, x0) 130.74/78.47 new_primPlusNat3(Zero) 130.74/78.47 new_primPlusNat7(x0, Zero) 130.74/78.47 new_primPlusNat7(x0, Succ(x1)) 130.74/78.47 new_primPlusNat4(Zero) 130.74/78.47 new_primPlusNat2(Succ(x0)) 130.74/78.47 new_primPlusNat0(Zero, Zero) 130.74/78.47 130.74/78.47 We have to consider all minimal (P,Q,R)-chains. 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (819) TransformationProof (EQUIVALENT) 130.74/78.47 By instantiating [LPAR04] the rule new_mkVBalBranch3MkVBalBranch121(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, zzz4827, bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Succ(zzz2502000), zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(Succ(zzz4827)), Succ(Succ(zzz2502000)), bb) we obtained the following new rules [LPAR04]: 130.74/78.47 130.74/78.47 (new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11),new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11)) 130.74/78.47 130.74/78.47 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (820) 130.74/78.47 Obligation: 130.74/78.47 Q DP problem: 130.74/78.47 The TRS P consists of the following rules: 130.74/78.47 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.47 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.47 130.74/78.47 The TRS R consists of the following rules: 130.74/78.47 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.47 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.47 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.47 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.47 new_primPlusNat2(Zero) -> Zero 130.74/78.47 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.47 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.47 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.47 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.47 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.47 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.47 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.47 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.47 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.47 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.47 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.47 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.47 130.74/78.47 The set Q consists of the following terms: 130.74/78.47 130.74/78.47 new_primPlusNat1(Succ(x0)) 130.74/78.47 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.47 new_primPlusNat1(Zero) 130.74/78.47 new_primPlusNat2(Zero) 130.74/78.47 new_primPlusNat3(Succ(x0)) 130.74/78.47 new_primPlusNat8(Succ(x0), x1) 130.74/78.47 new_primPlusNat6(x0, Succ(x1)) 130.74/78.47 new_primPlusNat0(Succ(x0), Zero) 130.74/78.47 new_primPlusNat6(x0, Zero) 130.74/78.47 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.47 new_primPlusNat4(Succ(x0)) 130.74/78.47 new_primPlusNat8(Zero, x0) 130.74/78.47 new_primPlusNat3(Zero) 130.74/78.47 new_primPlusNat7(x0, Zero) 130.74/78.47 new_primPlusNat7(x0, Succ(x1)) 130.74/78.47 new_primPlusNat4(Zero) 130.74/78.47 new_primPlusNat2(Succ(x0)) 130.74/78.47 new_primPlusNat0(Zero, Zero) 130.74/78.47 130.74/78.47 We have to consider all minimal (P,Q,R)-chains. 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (821) TransformationProof (EQUIVALENT) 130.74/78.47 By instantiating [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Zero), bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) we obtained the following new rules [LPAR04]: 130.74/78.47 130.74/78.47 (new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11),new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11)) 130.74/78.47 130.74/78.47 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (822) 130.74/78.47 Obligation: 130.74/78.47 Q DP problem: 130.74/78.47 The TRS P consists of the following rules: 130.74/78.47 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.47 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.47 130.74/78.47 The TRS R consists of the following rules: 130.74/78.47 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.47 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.47 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.47 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.47 new_primPlusNat2(Zero) -> Zero 130.74/78.47 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.47 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.47 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.47 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.47 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.47 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.47 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.47 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.47 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.47 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.47 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.47 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.47 130.74/78.47 The set Q consists of the following terms: 130.74/78.47 130.74/78.47 new_primPlusNat1(Succ(x0)) 130.74/78.47 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.47 new_primPlusNat1(Zero) 130.74/78.47 new_primPlusNat2(Zero) 130.74/78.47 new_primPlusNat3(Succ(x0)) 130.74/78.47 new_primPlusNat8(Succ(x0), x1) 130.74/78.47 new_primPlusNat6(x0, Succ(x1)) 130.74/78.47 new_primPlusNat0(Succ(x0), Zero) 130.74/78.47 new_primPlusNat6(x0, Zero) 130.74/78.47 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.47 new_primPlusNat4(Succ(x0)) 130.74/78.47 new_primPlusNat8(Zero, x0) 130.74/78.47 new_primPlusNat3(Zero) 130.74/78.47 new_primPlusNat7(x0, Zero) 130.74/78.47 new_primPlusNat7(x0, Succ(x1)) 130.74/78.47 new_primPlusNat4(Zero) 130.74/78.47 new_primPlusNat2(Succ(x0)) 130.74/78.47 new_primPlusNat0(Zero, Zero) 130.74/78.47 130.74/78.47 We have to consider all minimal (P,Q,R)-chains. 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (823) TransformationProof (EQUIVALENT) 130.74/78.47 By instantiating [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(Succ(zzz3887000)), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) we obtained the following new rules [LPAR04]: 130.74/78.47 130.74/78.47 (new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11),new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11)) 130.74/78.47 130.74/78.47 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (824) 130.74/78.47 Obligation: 130.74/78.47 Q DP problem: 130.74/78.47 The TRS P consists of the following rules: 130.74/78.47 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.47 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.47 130.74/78.47 The TRS R consists of the following rules: 130.74/78.47 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.47 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.47 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.47 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.47 new_primPlusNat2(Zero) -> Zero 130.74/78.47 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.47 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.47 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.47 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.47 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.47 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.47 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.47 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.47 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.47 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.47 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.47 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.47 130.74/78.47 The set Q consists of the following terms: 130.74/78.47 130.74/78.47 new_primPlusNat1(Succ(x0)) 130.74/78.47 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.47 new_primPlusNat1(Zero) 130.74/78.47 new_primPlusNat2(Zero) 130.74/78.47 new_primPlusNat3(Succ(x0)) 130.74/78.47 new_primPlusNat8(Succ(x0), x1) 130.74/78.47 new_primPlusNat6(x0, Succ(x1)) 130.74/78.47 new_primPlusNat0(Succ(x0), Zero) 130.74/78.47 new_primPlusNat6(x0, Zero) 130.74/78.47 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.47 new_primPlusNat4(Succ(x0)) 130.74/78.47 new_primPlusNat8(Zero, x0) 130.74/78.47 new_primPlusNat3(Zero) 130.74/78.47 new_primPlusNat7(x0, Zero) 130.74/78.47 new_primPlusNat7(x0, Succ(x1)) 130.74/78.47 new_primPlusNat4(Zero) 130.74/78.47 new_primPlusNat2(Succ(x0)) 130.74/78.47 new_primPlusNat0(Zero, Zero) 130.74/78.47 130.74/78.47 We have to consider all minimal (P,Q,R)-chains. 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (825) TransformationProof (EQUIVALENT) 130.74/78.47 By instantiating [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz4436, Zero, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) we obtained the following new rules [LPAR04]: 130.74/78.47 130.74/78.47 (new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), z11),new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), z11)) 130.74/78.47 130.74/78.47 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (826) 130.74/78.47 Obligation: 130.74/78.47 Q DP problem: 130.74/78.47 The TRS P consists of the following rules: 130.74/78.47 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.47 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), z11) 130.74/78.47 130.74/78.47 The TRS R consists of the following rules: 130.74/78.47 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.47 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.47 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.47 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.47 new_primPlusNat2(Zero) -> Zero 130.74/78.47 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.47 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.47 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.47 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.47 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.47 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.47 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.47 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.47 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.47 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.47 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.47 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.47 130.74/78.47 The set Q consists of the following terms: 130.74/78.47 130.74/78.47 new_primPlusNat1(Succ(x0)) 130.74/78.47 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.47 new_primPlusNat1(Zero) 130.74/78.47 new_primPlusNat2(Zero) 130.74/78.47 new_primPlusNat3(Succ(x0)) 130.74/78.47 new_primPlusNat8(Succ(x0), x1) 130.74/78.47 new_primPlusNat6(x0, Succ(x1)) 130.74/78.47 new_primPlusNat0(Succ(x0), Zero) 130.74/78.47 new_primPlusNat6(x0, Zero) 130.74/78.47 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.47 new_primPlusNat4(Succ(x0)) 130.74/78.47 new_primPlusNat8(Zero, x0) 130.74/78.47 new_primPlusNat3(Zero) 130.74/78.47 new_primPlusNat7(x0, Zero) 130.74/78.47 new_primPlusNat7(x0, Succ(x1)) 130.74/78.47 new_primPlusNat4(Zero) 130.74/78.47 new_primPlusNat2(Succ(x0)) 130.74/78.47 new_primPlusNat0(Zero, Zero) 130.74/78.47 130.74/78.47 We have to consider all minimal (P,Q,R)-chains. 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (827) TransformationProof (EQUIVALENT) 130.74/78.47 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))))), z11) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.74/78.47 130.74/78.47 (new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))))), z11),new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))))), z11)) 130.74/78.47 130.74/78.47 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (828) 130.74/78.47 Obligation: 130.74/78.47 Q DP problem: 130.74/78.47 The TRS P consists of the following rules: 130.74/78.47 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.47 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))))), z11) 130.74/78.47 130.74/78.47 The TRS R consists of the following rules: 130.74/78.47 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.47 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.47 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.47 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.47 new_primPlusNat2(Zero) -> Zero 130.74/78.47 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.47 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.47 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.47 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.47 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.47 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.47 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.47 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.47 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.47 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.47 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.47 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.47 130.74/78.47 The set Q consists of the following terms: 130.74/78.47 130.74/78.47 new_primPlusNat1(Succ(x0)) 130.74/78.47 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.47 new_primPlusNat1(Zero) 130.74/78.47 new_primPlusNat2(Zero) 130.74/78.47 new_primPlusNat3(Succ(x0)) 130.74/78.47 new_primPlusNat8(Succ(x0), x1) 130.74/78.47 new_primPlusNat6(x0, Succ(x1)) 130.74/78.47 new_primPlusNat0(Succ(x0), Zero) 130.74/78.47 new_primPlusNat6(x0, Zero) 130.74/78.47 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.47 new_primPlusNat4(Succ(x0)) 130.74/78.47 new_primPlusNat8(Zero, x0) 130.74/78.47 new_primPlusNat3(Zero) 130.74/78.47 new_primPlusNat7(x0, Zero) 130.74/78.47 new_primPlusNat7(x0, Succ(x1)) 130.74/78.47 new_primPlusNat4(Zero) 130.74/78.47 new_primPlusNat2(Succ(x0)) 130.74/78.47 new_primPlusNat0(Zero, Zero) 130.74/78.47 130.74/78.47 We have to consider all minimal (P,Q,R)-chains. 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (829) TransformationProof (EQUIVALENT) 130.74/78.47 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))))), z11) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.47 130.74/78.47 (new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))))))), z11),new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))))))), z11)) 130.74/78.47 130.74/78.47 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (830) 130.74/78.47 Obligation: 130.74/78.47 Q DP problem: 130.74/78.47 The TRS P consists of the following rules: 130.74/78.47 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.47 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))))))), z11) 130.74/78.47 130.74/78.47 The TRS R consists of the following rules: 130.74/78.47 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.47 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.47 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.47 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.47 new_primPlusNat2(Zero) -> Zero 130.74/78.47 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.47 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.47 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.47 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.47 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.47 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.47 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.47 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.47 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.47 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.47 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.47 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.47 130.74/78.47 The set Q consists of the following terms: 130.74/78.47 130.74/78.47 new_primPlusNat1(Succ(x0)) 130.74/78.47 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.47 new_primPlusNat1(Zero) 130.74/78.47 new_primPlusNat2(Zero) 130.74/78.47 new_primPlusNat3(Succ(x0)) 130.74/78.47 new_primPlusNat8(Succ(x0), x1) 130.74/78.47 new_primPlusNat6(x0, Succ(x1)) 130.74/78.47 new_primPlusNat0(Succ(x0), Zero) 130.74/78.47 new_primPlusNat6(x0, Zero) 130.74/78.47 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.47 new_primPlusNat4(Succ(x0)) 130.74/78.47 new_primPlusNat8(Zero, x0) 130.74/78.47 new_primPlusNat3(Zero) 130.74/78.47 new_primPlusNat7(x0, Zero) 130.74/78.47 new_primPlusNat7(x0, Succ(x1)) 130.74/78.47 new_primPlusNat4(Zero) 130.74/78.47 new_primPlusNat2(Succ(x0)) 130.74/78.47 new_primPlusNat0(Zero, Zero) 130.74/78.47 130.74/78.47 We have to consider all minimal (P,Q,R)-chains. 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (831) TransformationProof (EQUIVALENT) 130.74/78.47 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))))))), z11) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.47 130.74/78.47 (new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))), z11),new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))), z11)) 130.74/78.47 130.74/78.47 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (832) 130.74/78.47 Obligation: 130.74/78.47 Q DP problem: 130.74/78.47 The TRS P consists of the following rules: 130.74/78.47 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.47 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))), z11) 130.74/78.47 130.74/78.47 The TRS R consists of the following rules: 130.74/78.47 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.47 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.47 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.47 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.47 new_primPlusNat2(Zero) -> Zero 130.74/78.47 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.47 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.47 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.47 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.47 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.47 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.47 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.47 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.47 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.47 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.47 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.47 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.47 130.74/78.47 The set Q consists of the following terms: 130.74/78.47 130.74/78.47 new_primPlusNat1(Succ(x0)) 130.74/78.47 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.47 new_primPlusNat1(Zero) 130.74/78.47 new_primPlusNat2(Zero) 130.74/78.47 new_primPlusNat3(Succ(x0)) 130.74/78.47 new_primPlusNat8(Succ(x0), x1) 130.74/78.47 new_primPlusNat6(x0, Succ(x1)) 130.74/78.47 new_primPlusNat0(Succ(x0), Zero) 130.74/78.47 new_primPlusNat6(x0, Zero) 130.74/78.47 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.47 new_primPlusNat4(Succ(x0)) 130.74/78.47 new_primPlusNat8(Zero, x0) 130.74/78.47 new_primPlusNat3(Zero) 130.74/78.47 new_primPlusNat7(x0, Zero) 130.74/78.47 new_primPlusNat7(x0, Succ(x1)) 130.74/78.47 new_primPlusNat4(Zero) 130.74/78.47 new_primPlusNat2(Succ(x0)) 130.74/78.47 new_primPlusNat0(Zero, Zero) 130.74/78.47 130.74/78.47 We have to consider all minimal (P,Q,R)-chains. 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (833) TransformationProof (EQUIVALENT) 130.74/78.47 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))), z11) at position [11,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.47 130.74/78.47 (new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))), z11),new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))), z11)) 130.74/78.47 130.74/78.47 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (834) 130.74/78.47 Obligation: 130.74/78.47 Q DP problem: 130.74/78.47 The TRS P consists of the following rules: 130.74/78.47 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.47 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))), z11) 130.74/78.47 130.74/78.47 The TRS R consists of the following rules: 130.74/78.47 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.47 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.47 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.47 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.47 new_primPlusNat2(Zero) -> Zero 130.74/78.47 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.47 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.47 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.47 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.47 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.47 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.47 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.47 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.47 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.47 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.47 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.47 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.47 130.74/78.47 The set Q consists of the following terms: 130.74/78.47 130.74/78.47 new_primPlusNat1(Succ(x0)) 130.74/78.47 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.47 new_primPlusNat1(Zero) 130.74/78.47 new_primPlusNat2(Zero) 130.74/78.47 new_primPlusNat3(Succ(x0)) 130.74/78.47 new_primPlusNat8(Succ(x0), x1) 130.74/78.47 new_primPlusNat6(x0, Succ(x1)) 130.74/78.47 new_primPlusNat0(Succ(x0), Zero) 130.74/78.47 new_primPlusNat6(x0, Zero) 130.74/78.47 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.47 new_primPlusNat4(Succ(x0)) 130.74/78.47 new_primPlusNat8(Zero, x0) 130.74/78.47 new_primPlusNat3(Zero) 130.74/78.47 new_primPlusNat7(x0, Zero) 130.74/78.47 new_primPlusNat7(x0, Succ(x1)) 130.74/78.47 new_primPlusNat4(Zero) 130.74/78.47 new_primPlusNat2(Succ(x0)) 130.74/78.47 new_primPlusNat0(Zero, Zero) 130.74/78.47 130.74/78.47 We have to consider all minimal (P,Q,R)-chains. 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (835) TransformationProof (EQUIVALENT) 130.74/78.47 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.47 130.74/78.47 (new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))), z11),new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))), z11)) 130.74/78.47 130.74/78.47 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (836) 130.74/78.47 Obligation: 130.74/78.47 Q DP problem: 130.74/78.47 The TRS P consists of the following rules: 130.74/78.47 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.47 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))), z11) 130.74/78.47 130.74/78.47 The TRS R consists of the following rules: 130.74/78.47 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.47 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.47 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.47 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.47 new_primPlusNat2(Zero) -> Zero 130.74/78.47 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.47 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.47 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.47 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.47 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.47 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.47 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.47 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.47 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.47 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.47 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.47 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.47 130.74/78.47 The set Q consists of the following terms: 130.74/78.47 130.74/78.47 new_primPlusNat1(Succ(x0)) 130.74/78.47 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.47 new_primPlusNat1(Zero) 130.74/78.47 new_primPlusNat2(Zero) 130.74/78.47 new_primPlusNat3(Succ(x0)) 130.74/78.47 new_primPlusNat8(Succ(x0), x1) 130.74/78.47 new_primPlusNat6(x0, Succ(x1)) 130.74/78.47 new_primPlusNat0(Succ(x0), Zero) 130.74/78.47 new_primPlusNat6(x0, Zero) 130.74/78.47 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.47 new_primPlusNat4(Succ(x0)) 130.74/78.47 new_primPlusNat8(Zero, x0) 130.74/78.47 new_primPlusNat3(Zero) 130.74/78.47 new_primPlusNat7(x0, Zero) 130.74/78.47 new_primPlusNat7(x0, Succ(x1)) 130.74/78.47 new_primPlusNat4(Zero) 130.74/78.47 new_primPlusNat2(Succ(x0)) 130.74/78.47 new_primPlusNat0(Zero, Zero) 130.74/78.47 130.74/78.47 We have to consider all minimal (P,Q,R)-chains. 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (837) TransformationProof (EQUIVALENT) 130.74/78.47 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.47 130.74/78.47 (new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))), z11),new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))), z11)) 130.74/78.47 130.74/78.47 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (838) 130.74/78.47 Obligation: 130.74/78.47 Q DP problem: 130.74/78.47 The TRS P consists of the following rules: 130.74/78.47 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.47 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))), z11) 130.74/78.47 130.74/78.47 The TRS R consists of the following rules: 130.74/78.47 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.47 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.47 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.47 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.47 new_primPlusNat2(Zero) -> Zero 130.74/78.47 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.47 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.47 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.47 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.47 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.47 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.47 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.47 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.47 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.47 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.47 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.47 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.47 130.74/78.47 The set Q consists of the following terms: 130.74/78.47 130.74/78.47 new_primPlusNat1(Succ(x0)) 130.74/78.47 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.47 new_primPlusNat1(Zero) 130.74/78.47 new_primPlusNat2(Zero) 130.74/78.47 new_primPlusNat3(Succ(x0)) 130.74/78.47 new_primPlusNat8(Succ(x0), x1) 130.74/78.47 new_primPlusNat6(x0, Succ(x1)) 130.74/78.47 new_primPlusNat0(Succ(x0), Zero) 130.74/78.47 new_primPlusNat6(x0, Zero) 130.74/78.47 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.47 new_primPlusNat4(Succ(x0)) 130.74/78.47 new_primPlusNat8(Zero, x0) 130.74/78.47 new_primPlusNat3(Zero) 130.74/78.47 new_primPlusNat7(x0, Zero) 130.74/78.47 new_primPlusNat7(x0, Succ(x1)) 130.74/78.47 new_primPlusNat4(Zero) 130.74/78.47 new_primPlusNat2(Succ(x0)) 130.74/78.47 new_primPlusNat0(Zero, Zero) 130.74/78.47 130.74/78.47 We have to consider all minimal (P,Q,R)-chains. 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (839) TransformationProof (EQUIVALENT) 130.74/78.47 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))), z11) at position [11,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.47 130.74/78.47 (new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))))))), z11),new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))))))), z11)) 130.74/78.47 130.74/78.47 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (840) 130.74/78.47 Obligation: 130.74/78.47 Q DP problem: 130.74/78.47 The TRS P consists of the following rules: 130.74/78.47 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.47 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))))))), z11) 130.74/78.47 130.74/78.47 The TRS R consists of the following rules: 130.74/78.47 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.47 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.47 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.47 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.47 new_primPlusNat2(Zero) -> Zero 130.74/78.47 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.47 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.47 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.47 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.47 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.47 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.47 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.47 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.47 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.47 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.47 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.47 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.47 130.74/78.47 The set Q consists of the following terms: 130.74/78.47 130.74/78.47 new_primPlusNat1(Succ(x0)) 130.74/78.47 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.47 new_primPlusNat1(Zero) 130.74/78.47 new_primPlusNat2(Zero) 130.74/78.47 new_primPlusNat3(Succ(x0)) 130.74/78.47 new_primPlusNat8(Succ(x0), x1) 130.74/78.47 new_primPlusNat6(x0, Succ(x1)) 130.74/78.47 new_primPlusNat0(Succ(x0), Zero) 130.74/78.47 new_primPlusNat6(x0, Zero) 130.74/78.47 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.47 new_primPlusNat4(Succ(x0)) 130.74/78.47 new_primPlusNat8(Zero, x0) 130.74/78.47 new_primPlusNat3(Zero) 130.74/78.47 new_primPlusNat7(x0, Zero) 130.74/78.47 new_primPlusNat7(x0, Succ(x1)) 130.74/78.47 new_primPlusNat4(Zero) 130.74/78.47 new_primPlusNat2(Succ(x0)) 130.74/78.47 new_primPlusNat0(Zero, Zero) 130.74/78.47 130.74/78.47 We have to consider all minimal (P,Q,R)-chains. 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (841) TransformationProof (EQUIVALENT) 130.74/78.47 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero)))), Succ(Zero)))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.47 130.74/78.47 (new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))))))), z11),new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))))))), z11)) 130.74/78.47 130.74/78.47 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (842) 130.74/78.47 Obligation: 130.74/78.47 Q DP problem: 130.74/78.47 The TRS P consists of the following rules: 130.74/78.47 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.47 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))))))), z11) 130.74/78.47 130.74/78.47 The TRS R consists of the following rules: 130.74/78.47 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.47 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.47 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.47 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.47 new_primPlusNat2(Zero) -> Zero 130.74/78.47 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.47 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.47 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.47 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.47 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.47 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.47 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.47 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.47 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.47 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.47 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.47 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.47 130.74/78.47 The set Q consists of the following terms: 130.74/78.47 130.74/78.47 new_primPlusNat1(Succ(x0)) 130.74/78.47 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.47 new_primPlusNat1(Zero) 130.74/78.47 new_primPlusNat2(Zero) 130.74/78.47 new_primPlusNat3(Succ(x0)) 130.74/78.47 new_primPlusNat8(Succ(x0), x1) 130.74/78.47 new_primPlusNat6(x0, Succ(x1)) 130.74/78.47 new_primPlusNat0(Succ(x0), Zero) 130.74/78.47 new_primPlusNat6(x0, Zero) 130.74/78.47 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.47 new_primPlusNat4(Succ(x0)) 130.74/78.47 new_primPlusNat8(Zero, x0) 130.74/78.47 new_primPlusNat3(Zero) 130.74/78.47 new_primPlusNat7(x0, Zero) 130.74/78.47 new_primPlusNat7(x0, Succ(x1)) 130.74/78.47 new_primPlusNat4(Zero) 130.74/78.47 new_primPlusNat2(Succ(x0)) 130.74/78.47 new_primPlusNat0(Zero, Zero) 130.74/78.47 130.74/78.47 We have to consider all minimal (P,Q,R)-chains. 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (843) TransformationProof (EQUIVALENT) 130.74/78.47 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero)))), Succ(Succ(Zero))), Zero))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.47 130.74/78.47 (new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))))))), z11),new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))))))), z11)) 130.74/78.47 130.74/78.47 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (844) 130.74/78.47 Obligation: 130.74/78.47 Q DP problem: 130.74/78.47 The TRS P consists of the following rules: 130.74/78.47 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.47 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))))))), z11) 130.74/78.47 130.74/78.47 The TRS R consists of the following rules: 130.74/78.47 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.47 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.47 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.47 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.47 new_primPlusNat2(Zero) -> Zero 130.74/78.47 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.47 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.47 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.47 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.47 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.47 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.47 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.47 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.47 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.47 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.47 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.47 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.47 130.74/78.47 The set Q consists of the following terms: 130.74/78.47 130.74/78.47 new_primPlusNat1(Succ(x0)) 130.74/78.47 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.47 new_primPlusNat1(Zero) 130.74/78.47 new_primPlusNat2(Zero) 130.74/78.47 new_primPlusNat3(Succ(x0)) 130.74/78.47 new_primPlusNat8(Succ(x0), x1) 130.74/78.47 new_primPlusNat6(x0, Succ(x1)) 130.74/78.47 new_primPlusNat0(Succ(x0), Zero) 130.74/78.47 new_primPlusNat6(x0, Zero) 130.74/78.47 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.47 new_primPlusNat4(Succ(x0)) 130.74/78.47 new_primPlusNat8(Zero, x0) 130.74/78.47 new_primPlusNat3(Zero) 130.74/78.47 new_primPlusNat7(x0, Zero) 130.74/78.47 new_primPlusNat7(x0, Succ(x1)) 130.74/78.47 new_primPlusNat4(Zero) 130.74/78.47 new_primPlusNat2(Succ(x0)) 130.74/78.47 new_primPlusNat0(Zero, Zero) 130.74/78.47 130.74/78.47 We have to consider all minimal (P,Q,R)-chains. 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (845) TransformationProof (EQUIVALENT) 130.74/78.47 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))))), Succ(Succ(Zero))), Zero))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.47 130.74/78.47 (new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))))))), z11),new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))))))), z11)) 130.74/78.47 130.74/78.47 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (846) 130.74/78.47 Obligation: 130.74/78.47 Q DP problem: 130.74/78.47 The TRS P consists of the following rules: 130.74/78.47 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.47 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))))))), z11) 130.74/78.47 130.74/78.47 The TRS R consists of the following rules: 130.74/78.47 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.47 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.47 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.47 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.47 new_primPlusNat2(Zero) -> Zero 130.74/78.47 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.47 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.47 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.47 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.47 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.47 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.47 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.47 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.47 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.47 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.47 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.47 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.47 130.74/78.47 The set Q consists of the following terms: 130.74/78.47 130.74/78.47 new_primPlusNat1(Succ(x0)) 130.74/78.47 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.47 new_primPlusNat1(Zero) 130.74/78.47 new_primPlusNat2(Zero) 130.74/78.47 new_primPlusNat3(Succ(x0)) 130.74/78.47 new_primPlusNat8(Succ(x0), x1) 130.74/78.47 new_primPlusNat6(x0, Succ(x1)) 130.74/78.47 new_primPlusNat0(Succ(x0), Zero) 130.74/78.47 new_primPlusNat6(x0, Zero) 130.74/78.47 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.47 new_primPlusNat4(Succ(x0)) 130.74/78.47 new_primPlusNat8(Zero, x0) 130.74/78.47 new_primPlusNat3(Zero) 130.74/78.47 new_primPlusNat7(x0, Zero) 130.74/78.47 new_primPlusNat7(x0, Succ(x1)) 130.74/78.47 new_primPlusNat4(Zero) 130.74/78.47 new_primPlusNat2(Succ(x0)) 130.74/78.47 new_primPlusNat0(Zero, Zero) 130.74/78.47 130.74/78.47 We have to consider all minimal (P,Q,R)-chains. 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (847) TransformationProof (EQUIVALENT) 130.74/78.47 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))), Zero))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.47 130.74/78.47 (new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))))))))))))))), z11),new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))))))))))))))), z11)) 130.74/78.47 130.74/78.47 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (848) 130.74/78.47 Obligation: 130.74/78.47 Q DP problem: 130.74/78.47 The TRS P consists of the following rules: 130.74/78.47 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.47 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.47 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))))))))))))))), z11) 130.74/78.47 130.74/78.47 The TRS R consists of the following rules: 130.74/78.47 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.47 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.47 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.47 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.47 new_primPlusNat2(Zero) -> Zero 130.74/78.47 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.47 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.47 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.47 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.47 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.47 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.47 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.47 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.47 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.47 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.47 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.47 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.47 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.47 130.74/78.47 The set Q consists of the following terms: 130.74/78.47 130.74/78.47 new_primPlusNat1(Succ(x0)) 130.74/78.47 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.47 new_primPlusNat1(Zero) 130.74/78.47 new_primPlusNat2(Zero) 130.74/78.47 new_primPlusNat3(Succ(x0)) 130.74/78.47 new_primPlusNat8(Succ(x0), x1) 130.74/78.47 new_primPlusNat6(x0, Succ(x1)) 130.74/78.47 new_primPlusNat0(Succ(x0), Zero) 130.74/78.47 new_primPlusNat6(x0, Zero) 130.74/78.47 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.47 new_primPlusNat4(Succ(x0)) 130.74/78.47 new_primPlusNat8(Zero, x0) 130.74/78.47 new_primPlusNat3(Zero) 130.74/78.47 new_primPlusNat7(x0, Zero) 130.74/78.47 new_primPlusNat7(x0, Succ(x1)) 130.74/78.47 new_primPlusNat4(Zero) 130.74/78.47 new_primPlusNat2(Succ(x0)) 130.74/78.47 new_primPlusNat0(Zero, Zero) 130.74/78.47 130.74/78.47 We have to consider all minimal (P,Q,R)-chains. 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (849) TransformationProof (EQUIVALENT) 130.74/78.47 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero)))), Succ(Zero)))))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.47 130.74/78.47 (new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))), Zero))))))))))))))))), z11),new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))), Zero))))))))))))))))), z11)) 130.74/78.47 130.74/78.47 130.74/78.47 ---------------------------------------- 130.74/78.47 130.74/78.47 (850) 130.74/78.47 Obligation: 130.74/78.47 Q DP problem: 130.74/78.47 The TRS P consists of the following rules: 130.74/78.47 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.47 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.47 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.47 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.48 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))), Zero))))))))))))))))), z11) 130.74/78.48 130.74/78.48 The TRS R consists of the following rules: 130.74/78.48 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.48 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.48 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.48 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.48 new_primPlusNat2(Zero) -> Zero 130.74/78.48 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.48 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.48 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.48 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.48 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.48 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.48 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.48 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.48 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.48 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.48 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.48 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.48 130.74/78.48 The set Q consists of the following terms: 130.74/78.48 130.74/78.48 new_primPlusNat1(Succ(x0)) 130.74/78.48 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.48 new_primPlusNat1(Zero) 130.74/78.48 new_primPlusNat2(Zero) 130.74/78.48 new_primPlusNat3(Succ(x0)) 130.74/78.48 new_primPlusNat8(Succ(x0), x1) 130.74/78.48 new_primPlusNat6(x0, Succ(x1)) 130.74/78.48 new_primPlusNat0(Succ(x0), Zero) 130.74/78.48 new_primPlusNat6(x0, Zero) 130.74/78.48 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.48 new_primPlusNat4(Succ(x0)) 130.74/78.48 new_primPlusNat8(Zero, x0) 130.74/78.48 new_primPlusNat3(Zero) 130.74/78.48 new_primPlusNat7(x0, Zero) 130.74/78.48 new_primPlusNat7(x0, Succ(x1)) 130.74/78.48 new_primPlusNat4(Zero) 130.74/78.48 new_primPlusNat2(Succ(x0)) 130.74/78.48 new_primPlusNat0(Zero, Zero) 130.74/78.48 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (851) TransformationProof (EQUIVALENT) 130.74/78.48 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))), Zero))))))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.48 130.74/78.48 (new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))), Zero))))))))))))))))), z11),new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))), Zero))))))))))))))))), z11)) 130.74/78.48 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (852) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.48 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.48 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))), Zero))))))))))))))))), z11) 130.74/78.48 130.74/78.48 The TRS R consists of the following rules: 130.74/78.48 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.48 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.48 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.48 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.48 new_primPlusNat2(Zero) -> Zero 130.74/78.48 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.48 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.48 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.48 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.48 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.48 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.48 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.48 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.48 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.48 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.48 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.48 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.48 130.74/78.48 The set Q consists of the following terms: 130.74/78.48 130.74/78.48 new_primPlusNat1(Succ(x0)) 130.74/78.48 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.48 new_primPlusNat1(Zero) 130.74/78.48 new_primPlusNat2(Zero) 130.74/78.48 new_primPlusNat3(Succ(x0)) 130.74/78.48 new_primPlusNat8(Succ(x0), x1) 130.74/78.48 new_primPlusNat6(x0, Succ(x1)) 130.74/78.48 new_primPlusNat0(Succ(x0), Zero) 130.74/78.48 new_primPlusNat6(x0, Zero) 130.74/78.48 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.48 new_primPlusNat4(Succ(x0)) 130.74/78.48 new_primPlusNat8(Zero, x0) 130.74/78.48 new_primPlusNat3(Zero) 130.74/78.48 new_primPlusNat7(x0, Zero) 130.74/78.48 new_primPlusNat7(x0, Succ(x1)) 130.74/78.48 new_primPlusNat4(Zero) 130.74/78.48 new_primPlusNat2(Succ(x0)) 130.74/78.48 new_primPlusNat0(Zero, Zero) 130.74/78.48 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (853) TransformationProof (EQUIVALENT) 130.74/78.48 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))), Zero))))))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.48 130.74/78.48 (new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))))))))))), z11),new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))))))))))), z11)) 130.74/78.48 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (854) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.48 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.48 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))))))))))), z11) 130.74/78.48 130.74/78.48 The TRS R consists of the following rules: 130.74/78.48 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.48 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.48 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.48 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.48 new_primPlusNat2(Zero) -> Zero 130.74/78.48 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.48 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.48 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.48 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.48 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.48 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.48 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.48 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.48 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.48 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.48 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.48 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.48 130.74/78.48 The set Q consists of the following terms: 130.74/78.48 130.74/78.48 new_primPlusNat1(Succ(x0)) 130.74/78.48 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.48 new_primPlusNat1(Zero) 130.74/78.48 new_primPlusNat2(Zero) 130.74/78.48 new_primPlusNat3(Succ(x0)) 130.74/78.48 new_primPlusNat8(Succ(x0), x1) 130.74/78.48 new_primPlusNat6(x0, Succ(x1)) 130.74/78.48 new_primPlusNat0(Succ(x0), Zero) 130.74/78.48 new_primPlusNat6(x0, Zero) 130.74/78.48 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.48 new_primPlusNat4(Succ(x0)) 130.74/78.48 new_primPlusNat8(Zero, x0) 130.74/78.48 new_primPlusNat3(Zero) 130.74/78.48 new_primPlusNat7(x0, Zero) 130.74/78.48 new_primPlusNat7(x0, Succ(x1)) 130.74/78.48 new_primPlusNat4(Zero) 130.74/78.48 new_primPlusNat2(Succ(x0)) 130.74/78.48 new_primPlusNat0(Zero, Zero) 130.74/78.48 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (855) TransformationProof (EQUIVALENT) 130.74/78.48 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(Zero), Succ(Zero)))))))))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.48 130.74/78.48 (new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero))))))))))))))))))))), z11),new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero))))))))))))))))))))), z11)) 130.74/78.48 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (856) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.48 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.48 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero))))))))))))))))))))), z11) 130.74/78.48 130.74/78.48 The TRS R consists of the following rules: 130.74/78.48 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.48 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.48 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.48 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.48 new_primPlusNat2(Zero) -> Zero 130.74/78.48 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.48 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.48 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.48 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.48 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.48 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.48 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.48 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.48 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.48 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.48 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.48 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.48 130.74/78.48 The set Q consists of the following terms: 130.74/78.48 130.74/78.48 new_primPlusNat1(Succ(x0)) 130.74/78.48 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.48 new_primPlusNat1(Zero) 130.74/78.48 new_primPlusNat2(Zero) 130.74/78.48 new_primPlusNat3(Succ(x0)) 130.74/78.48 new_primPlusNat8(Succ(x0), x1) 130.74/78.48 new_primPlusNat6(x0, Succ(x1)) 130.74/78.48 new_primPlusNat0(Succ(x0), Zero) 130.74/78.48 new_primPlusNat6(x0, Zero) 130.74/78.48 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.48 new_primPlusNat4(Succ(x0)) 130.74/78.48 new_primPlusNat8(Zero, x0) 130.74/78.48 new_primPlusNat3(Zero) 130.74/78.48 new_primPlusNat7(x0, Zero) 130.74/78.48 new_primPlusNat7(x0, Succ(x1)) 130.74/78.48 new_primPlusNat4(Zero) 130.74/78.48 new_primPlusNat2(Succ(x0)) 130.74/78.48 new_primPlusNat0(Zero, Zero) 130.74/78.48 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (857) TransformationProof (EQUIVALENT) 130.74/78.48 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero))))))))))))))))))))), z11) at position [11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.48 130.74/78.48 (new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z11),new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z11)) 130.74/78.48 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (858) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.48 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.48 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z11) 130.74/78.48 130.74/78.48 The TRS R consists of the following rules: 130.74/78.48 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.48 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.48 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.48 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.48 new_primPlusNat2(Zero) -> Zero 130.74/78.48 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.48 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.48 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.48 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.48 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.48 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.48 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.48 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.48 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.48 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.48 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.48 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.48 130.74/78.48 The set Q consists of the following terms: 130.74/78.48 130.74/78.48 new_primPlusNat1(Succ(x0)) 130.74/78.48 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.48 new_primPlusNat1(Zero) 130.74/78.48 new_primPlusNat2(Zero) 130.74/78.48 new_primPlusNat3(Succ(x0)) 130.74/78.48 new_primPlusNat8(Succ(x0), x1) 130.74/78.48 new_primPlusNat6(x0, Succ(x1)) 130.74/78.48 new_primPlusNat0(Succ(x0), Zero) 130.74/78.48 new_primPlusNat6(x0, Zero) 130.74/78.48 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.48 new_primPlusNat4(Succ(x0)) 130.74/78.48 new_primPlusNat8(Zero, x0) 130.74/78.48 new_primPlusNat3(Zero) 130.74/78.48 new_primPlusNat7(x0, Zero) 130.74/78.48 new_primPlusNat7(x0, Succ(x1)) 130.74/78.48 new_primPlusNat4(Zero) 130.74/78.48 new_primPlusNat2(Succ(x0)) 130.74/78.48 new_primPlusNat0(Zero, Zero) 130.74/78.48 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (859) TransformationProof (EQUIVALENT) 130.74/78.48 By instantiating [LPAR04] the rule new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Zero)), zzz343, zzz344, zzz300, zzz31, Succ(zzz48090), Succ(Zero), bb) we obtained the following new rules [LPAR04]: 130.74/78.48 130.74/78.48 (new_mkVBalBranch3MkVBalBranch116(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Zero)), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Zero), z10),new_mkVBalBranch3MkVBalBranch116(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Zero)), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Zero), z10)) 130.74/78.48 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (860) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.48 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.48 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch116(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Zero)), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Zero), z10) 130.74/78.48 130.74/78.48 The TRS R consists of the following rules: 130.74/78.48 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.48 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.48 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.48 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.48 new_primPlusNat2(Zero) -> Zero 130.74/78.48 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.48 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.48 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.48 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.48 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.48 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.48 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.48 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.48 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.48 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.48 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.48 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.48 130.74/78.48 The set Q consists of the following terms: 130.74/78.48 130.74/78.48 new_primPlusNat1(Succ(x0)) 130.74/78.48 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.48 new_primPlusNat1(Zero) 130.74/78.48 new_primPlusNat2(Zero) 130.74/78.48 new_primPlusNat3(Succ(x0)) 130.74/78.48 new_primPlusNat8(Succ(x0), x1) 130.74/78.48 new_primPlusNat6(x0, Succ(x1)) 130.74/78.48 new_primPlusNat0(Succ(x0), Zero) 130.74/78.48 new_primPlusNat6(x0, Zero) 130.74/78.48 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.48 new_primPlusNat4(Succ(x0)) 130.74/78.48 new_primPlusNat8(Zero, x0) 130.74/78.48 new_primPlusNat3(Zero) 130.74/78.48 new_primPlusNat7(x0, Zero) 130.74/78.48 new_primPlusNat7(x0, Succ(x1)) 130.74/78.48 new_primPlusNat4(Zero) 130.74/78.48 new_primPlusNat2(Succ(x0)) 130.74/78.48 new_primPlusNat0(Zero, Zero) 130.74/78.48 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (861) TransformationProof (EQUIVALENT) 130.74/78.48 By instantiating [LPAR04] the rule new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Zero)))), zzz343, zzz344, zzz300, zzz31, Succ(zzz49610), Succ(Zero), bb) we obtained the following new rules [LPAR04]: 130.74/78.48 130.74/78.48 (new_mkVBalBranch3MkVBalBranch114(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), Succ(Zero), z10),new_mkVBalBranch3MkVBalBranch114(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), Succ(Zero), z10)) 130.74/78.48 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (862) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.48 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.48 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch116(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Zero)), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Zero), z10) 130.74/78.48 new_mkVBalBranch3MkVBalBranch114(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), Succ(Zero), z10) 130.74/78.48 130.74/78.48 The TRS R consists of the following rules: 130.74/78.48 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.48 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.48 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.48 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.48 new_primPlusNat2(Zero) -> Zero 130.74/78.48 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.48 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.48 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.48 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.48 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.48 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.48 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.48 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.48 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.48 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.48 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.48 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.48 130.74/78.48 The set Q consists of the following terms: 130.74/78.48 130.74/78.48 new_primPlusNat1(Succ(x0)) 130.74/78.48 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.48 new_primPlusNat1(Zero) 130.74/78.48 new_primPlusNat2(Zero) 130.74/78.48 new_primPlusNat3(Succ(x0)) 130.74/78.48 new_primPlusNat8(Succ(x0), x1) 130.74/78.48 new_primPlusNat6(x0, Succ(x1)) 130.74/78.48 new_primPlusNat0(Succ(x0), Zero) 130.74/78.48 new_primPlusNat6(x0, Zero) 130.74/78.48 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.48 new_primPlusNat4(Succ(x0)) 130.74/78.48 new_primPlusNat8(Zero, x0) 130.74/78.48 new_primPlusNat3(Zero) 130.74/78.48 new_primPlusNat7(x0, Zero) 130.74/78.48 new_primPlusNat7(x0, Succ(x1)) 130.74/78.48 new_primPlusNat4(Zero) 130.74/78.48 new_primPlusNat2(Succ(x0)) 130.74/78.48 new_primPlusNat0(Zero, Zero) 130.74/78.48 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (863) TransformationProof (EQUIVALENT) 130.74/78.48 By instantiating [LPAR04] the rule new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), bb) -> new_mkVBalBranch3MkVBalBranch111(zzz2500, zzz2501, Zero, zzz2503, zzz2504, zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz300, zzz31, Succ(zzz47190), Succ(Zero), bb) we obtained the following new rules [LPAR04]: 130.74/78.48 130.74/78.48 (new_mkVBalBranch3MkVBalBranch117(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Zero), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Zero), z10),new_mkVBalBranch3MkVBalBranch117(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Zero), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Zero), z10)) 130.74/78.48 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (864) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.48 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.48 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch116(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Zero)), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Zero), z10) 130.74/78.48 new_mkVBalBranch3MkVBalBranch114(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), Succ(Zero), z10) 130.74/78.48 new_mkVBalBranch3MkVBalBranch117(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Zero), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Zero), z10) 130.74/78.48 130.74/78.48 The TRS R consists of the following rules: 130.74/78.48 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.48 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.48 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.48 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.48 new_primPlusNat2(Zero) -> Zero 130.74/78.48 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.48 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.48 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.48 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.48 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.48 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.48 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.48 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.48 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.48 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.48 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.48 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.48 130.74/78.48 The set Q consists of the following terms: 130.74/78.48 130.74/78.48 new_primPlusNat1(Succ(x0)) 130.74/78.48 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.48 new_primPlusNat1(Zero) 130.74/78.48 new_primPlusNat2(Zero) 130.74/78.48 new_primPlusNat3(Succ(x0)) 130.74/78.48 new_primPlusNat8(Succ(x0), x1) 130.74/78.48 new_primPlusNat6(x0, Succ(x1)) 130.74/78.48 new_primPlusNat0(Succ(x0), Zero) 130.74/78.48 new_primPlusNat6(x0, Zero) 130.74/78.48 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.48 new_primPlusNat4(Succ(x0)) 130.74/78.48 new_primPlusNat8(Zero, x0) 130.74/78.48 new_primPlusNat3(Zero) 130.74/78.48 new_primPlusNat7(x0, Zero) 130.74/78.48 new_primPlusNat7(x0, Succ(x1)) 130.74/78.48 new_primPlusNat4(Zero) 130.74/78.48 new_primPlusNat2(Succ(x0)) 130.74/78.48 new_primPlusNat0(Zero, Zero) 130.74/78.48 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (865) QDPOrderProof (EQUIVALENT) 130.74/78.48 We use the reduction pair processor [LPAR04,JAR06]. 130.74/78.48 130.74/78.48 130.74/78.48 The following pairs can be oriented strictly and are deleted. 130.74/78.48 130.74/78.48 new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), h) -> new_mkVBalBranch3MkVBalBranch111(zzz4701, zzz4702, Succ(Succ(zzz4703)), zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz49560), Succ(Succ(Succ(zzz4703))), h) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(zzz250200)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch118(zzz2500, zzz2501, zzz250200, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch112(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch117(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Zero)))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch116(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Zero))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch115(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch114(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch113(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Succ(z4), z5, z6, z7, z8, Succ(Zero), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Succ(z4)), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Zero, z11) -> new_mkVBalBranch3MkVBalBranch120(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z11) 130.74/78.48 The remaining pairs can at least be oriented weakly. 130.74/78.48 Used ordering: Polynomial interpretation [POLO]: 130.74/78.48 130.74/78.48 POL(Branch(x_1, x_2, x_3, x_4, x_5)) = 1 + x_1 + x_2 + x_4 + x_5 130.74/78.48 POL(Pos(x_1)) = 0 130.74/78.48 POL(Succ(x_1)) = 0 130.74/78.48 POL(Zero) = 0 130.74/78.48 POL(new_mkVBalBranch3MkVBalBranch110(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13, x_14)) = 1 + x_1 + x_2 + x_4 + x_5 130.74/78.48 POL(new_mkVBalBranch3MkVBalBranch111(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13, x_14, x_15)) = x_5 130.74/78.48 POL(new_mkVBalBranch3MkVBalBranch112(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13)) = x_1 + x_2 + x_4 + x_5 130.74/78.48 POL(new_mkVBalBranch3MkVBalBranch113(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13)) = 1 + x_4 + x_5 130.74/78.48 POL(new_mkVBalBranch3MkVBalBranch114(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12)) = x_1 + x_2 + x_3 + x_4 130.74/78.48 POL(new_mkVBalBranch3MkVBalBranch115(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12)) = x_2 + x_3 + x_4 130.74/78.48 POL(new_mkVBalBranch3MkVBalBranch116(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12)) = x_3 + x_4 130.74/78.48 POL(new_mkVBalBranch3MkVBalBranch117(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12)) = x_1 + x_4 130.74/78.48 POL(new_mkVBalBranch3MkVBalBranch118(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13)) = x_5 130.74/78.48 POL(new_mkVBalBranch3MkVBalBranch120(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13)) = x_1 + x_2 + x_3 + x_4 130.74/78.48 POL(new_mkVBalBranch3MkVBalBranch121(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13)) = x_1 + x_2 + x_4 + x_5 130.74/78.48 POL(new_mkVBalBranch3MkVBalBranch210(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12)) = 1 + x_1 + x_2 + x_3 + x_4 130.74/78.48 POL(new_mkVBalBranch3MkVBalBranch214(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13, x_14)) = 1 + x_1 + x_2 + x_3 + x_4 130.74/78.48 POL(new_mkVBalBranch3MkVBalBranch215(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12)) = 1 + x_1 + x_2 + x_3 + x_4 130.74/78.48 POL(new_mkVBalBranch3MkVBalBranch216(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12)) = x_1 + x_2 + x_3 + x_4 130.74/78.48 POL(new_mkVBalBranch3MkVBalBranch27(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13, x_14, x_15)) = 1 + x_1 + x_2 + x_4 + x_5 130.74/78.48 POL(new_mkVBalBranch3MkVBalBranch28(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13)) = 1 + x_1 + x_2 + x_4 + x_5 130.74/78.48 POL(new_mkVBalBranch3MkVBalBranch29(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13, x_14)) = 1 + x_1 + x_2 + x_3 + x_4 130.74/78.48 POL(new_mkVBalBranch4(x_1, x_2, x_3, x_4, x_5)) = x_3 130.74/78.48 POL(new_primPlusNat0(x_1, x_2)) = 0 130.74/78.48 POL(new_primPlusNat1(x_1)) = 0 130.74/78.48 POL(new_primPlusNat2(x_1)) = 1 + x_1 130.74/78.48 POL(new_primPlusNat3(x_1)) = 0 130.74/78.48 POL(new_primPlusNat4(x_1)) = 0 130.74/78.48 POL(new_primPlusNat6(x_1, x_2)) = x_1 130.74/78.48 POL(new_primPlusNat7(x_1, x_2)) = x_1 130.74/78.48 POL(new_primPlusNat8(x_1, x_2)) = x_2 130.74/78.48 130.74/78.48 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 130.74/78.48 none 130.74/78.48 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (866) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.48 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Zero, Succ(zzz60330), ba) -> new_mkVBalBranch4(zzz6030, zzz6031, zzz6024, Branch(zzz6025, zzz6026, Pos(Succ(zzz6027)), zzz6028, zzz6029), ba) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Zero, h) -> new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch28(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Zero, h) -> new_mkVBalBranch3MkVBalBranch110(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz4708, zzz4708)), zzz4708)), zzz4708)), zzz4708))), h) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), bc) -> new_mkVBalBranch3MkVBalBranch111(zzz3876, zzz3877, Succ(Zero), zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz49580), Succ(Succ(Zero)), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Zero, bc) -> new_mkVBalBranch3MkVBalBranch215(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch216(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, bc) -> new_mkVBalBranch3MkVBalBranch120(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz3882, zzz3882)), zzz3882)), zzz3882)), zzz3882))), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(zzz2502000))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Zero))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch113(zzz2500, zzz2501, zzz2502000, zzz2503, zzz2504, zzz340, zzz341, zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch115(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Zero))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))), Succ(Zero), z10) 130.74/78.48 new_mkVBalBranch3MkVBalBranch118(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch112(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch121(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch121(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))), z11) -> new_mkVBalBranch3MkVBalBranch111(z0, z1, Succ(z2), z3, z4, z5, z6, Succ(Succ(Zero)), z7, z8, z9, z10, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Succ(z2)), z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Zero), z11) -> new_mkVBalBranch3MkVBalBranch215(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z9, z10, z0, z1, z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch116(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Zero)), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))), Succ(Zero), z10) 130.74/78.48 new_mkVBalBranch3MkVBalBranch114(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Zero)))), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))), Succ(Zero), z10) 130.74/78.48 new_mkVBalBranch3MkVBalBranch117(z2, z3, z4, z5, z6, z7, z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), z10) -> new_mkVBalBranch3MkVBalBranch111(z2, z3, Zero, z4, z5, z6, z7, Succ(Zero), z8, z9, z0, z1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), Succ(Zero), z10) 130.74/78.48 130.74/78.48 The TRS R consists of the following rules: 130.74/78.48 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.48 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.48 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.48 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.48 new_primPlusNat2(Zero) -> Zero 130.74/78.48 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.48 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.48 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.48 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.48 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.48 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.48 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.48 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.48 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.48 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.48 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.48 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.48 130.74/78.48 The set Q consists of the following terms: 130.74/78.48 130.74/78.48 new_primPlusNat1(Succ(x0)) 130.74/78.48 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.48 new_primPlusNat1(Zero) 130.74/78.48 new_primPlusNat2(Zero) 130.74/78.48 new_primPlusNat3(Succ(x0)) 130.74/78.48 new_primPlusNat8(Succ(x0), x1) 130.74/78.48 new_primPlusNat6(x0, Succ(x1)) 130.74/78.48 new_primPlusNat0(Succ(x0), Zero) 130.74/78.48 new_primPlusNat6(x0, Zero) 130.74/78.48 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.48 new_primPlusNat4(Succ(x0)) 130.74/78.48 new_primPlusNat8(Zero, x0) 130.74/78.48 new_primPlusNat3(Zero) 130.74/78.48 new_primPlusNat7(x0, Zero) 130.74/78.48 new_primPlusNat7(x0, Succ(x1)) 130.74/78.48 new_primPlusNat4(Zero) 130.74/78.48 new_primPlusNat2(Succ(x0)) 130.74/78.48 new_primPlusNat0(Zero, Zero) 130.74/78.48 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (867) DependencyGraphProof (EQUIVALENT) 130.74/78.48 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 4 SCCs with 16 less nodes. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (868) 130.74/78.48 Complex Obligation (AND) 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (869) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.48 130.74/78.48 The TRS R consists of the following rules: 130.74/78.48 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.48 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.48 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.48 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.48 new_primPlusNat2(Zero) -> Zero 130.74/78.48 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.48 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.48 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.48 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.48 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.48 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.48 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.48 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.48 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.48 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.48 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.48 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.48 130.74/78.48 The set Q consists of the following terms: 130.74/78.48 130.74/78.48 new_primPlusNat1(Succ(x0)) 130.74/78.48 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.48 new_primPlusNat1(Zero) 130.74/78.48 new_primPlusNat2(Zero) 130.74/78.48 new_primPlusNat3(Succ(x0)) 130.74/78.48 new_primPlusNat8(Succ(x0), x1) 130.74/78.48 new_primPlusNat6(x0, Succ(x1)) 130.74/78.48 new_primPlusNat0(Succ(x0), Zero) 130.74/78.48 new_primPlusNat6(x0, Zero) 130.74/78.48 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.48 new_primPlusNat4(Succ(x0)) 130.74/78.48 new_primPlusNat8(Zero, x0) 130.74/78.48 new_primPlusNat3(Zero) 130.74/78.48 new_primPlusNat7(x0, Zero) 130.74/78.48 new_primPlusNat7(x0, Succ(x1)) 130.74/78.48 new_primPlusNat4(Zero) 130.74/78.48 new_primPlusNat2(Succ(x0)) 130.74/78.48 new_primPlusNat0(Zero, Zero) 130.74/78.48 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (870) QDPSizeChangeProof (EQUIVALENT) 130.74/78.48 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. 130.74/78.48 130.74/78.48 From the DPs we obtained the following set of size-change graphs: 130.74/78.48 *new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Succ(zzz44360), Succ(zzz3887000), bc) -> new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, zzz44360, zzz3887000, bc) 130.74/78.48 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 > 12, 13 > 13, 14 >= 14 130.74/78.48 130.74/78.48 130.74/78.48 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Zero))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch29(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), zzz34200000, bb) 130.74/78.48 The graph contains the following edges 3 > 1, 3 > 2, 3 > 3, 3 > 4, 4 > 5, 4 > 6, 4 > 7, 4 > 8, 4 > 9, 1 >= 10, 2 >= 11, 4 > 13, 5 >= 14 130.74/78.48 130.74/78.48 130.74/78.48 *new_mkVBalBranch3MkVBalBranch214(zzz3876, zzz3877, zzz3878, zzz3879, zzz3880, zzz3881, zzz3882, zzz3883, zzz3884, zzz3885, zzz3886, Zero, Succ(zzz3887000), bc) -> new_mkVBalBranch4(zzz3885, zzz3886, Branch(zzz3876, zzz3877, Pos(Succ(Succ(Zero))), zzz3878, zzz3879), zzz3883, bc) 130.74/78.48 The graph contains the following edges 10 >= 1, 11 >= 2, 8 >= 4, 14 >= 5 130.74/78.48 130.74/78.48 130.74/78.48 *new_mkVBalBranch3MkVBalBranch29(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(Succ(x12)), z11) -> new_mkVBalBranch3MkVBalBranch214(z2, z3, z4, z5, z6, z7, Succ(Succ(Succ(Succ(Succ(x12))))), z9, z10, z0, z1, Succ(Succ(Succ(Succ(Zero)))), x12, z11) 130.74/78.48 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 > 12, 7 > 13, 13 > 13, 14 >= 14 130.74/78.48 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (871) 130.74/78.48 YES 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (872) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.48 130.74/78.48 The TRS R consists of the following rules: 130.74/78.48 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.48 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.48 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.48 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.48 new_primPlusNat2(Zero) -> Zero 130.74/78.48 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.48 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.48 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.48 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.48 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.48 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.48 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.48 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.48 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.48 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.48 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.48 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.48 130.74/78.48 The set Q consists of the following terms: 130.74/78.48 130.74/78.48 new_primPlusNat1(Succ(x0)) 130.74/78.48 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.48 new_primPlusNat1(Zero) 130.74/78.48 new_primPlusNat2(Zero) 130.74/78.48 new_primPlusNat3(Succ(x0)) 130.74/78.48 new_primPlusNat8(Succ(x0), x1) 130.74/78.48 new_primPlusNat6(x0, Succ(x1)) 130.74/78.48 new_primPlusNat0(Succ(x0), Zero) 130.74/78.48 new_primPlusNat6(x0, Zero) 130.74/78.48 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.48 new_primPlusNat4(Succ(x0)) 130.74/78.48 new_primPlusNat8(Zero, x0) 130.74/78.48 new_primPlusNat3(Zero) 130.74/78.48 new_primPlusNat7(x0, Zero) 130.74/78.48 new_primPlusNat7(x0, Succ(x1)) 130.74/78.48 new_primPlusNat4(Zero) 130.74/78.48 new_primPlusNat2(Succ(x0)) 130.74/78.48 new_primPlusNat0(Zero, Zero) 130.74/78.48 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (873) QDPSizeChangeProof (EQUIVALENT) 130.74/78.48 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. 130.74/78.48 130.74/78.48 From the DPs we obtained the following set of size-change graphs: 130.74/78.48 *new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Succ(zzz47130), Succ(zzz47140), h) -> new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, zzz47130, zzz47140, h) 130.74/78.48 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 > 13, 14 > 14, 15 >= 15 130.74/78.48 130.74/78.48 130.74/78.48 *new_mkVBalBranch3MkVBalBranch27(zzz4701, zzz4702, zzz4703, zzz4704, zzz4705, zzz4706, zzz4707, zzz4708, zzz4709, zzz4710, zzz4711, zzz4712, Zero, Succ(zzz47140), h) -> new_mkVBalBranch4(zzz4711, zzz4712, Branch(zzz4701, zzz4702, Pos(Succ(Succ(Succ(zzz4703)))), zzz4704, zzz4705), zzz4709, h) 130.74/78.48 The graph contains the following edges 11 >= 1, 12 >= 2, 9 >= 4, 15 >= 5 130.74/78.48 130.74/78.48 130.74/78.48 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Succ(Succ(zzz25020000)))), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(zzz34200000))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch27(zzz2500, zzz2501, zzz25020000, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(zzz34200000))), zzz343, zzz344, zzz300, zzz31, Succ(Succ(new_primPlusNat1(zzz25020000))), zzz34200000, bb) 130.74/78.48 The graph contains the following edges 3 > 1, 3 > 2, 3 > 3, 3 > 4, 3 > 5, 4 > 6, 4 > 7, 4 > 8, 4 > 9, 4 > 10, 1 >= 11, 2 >= 12, 4 > 14, 5 >= 15 130.74/78.48 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (874) 130.74/78.48 YES 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (875) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.48 new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.48 130.74/78.48 The TRS R consists of the following rules: 130.74/78.48 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.48 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.48 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.48 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.48 new_primPlusNat2(Zero) -> Zero 130.74/78.48 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.48 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.48 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.48 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.48 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.48 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.48 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.48 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.48 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.48 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.48 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.48 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.48 130.74/78.48 The set Q consists of the following terms: 130.74/78.48 130.74/78.48 new_primPlusNat1(Succ(x0)) 130.74/78.48 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.48 new_primPlusNat1(Zero) 130.74/78.48 new_primPlusNat2(Zero) 130.74/78.48 new_primPlusNat3(Succ(x0)) 130.74/78.48 new_primPlusNat8(Succ(x0), x1) 130.74/78.48 new_primPlusNat6(x0, Succ(x1)) 130.74/78.48 new_primPlusNat0(Succ(x0), Zero) 130.74/78.48 new_primPlusNat6(x0, Zero) 130.74/78.48 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.48 new_primPlusNat4(Succ(x0)) 130.74/78.48 new_primPlusNat8(Zero, x0) 130.74/78.48 new_primPlusNat3(Zero) 130.74/78.48 new_primPlusNat7(x0, Zero) 130.74/78.48 new_primPlusNat7(x0, Succ(x1)) 130.74/78.48 new_primPlusNat4(Zero) 130.74/78.48 new_primPlusNat2(Succ(x0)) 130.74/78.48 new_primPlusNat0(Zero, Zero) 130.74/78.48 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (876) QDPSizeChangeProof (EQUIVALENT) 130.74/78.48 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. 130.74/78.48 130.74/78.48 From the DPs we obtained the following set of size-change graphs: 130.74/78.48 *new_mkVBalBranch4(zzz300, zzz31, Branch(zzz2500, zzz2501, Pos(Succ(Zero)), zzz2503, zzz2504), Branch(zzz340, zzz341, Pos(Succ(Succ(Succ(Succ(Succ(Succ(zzz3420000000))))))), zzz343, zzz344), bb) -> new_mkVBalBranch3MkVBalBranch210(zzz2500, zzz2501, zzz2503, zzz2504, zzz340, zzz341, Succ(Succ(Succ(Succ(Succ(zzz3420000000))))), zzz343, zzz344, zzz300, zzz31, bb) 130.74/78.48 The graph contains the following edges 3 > 1, 3 > 2, 3 > 3, 3 > 4, 4 > 5, 4 > 6, 4 > 7, 4 > 8, 4 > 9, 1 >= 10, 2 >= 11, 5 >= 12 130.74/78.48 130.74/78.48 130.74/78.48 *new_mkVBalBranch3MkVBalBranch210(zzz3889, zzz3890, zzz3891, zzz3892, zzz3893, zzz3894, zzz3895, zzz3896, zzz3897, zzz3898, zzz3899, bd) -> new_mkVBalBranch4(zzz3898, zzz3899, Branch(zzz3889, zzz3890, Pos(Succ(Zero)), zzz3891, zzz3892), zzz3896, bd) 130.74/78.48 The graph contains the following edges 10 >= 1, 11 >= 2, 8 >= 4, 12 >= 5 130.74/78.48 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (877) 130.74/78.48 YES 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (878) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.48 130.74/78.48 The TRS R consists of the following rules: 130.74/78.48 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.48 new_primPlusNat4(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat3(zzz37520))) 130.74/78.48 new_primPlusNat3(Succ(zzz37520)) -> Succ(Succ(new_primPlusNat2(zzz37520))) 130.74/78.48 new_primPlusNat3(Zero) -> Succ(Zero) 130.74/78.48 new_primPlusNat2(Zero) -> Zero 130.74/78.48 new_primPlusNat2(Succ(zzz375200)) -> Succ(zzz375200) 130.74/78.48 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.48 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.48 new_primPlusNat4(Zero) -> Succ(Succ(Zero)) 130.74/78.48 new_primPlusNat1(Succ(zzz6200000)) -> Succ(Succ(new_primPlusNat6(Succ(Succ(Succ(Succ(Succ(new_primPlusNat6(Succ(zzz6200000), zzz6200000)))))), zzz6200000))) 130.74/78.48 new_primPlusNat1(Zero) -> Succ(Succ(Succ(Succ(new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(Zero))))))))) 130.74/78.48 new_primPlusNat6(zzz3752, Zero) -> Succ(Succ(new_primPlusNat3(zzz3752))) 130.74/78.48 new_primPlusNat6(zzz3752, Succ(zzz37530)) -> Succ(Succ(new_primPlusNat7(zzz3752, zzz37530))) 130.74/78.48 new_primPlusNat7(zzz3752, Succ(zzz375300)) -> Succ(Succ(new_primPlusNat8(zzz3752, zzz375300))) 130.74/78.48 new_primPlusNat7(zzz3752, Zero) -> Succ(new_primPlusNat4(zzz3752)) 130.74/78.48 new_primPlusNat8(Succ(zzz37520), zzz375300) -> new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz37520, Succ(Succ(zzz375300))))), zzz375300) 130.74/78.48 new_primPlusNat8(Zero, zzz375300) -> new_primPlusNat0(Succ(Succ(Succ(zzz375300))), zzz375300) 130.74/78.48 130.74/78.48 The set Q consists of the following terms: 130.74/78.48 130.74/78.48 new_primPlusNat1(Succ(x0)) 130.74/78.48 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.48 new_primPlusNat1(Zero) 130.74/78.48 new_primPlusNat2(Zero) 130.74/78.48 new_primPlusNat3(Succ(x0)) 130.74/78.48 new_primPlusNat8(Succ(x0), x1) 130.74/78.48 new_primPlusNat6(x0, Succ(x1)) 130.74/78.48 new_primPlusNat0(Succ(x0), Zero) 130.74/78.48 new_primPlusNat6(x0, Zero) 130.74/78.48 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.48 new_primPlusNat4(Succ(x0)) 130.74/78.48 new_primPlusNat8(Zero, x0) 130.74/78.48 new_primPlusNat3(Zero) 130.74/78.48 new_primPlusNat7(x0, Zero) 130.74/78.48 new_primPlusNat7(x0, Succ(x1)) 130.74/78.48 new_primPlusNat4(Zero) 130.74/78.48 new_primPlusNat2(Succ(x0)) 130.74/78.48 new_primPlusNat0(Zero, Zero) 130.74/78.48 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (879) QDPSizeChangeProof (EQUIVALENT) 130.74/78.48 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. 130.74/78.48 130.74/78.48 From the DPs we obtained the following set of size-change graphs: 130.74/78.48 *new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, Succ(zzz60320), Succ(zzz60330), ba) -> new_mkVBalBranch3MkVBalBranch111(zzz6020, zzz6021, zzz6022, zzz6023, zzz6024, zzz6025, zzz6026, zzz6027, zzz6028, zzz6029, zzz6030, zzz6031, zzz60320, zzz60330, ba) 130.74/78.48 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 > 13, 14 > 14, 15 >= 15 130.74/78.48 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (880) 130.74/78.48 YES 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (881) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_glueBal2Mid_key10(zzz6411, zzz6412, zzz6413, zzz6414, zzz6415, zzz6416, zzz6417, zzz6418, zzz6419, zzz6420, zzz6421, zzz6422, zzz6423, zzz6424, Branch(zzz64250, zzz64251, zzz64252, zzz64253, zzz64254), h, ba) -> new_glueBal2Mid_key10(zzz6411, zzz6412, zzz6413, zzz6414, zzz6415, zzz6416, zzz6417, zzz6418, zzz6419, zzz6420, zzz64250, zzz64251, zzz64252, zzz64253, zzz64254, h, ba) 130.74/78.48 130.74/78.48 R is empty. 130.74/78.48 Q is empty. 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (882) QDPSizeChangeProof (EQUIVALENT) 130.74/78.48 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. 130.74/78.48 130.74/78.48 From the DPs we obtained the following set of size-change graphs: 130.74/78.48 *new_glueBal2Mid_key10(zzz6411, zzz6412, zzz6413, zzz6414, zzz6415, zzz6416, zzz6417, zzz6418, zzz6419, zzz6420, zzz6421, zzz6422, zzz6423, zzz6424, Branch(zzz64250, zzz64251, zzz64252, zzz64253, zzz64254), h, ba) -> new_glueBal2Mid_key10(zzz6411, zzz6412, zzz6413, zzz6414, zzz6415, zzz6416, zzz6417, zzz6418, zzz6419, zzz6420, zzz64250, zzz64251, zzz64252, zzz64253, zzz64254, h, ba) 130.74/78.48 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 15 > 11, 15 > 12, 15 > 13, 15 > 14, 15 > 15, 16 >= 16, 17 >= 17 130.74/78.48 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (883) 130.74/78.48 YES 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (884) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch1(zzz31, Branch(zzz3530, zzz3531, Pos(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) -> new_mkVBalBranch1(zzz31, zzz3534, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) 130.74/78.48 new_mkVBalBranch1(zzz31, Branch(zzz3530, zzz3531, Pos(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) -> new_mkVBalBranch1(zzz31, zzz3534, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) 130.74/78.48 130.74/78.48 R is empty. 130.74/78.48 Q is empty. 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (885) DependencyGraphProof (EQUIVALENT) 130.74/78.48 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (886) 130.74/78.48 Complex Obligation (AND) 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (887) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch1(zzz31, Branch(zzz3530, zzz3531, Pos(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) -> new_mkVBalBranch1(zzz31, zzz3534, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) 130.74/78.48 130.74/78.48 R is empty. 130.74/78.48 Q is empty. 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (888) QDPSizeChangeProof (EQUIVALENT) 130.74/78.48 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. 130.74/78.48 130.74/78.48 From the DPs we obtained the following set of size-change graphs: 130.74/78.48 *new_mkVBalBranch1(zzz31, Branch(zzz3530, zzz3531, Pos(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) -> new_mkVBalBranch1(zzz31, zzz3534, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) 130.74/78.48 The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4 130.74/78.48 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (889) 130.74/78.48 YES 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (890) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch1(zzz31, Branch(zzz3530, zzz3531, Pos(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) -> new_mkVBalBranch1(zzz31, zzz3534, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) 130.74/78.48 130.74/78.48 R is empty. 130.74/78.48 Q is empty. 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (891) QDPSizeChangeProof (EQUIVALENT) 130.74/78.48 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. 130.74/78.48 130.74/78.48 From the DPs we obtained the following set of size-change graphs: 130.74/78.48 *new_mkVBalBranch1(zzz31, Branch(zzz3530, zzz3531, Pos(Succ(zzz353200)), zzz3533, zzz3534), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) -> new_mkVBalBranch1(zzz31, zzz3534, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) 130.74/78.48 The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4 130.74/78.48 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (892) 130.74/78.48 YES 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (893) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Zero, bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.48 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(zzz523200)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(zzz523200)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz5232000, h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(Zero), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primMulNat3(zzz5253), bf) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primMulNat3(zzz5000), ba) 130.74/78.48 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.74/78.48 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.74/78.48 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primMulNat3(zzz5096), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primMulNat3(zzz5000), ba) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), Branch(zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primMulNat3(zzz5096), bc) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz5232000, h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz5232000, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(Zero), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Zero, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz5232000, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primMulNat3(zzz5253), bf) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234, h) 130.74/78.48 130.74/78.48 The TRS R consists of the following rules: 130.74/78.48 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.48 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.48 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.48 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.48 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.74/78.48 new_primMulNat2(zzz4739) -> Zero 130.74/78.48 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.48 130.74/78.48 The set Q consists of the following terms: 130.74/78.48 130.74/78.48 new_primMulNat2(x0) 130.74/78.48 new_primPlusNat0(Succ(x0), Zero) 130.74/78.48 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.48 new_primMulNat0(x0) 130.74/78.48 new_primMulNat1(x0) 130.74/78.48 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.48 new_primMulNat3(x0) 130.74/78.48 new_primPlusNat0(Zero, Zero) 130.74/78.48 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (894) DependencyGraphProof (EQUIVALENT) 130.74/78.48 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 6 SCCs with 11 less nodes. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (895) 130.74/78.48 Complex Obligation (AND) 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (896) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.48 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.48 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primMulNat3(zzz5253), bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primMulNat3(zzz5253), bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 130.74/78.48 The TRS R consists of the following rules: 130.74/78.48 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.48 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.48 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.48 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.48 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.74/78.48 new_primMulNat2(zzz4739) -> Zero 130.74/78.48 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.48 130.74/78.48 The set Q consists of the following terms: 130.74/78.48 130.74/78.48 new_primMulNat2(x0) 130.74/78.48 new_primPlusNat0(Succ(x0), Zero) 130.74/78.48 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.48 new_primMulNat0(x0) 130.74/78.48 new_primMulNat1(x0) 130.74/78.48 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.48 new_primMulNat3(x0) 130.74/78.48 new_primPlusNat0(Zero, Zero) 130.74/78.48 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (897) TransformationProof (EQUIVALENT) 130.74/78.48 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), h) at position [11] we obtained the following new rules [LPAR04]: 130.74/78.48 130.74/78.48 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h)) 130.74/78.48 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (898) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.48 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.48 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primMulNat3(zzz5253), bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primMulNat3(zzz5253), bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.48 130.74/78.48 The TRS R consists of the following rules: 130.74/78.48 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.48 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.48 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.48 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.48 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.74/78.48 new_primMulNat2(zzz4739) -> Zero 130.74/78.48 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.48 130.74/78.48 The set Q consists of the following terms: 130.74/78.48 130.74/78.48 new_primMulNat2(x0) 130.74/78.48 new_primPlusNat0(Succ(x0), Zero) 130.74/78.48 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.48 new_primMulNat0(x0) 130.74/78.48 new_primMulNat1(x0) 130.74/78.48 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.48 new_primMulNat3(x0) 130.74/78.48 new_primPlusNat0(Zero, Zero) 130.74/78.48 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (899) TransformationProof (EQUIVALENT) 130.74/78.48 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) at position [13,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.48 130.74/78.48 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h)) 130.74/78.48 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (900) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.48 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.48 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primMulNat3(zzz5253), bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primMulNat3(zzz5253), bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.48 130.74/78.48 The TRS R consists of the following rules: 130.74/78.48 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.48 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.48 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.48 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.48 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.74/78.48 new_primMulNat2(zzz4739) -> Zero 130.74/78.48 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.48 130.74/78.48 The set Q consists of the following terms: 130.74/78.48 130.74/78.48 new_primMulNat2(x0) 130.74/78.48 new_primPlusNat0(Succ(x0), Zero) 130.74/78.48 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.48 new_primMulNat0(x0) 130.74/78.48 new_primMulNat1(x0) 130.74/78.48 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.48 new_primMulNat3(x0) 130.74/78.48 new_primPlusNat0(Zero, Zero) 130.74/78.48 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (901) TransformationProof (EQUIVALENT) 130.74/78.48 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) at position [13,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.48 130.74/78.48 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h)) 130.74/78.48 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (902) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.48 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.48 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primMulNat3(zzz5253), bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primMulNat3(zzz5253), bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.48 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.48 130.74/78.48 The TRS R consists of the following rules: 130.74/78.48 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.48 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.48 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.48 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.48 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.48 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.74/78.48 new_primMulNat2(zzz4739) -> Zero 130.74/78.48 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.48 130.74/78.48 The set Q consists of the following terms: 130.74/78.48 130.74/78.48 new_primMulNat2(x0) 130.74/78.48 new_primPlusNat0(Succ(x0), Zero) 130.74/78.48 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.48 new_primMulNat0(x0) 130.74/78.48 new_primMulNat1(x0) 130.74/78.48 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.48 new_primMulNat3(x0) 130.74/78.48 new_primPlusNat0(Zero, Zero) 130.74/78.48 130.74/78.48 We have to consider all minimal (P,Q,R)-chains. 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (903) TransformationProof (EQUIVALENT) 130.74/78.48 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) at position [12,0] we obtained the following new rules [LPAR04]: 130.74/78.48 130.74/78.48 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h)) 130.74/78.48 130.74/78.48 130.74/78.48 ---------------------------------------- 130.74/78.48 130.74/78.48 (904) 130.74/78.48 Obligation: 130.74/78.48 Q DP problem: 130.74/78.48 The TRS P consists of the following rules: 130.74/78.48 130.74/78.48 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.48 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.48 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primMulNat3(zzz5253), bf) 130.74/78.48 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primMulNat3(zzz5253), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primMulNat3(x0) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (905) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primMulNat3(zzz5253), bf) at position [11] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf),new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (906) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primMulNat3(zzz5253), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primMulNat3(x0) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (907) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primMulNat3(zzz5253), bf) at position [11] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf),new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (908) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primMulNat3(x0) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (909) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) at position [12,0] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (910) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primMulNat3(x0) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (911) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) at position [13,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (912) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primMulNat3(x0) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (913) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) at position [12] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd),new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (914) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primMulNat3(x0) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (915) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primMulNat3(zzz5137), bd) at position [12] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd),new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (916) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primMulNat3(x0) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (917) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(zzz523200), h) at position [11] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (918) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primMulNat3(x0) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (919) UsableRulesProof (EQUIVALENT) 130.74/78.49 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (920) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primMulNat3(x0) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (921) QReductionProof (EQUIVALENT) 130.74/78.49 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.74/78.49 130.74/78.49 new_primMulNat3(x0) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (922) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (923) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) at position [12,0] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (924) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (925) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) at position [12,0] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (926) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (927) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), h) at position [13,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (928) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (929) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), h) at position [12,0] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (930) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (931) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) at position [11,0] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (932) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (933) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) at position [13,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (934) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (935) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) at position [13,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (936) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (937) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) at position [12,0,0] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (938) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (939) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) at position [11,0] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf),new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (940) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (941) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primMulNat0(zzz5253), Succ(zzz5253)), bf) at position [11,0] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf),new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (942) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (943) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) at position [12,0,0] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (944) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (945) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) at position [13,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (946) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.49 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.49 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.49 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.49 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.49 130.74/78.49 The TRS R consists of the following rules: 130.74/78.49 130.74/78.49 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.49 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.49 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.49 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.49 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.49 new_primMulNat2(zzz4739) -> Zero 130.74/78.49 130.74/78.49 The set Q consists of the following terms: 130.74/78.49 130.74/78.49 new_primMulNat2(x0) 130.74/78.49 new_primPlusNat0(Succ(x0), Zero) 130.74/78.49 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.49 new_primMulNat0(x0) 130.74/78.49 new_primMulNat1(x0) 130.74/78.49 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.49 new_primPlusNat0(Zero, Zero) 130.74/78.49 130.74/78.49 We have to consider all minimal (P,Q,R)-chains. 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (947) TransformationProof (EQUIVALENT) 130.74/78.49 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) at position [12,0] we obtained the following new rules [LPAR04]: 130.74/78.49 130.74/78.49 (new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd),new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd)) 130.74/78.49 130.74/78.49 130.74/78.49 ---------------------------------------- 130.74/78.49 130.74/78.49 (948) 130.74/78.49 Obligation: 130.74/78.49 Q DP problem: 130.74/78.49 The TRS P consists of the following rules: 130.74/78.49 130.74/78.49 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.49 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat0(x0) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (949) TransformationProof (EQUIVALENT) 130.74/78.50 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primMulNat0(zzz5137), Succ(zzz5137)), bd) at position [12,0] we obtained the following new rules [LPAR04]: 130.74/78.50 130.74/78.50 (new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd),new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd)) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (950) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat0(x0) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (951) TransformationProof (EQUIVALENT) 130.74/78.50 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(zzz523200), Succ(zzz523200)), h) at position [11,0] we obtained the following new rules [LPAR04]: 130.74/78.50 130.74/78.50 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h)) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (952) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat0(x0) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (953) UsableRulesProof (EQUIVALENT) 130.74/78.50 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (954) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat0(x0) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (955) QReductionProof (EQUIVALENT) 130.74/78.50 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.74/78.50 130.74/78.50 new_primMulNat0(x0) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (956) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (957) TransformationProof (EQUIVALENT) 130.74/78.50 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) at position [12,0,0] we obtained the following new rules [LPAR04]: 130.74/78.50 130.74/78.50 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h)) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (958) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (959) TransformationProof (EQUIVALENT) 130.74/78.50 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.50 130.74/78.50 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h)) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (960) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (961) TransformationProof (EQUIVALENT) 130.74/78.50 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), h) at position [13,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.50 130.74/78.50 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h)) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (962) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (963) TransformationProof (EQUIVALENT) 130.74/78.50 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), h) at position [12,0,0] we obtained the following new rules [LPAR04]: 130.74/78.50 130.74/78.50 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h)) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (964) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (965) TransformationProof (EQUIVALENT) 130.74/78.50 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.50 130.74/78.50 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h)) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (966) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (967) TransformationProof (EQUIVALENT) 130.74/78.50 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) at position [13,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.50 130.74/78.50 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h)) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (968) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (969) TransformationProof (EQUIVALENT) 130.74/78.50 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) at position [13,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.50 130.74/78.50 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h)) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (970) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (971) TransformationProof (EQUIVALENT) 130.74/78.50 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) at position [12,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.50 130.74/78.50 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h)) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (972) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (973) TransformationProof (EQUIVALENT) 130.74/78.50 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.50 130.74/78.50 (new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf),new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf)) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (974) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (975) TransformationProof (EQUIVALENT) 130.74/78.50 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.50 130.74/78.50 (new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf),new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf)) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (976) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (977) TransformationProof (EQUIVALENT) 130.74/78.50 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) at position [12,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.50 130.74/78.50 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h)) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (978) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (979) TransformationProof (EQUIVALENT) 130.74/78.50 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) at position [13,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.50 130.74/78.50 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h)) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (980) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (981) TransformationProof (EQUIVALENT) 130.74/78.50 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.50 130.74/78.50 (new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd),new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd)) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (982) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (983) TransformationProof (EQUIVALENT) 130.74/78.50 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.50 130.74/78.50 (new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd),new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd)) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (984) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (985) TransformationProof (EQUIVALENT) 130.74/78.50 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.50 130.74/78.50 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h)) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (986) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (987) UsableRulesProof (EQUIVALENT) 130.74/78.50 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (988) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (989) QReductionProof (EQUIVALENT) 130.74/78.50 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.74/78.50 130.74/78.50 new_primMulNat1(x0) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (990) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.50 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.50 130.74/78.50 The TRS R consists of the following rules: 130.74/78.50 130.74/78.50 new_primMulNat2(zzz4739) -> Zero 130.74/78.50 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.50 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.50 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.50 130.74/78.50 The set Q consists of the following terms: 130.74/78.50 130.74/78.50 new_primMulNat2(x0) 130.74/78.50 new_primPlusNat0(Succ(x0), Zero) 130.74/78.50 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.50 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.50 new_primPlusNat0(Zero, Zero) 130.74/78.50 130.74/78.50 We have to consider all minimal (P,Q,R)-chains. 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (991) TransformationProof (EQUIVALENT) 130.74/78.50 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) at position [12,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.50 130.74/78.50 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h)) 130.74/78.50 130.74/78.50 130.74/78.50 ---------------------------------------- 130.74/78.50 130.74/78.50 (992) 130.74/78.50 Obligation: 130.74/78.50 Q DP problem: 130.74/78.50 The TRS P consists of the following rules: 130.74/78.50 130.74/78.50 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.50 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.50 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.50 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.50 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.50 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primMulNat2(zzz4739) -> Zero 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primMulNat2(x0) 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (993) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) at position [12,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (994) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primMulNat2(zzz4739) -> Zero 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primMulNat2(x0) 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (995) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), h) at position [13,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (996) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primMulNat2(zzz4739) -> Zero 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primMulNat2(x0) 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (997) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), h) at position [12,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (998) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primMulNat2(zzz4739) -> Zero 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primMulNat2(x0) 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (999) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1000) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primMulNat2(zzz4739) -> Zero 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primMulNat2(x0) 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1001) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf),new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1002) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primMulNat2(zzz4739) -> Zero 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primMulNat2(x0) 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1003) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf),new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1004) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primMulNat2(zzz4739) -> Zero 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primMulNat2(x0) 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1005) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) at position [12,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd),new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1006) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primMulNat2(zzz4739) -> Zero 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primMulNat2(x0) 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1007) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) at position [12,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd),new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1008) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primMulNat2(zzz4739) -> Zero 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primMulNat2(x0) 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1009) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1010) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primMulNat2(zzz4739) -> Zero 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primMulNat2(x0) 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1011) UsableRulesProof (EQUIVALENT) 130.74/78.51 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1012) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primMulNat2(x0) 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1013) QReductionProof (EQUIVALENT) 130.74/78.51 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.74/78.51 130.74/78.51 new_primMulNat2(x0) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1014) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1015) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1016) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1017) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1018) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1019) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf),new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1020) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1021) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf),new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1022) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1023) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd),new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1024) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1025) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd),new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1026) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1027) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1028) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1029) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) at position [12,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1030) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1031) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1032) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1033) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf),new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1034) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1035) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5253), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf),new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1036) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.51 130.74/78.51 The TRS R consists of the following rules: 130.74/78.51 130.74/78.51 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.51 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.51 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.51 130.74/78.51 The set Q consists of the following terms: 130.74/78.51 130.74/78.51 new_primPlusNat0(Succ(x0), Zero) 130.74/78.51 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.51 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.51 new_primPlusNat0(Zero, Zero) 130.74/78.51 130.74/78.51 We have to consider all minimal (P,Q,R)-chains. 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1037) TransformationProof (EQUIVALENT) 130.74/78.51 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) at position [12,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.51 130.74/78.51 (new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd),new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd)) 130.74/78.51 130.74/78.51 130.74/78.51 ---------------------------------------- 130.74/78.51 130.74/78.51 (1038) 130.74/78.51 Obligation: 130.74/78.51 Q DP problem: 130.74/78.51 The TRS P consists of the following rules: 130.74/78.51 130.74/78.51 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.51 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.51 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.51 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.51 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.51 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.51 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.52 130.74/78.52 The TRS R consists of the following rules: 130.74/78.52 130.74/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.52 130.74/78.52 The set Q consists of the following terms: 130.74/78.52 130.74/78.52 new_primPlusNat0(Succ(x0), Zero) 130.74/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.52 new_primPlusNat0(Zero, Zero) 130.74/78.52 130.74/78.52 We have to consider all minimal (P,Q,R)-chains. 130.74/78.52 ---------------------------------------- 130.74/78.52 130.74/78.52 (1039) TransformationProof (EQUIVALENT) 130.74/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5137), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) at position [12,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.52 130.74/78.52 (new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd),new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd)) 130.74/78.52 130.74/78.52 130.74/78.52 ---------------------------------------- 130.74/78.52 130.74/78.52 (1040) 130.74/78.52 Obligation: 130.74/78.52 Q DP problem: 130.74/78.52 The TRS P consists of the following rules: 130.74/78.52 130.74/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.52 130.74/78.52 The TRS R consists of the following rules: 130.74/78.52 130.74/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.52 130.74/78.52 The set Q consists of the following terms: 130.74/78.52 130.74/78.52 new_primPlusNat0(Succ(x0), Zero) 130.74/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.52 new_primPlusNat0(Zero, Zero) 130.74/78.52 130.74/78.52 We have to consider all minimal (P,Q,R)-chains. 130.74/78.52 ---------------------------------------- 130.74/78.52 130.74/78.52 (1041) TransformationProof (EQUIVALENT) 130.74/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz523200), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.74/78.52 130.74/78.52 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h)) 130.74/78.52 130.74/78.52 130.74/78.52 ---------------------------------------- 130.74/78.52 130.74/78.52 (1042) 130.74/78.52 Obligation: 130.74/78.52 Q DP problem: 130.74/78.52 The TRS P consists of the following rules: 130.74/78.52 130.74/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.52 130.74/78.52 The TRS R consists of the following rules: 130.74/78.52 130.74/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.52 130.74/78.52 The set Q consists of the following terms: 130.74/78.52 130.74/78.52 new_primPlusNat0(Succ(x0), Zero) 130.74/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.52 new_primPlusNat0(Zero, Zero) 130.74/78.52 130.74/78.52 We have to consider all minimal (P,Q,R)-chains. 130.74/78.52 ---------------------------------------- 130.74/78.52 130.74/78.52 (1043) TransformationProof (EQUIVALENT) 130.74/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) at position [12,0,0] we obtained the following new rules [LPAR04]: 130.74/78.52 130.74/78.52 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h)) 130.74/78.52 130.74/78.52 130.74/78.52 ---------------------------------------- 130.74/78.52 130.74/78.52 (1044) 130.74/78.52 Obligation: 130.74/78.52 Q DP problem: 130.74/78.52 The TRS P consists of the following rules: 130.74/78.52 130.74/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.52 130.74/78.52 The TRS R consists of the following rules: 130.74/78.52 130.74/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.52 130.74/78.52 The set Q consists of the following terms: 130.74/78.52 130.74/78.52 new_primPlusNat0(Succ(x0), Zero) 130.74/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.52 new_primPlusNat0(Zero, Zero) 130.74/78.52 130.74/78.52 We have to consider all minimal (P,Q,R)-chains. 130.74/78.52 ---------------------------------------- 130.74/78.52 130.74/78.52 (1045) TransformationProof (EQUIVALENT) 130.74/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.74/78.52 130.74/78.52 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h)) 130.74/78.52 130.74/78.52 130.74/78.52 ---------------------------------------- 130.74/78.52 130.74/78.52 (1046) 130.74/78.52 Obligation: 130.74/78.52 Q DP problem: 130.74/78.52 The TRS P consists of the following rules: 130.74/78.52 130.74/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.52 130.74/78.52 The TRS R consists of the following rules: 130.74/78.52 130.74/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.52 130.74/78.52 The set Q consists of the following terms: 130.74/78.52 130.74/78.52 new_primPlusNat0(Succ(x0), Zero) 130.74/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.52 new_primPlusNat0(Zero, Zero) 130.74/78.52 130.74/78.52 We have to consider all minimal (P,Q,R)-chains. 130.74/78.52 ---------------------------------------- 130.74/78.52 130.74/78.52 (1047) TransformationProof (EQUIVALENT) 130.74/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.74/78.52 130.74/78.52 (new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf),new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf)) 130.74/78.52 130.74/78.52 130.74/78.52 ---------------------------------------- 130.74/78.52 130.74/78.52 (1048) 130.74/78.52 Obligation: 130.74/78.52 Q DP problem: 130.74/78.52 The TRS P consists of the following rules: 130.74/78.52 130.74/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf) 130.74/78.52 130.74/78.52 The TRS R consists of the following rules: 130.74/78.52 130.74/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.74/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.74/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.74/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.74/78.52 130.74/78.52 The set Q consists of the following terms: 130.74/78.52 130.74/78.52 new_primPlusNat0(Succ(x0), Zero) 130.74/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.74/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.74/78.52 new_primPlusNat0(Zero, Zero) 130.74/78.52 130.74/78.52 We have to consider all minimal (P,Q,R)-chains. 130.74/78.52 ---------------------------------------- 130.74/78.52 130.74/78.52 (1049) TransformationProof (EQUIVALENT) 130.74/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5253, zzz5253))), Succ(zzz5253)), Succ(zzz5253)), Succ(zzz5253)), bf) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.74/78.52 130.74/78.52 (new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf),new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf)) 130.74/78.52 130.74/78.52 130.74/78.52 ---------------------------------------- 130.74/78.52 130.74/78.52 (1050) 130.74/78.52 Obligation: 130.74/78.52 Q DP problem: 130.74/78.52 The TRS P consists of the following rules: 130.74/78.52 130.74/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.74/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.74/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.74/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.74/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.74/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.74/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.74/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.74/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf) 130.76/78.52 130.76/78.52 The TRS R consists of the following rules: 130.76/78.52 130.76/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.52 130.76/78.52 The set Q consists of the following terms: 130.76/78.52 130.76/78.52 new_primPlusNat0(Succ(x0), Zero) 130.76/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.52 new_primPlusNat0(Zero, Zero) 130.76/78.52 130.76/78.52 We have to consider all minimal (P,Q,R)-chains. 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1051) TransformationProof (EQUIVALENT) 130.76/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) at position [12,0,0] we obtained the following new rules [LPAR04]: 130.76/78.52 130.76/78.52 (new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd),new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd)) 130.76/78.52 130.76/78.52 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1052) 130.76/78.52 Obligation: 130.76/78.52 Q DP problem: 130.76/78.52 The TRS P consists of the following rules: 130.76/78.52 130.76/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.76/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd) 130.76/78.52 130.76/78.52 The TRS R consists of the following rules: 130.76/78.52 130.76/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.52 130.76/78.52 The set Q consists of the following terms: 130.76/78.52 130.76/78.52 new_primPlusNat0(Succ(x0), Zero) 130.76/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.52 new_primPlusNat0(Zero, Zero) 130.76/78.52 130.76/78.52 We have to consider all minimal (P,Q,R)-chains. 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1053) TransformationProof (EQUIVALENT) 130.76/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5137, zzz5137))), Succ(zzz5137)), Succ(zzz5137)), Succ(zzz5137)), bd) at position [12,0,0] we obtained the following new rules [LPAR04]: 130.76/78.52 130.76/78.52 (new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd),new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd)) 130.76/78.52 130.76/78.52 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1054) 130.76/78.52 Obligation: 130.76/78.52 Q DP problem: 130.76/78.52 The TRS P consists of the following rules: 130.76/78.52 130.76/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.76/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd) 130.76/78.52 130.76/78.52 The TRS R consists of the following rules: 130.76/78.52 130.76/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.52 130.76/78.52 The set Q consists of the following terms: 130.76/78.52 130.76/78.52 new_primPlusNat0(Succ(x0), Zero) 130.76/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.52 new_primPlusNat0(Zero, Zero) 130.76/78.52 130.76/78.52 We have to consider all minimal (P,Q,R)-chains. 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1055) TransformationProof (EQUIVALENT) 130.76/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz523200, zzz523200))), Succ(zzz523200)), Succ(zzz523200)), Succ(zzz523200)), h) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.76/78.52 130.76/78.52 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h)) 130.76/78.52 130.76/78.52 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1056) 130.76/78.52 Obligation: 130.76/78.52 Q DP problem: 130.76/78.52 The TRS P consists of the following rules: 130.76/78.52 130.76/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.76/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.76/78.52 130.76/78.52 The TRS R consists of the following rules: 130.76/78.52 130.76/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.52 130.76/78.52 The set Q consists of the following terms: 130.76/78.52 130.76/78.52 new_primPlusNat0(Succ(x0), Zero) 130.76/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.52 new_primPlusNat0(Zero, Zero) 130.76/78.52 130.76/78.52 We have to consider all minimal (P,Q,R)-chains. 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1057) TransformationProof (EQUIVALENT) 130.76/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) at position [12,0] we obtained the following new rules [LPAR04]: 130.76/78.52 130.76/78.52 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h)) 130.76/78.52 130.76/78.52 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1058) 130.76/78.52 Obligation: 130.76/78.52 Q DP problem: 130.76/78.52 The TRS P consists of the following rules: 130.76/78.52 130.76/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.76/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 130.76/78.52 The TRS R consists of the following rules: 130.76/78.52 130.76/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.52 130.76/78.52 The set Q consists of the following terms: 130.76/78.52 130.76/78.52 new_primPlusNat0(Succ(x0), Zero) 130.76/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.52 new_primPlusNat0(Zero, Zero) 130.76/78.52 130.76/78.52 We have to consider all minimal (P,Q,R)-chains. 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1059) TransformationProof (EQUIVALENT) 130.76/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) at position [11,0] we obtained the following new rules [LPAR04]: 130.76/78.52 130.76/78.52 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h)) 130.76/78.52 130.76/78.52 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1060) 130.76/78.52 Obligation: 130.76/78.52 Q DP problem: 130.76/78.52 The TRS P consists of the following rules: 130.76/78.52 130.76/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.76/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 130.76/78.52 The TRS R consists of the following rules: 130.76/78.52 130.76/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.52 130.76/78.52 The set Q consists of the following terms: 130.76/78.52 130.76/78.52 new_primPlusNat0(Succ(x0), Zero) 130.76/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.52 new_primPlusNat0(Zero, Zero) 130.76/78.52 130.76/78.52 We have to consider all minimal (P,Q,R)-chains. 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1061) TransformationProof (EQUIVALENT) 130.76/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf) at position [11,0] we obtained the following new rules [LPAR04]: 130.76/78.52 130.76/78.52 (new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf),new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf)) 130.76/78.52 130.76/78.52 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1062) 130.76/78.52 Obligation: 130.76/78.52 Q DP problem: 130.76/78.52 The TRS P consists of the following rules: 130.76/78.52 130.76/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.76/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) 130.76/78.52 130.76/78.52 The TRS R consists of the following rules: 130.76/78.52 130.76/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.52 130.76/78.52 The set Q consists of the following terms: 130.76/78.52 130.76/78.52 new_primPlusNat0(Succ(x0), Zero) 130.76/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.52 new_primPlusNat0(Zero, Zero) 130.76/78.52 130.76/78.52 We have to consider all minimal (P,Q,R)-chains. 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1063) TransformationProof (EQUIVALENT) 130.76/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253))), Succ(zzz5253)), Succ(zzz5253)), bf) at position [11,0] we obtained the following new rules [LPAR04]: 130.76/78.52 130.76/78.52 (new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf),new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf)) 130.76/78.52 130.76/78.52 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1064) 130.76/78.52 Obligation: 130.76/78.52 Q DP problem: 130.76/78.52 The TRS P consists of the following rules: 130.76/78.52 130.76/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.76/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) 130.76/78.52 130.76/78.52 The TRS R consists of the following rules: 130.76/78.52 130.76/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.52 130.76/78.52 The set Q consists of the following terms: 130.76/78.52 130.76/78.52 new_primPlusNat0(Succ(x0), Zero) 130.76/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.52 new_primPlusNat0(Zero, Zero) 130.76/78.52 130.76/78.52 We have to consider all minimal (P,Q,R)-chains. 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1065) TransformationProof (EQUIVALENT) 130.76/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd) at position [12,0] we obtained the following new rules [LPAR04]: 130.76/78.52 130.76/78.52 (new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137))), Succ(zzz5137)), bd),new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137))), Succ(zzz5137)), bd)) 130.76/78.52 130.76/78.52 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1066) 130.76/78.52 Obligation: 130.76/78.52 Q DP problem: 130.76/78.52 The TRS P consists of the following rules: 130.76/78.52 130.76/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.76/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137))), Succ(zzz5137)), bd) 130.76/78.52 130.76/78.52 The TRS R consists of the following rules: 130.76/78.52 130.76/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.52 130.76/78.52 The set Q consists of the following terms: 130.76/78.52 130.76/78.52 new_primPlusNat0(Succ(x0), Zero) 130.76/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.52 new_primPlusNat0(Zero, Zero) 130.76/78.52 130.76/78.52 We have to consider all minimal (P,Q,R)-chains. 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1067) TransformationProof (EQUIVALENT) 130.76/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137))), Succ(zzz5137)), Succ(zzz5137)), bd) at position [12,0] we obtained the following new rules [LPAR04]: 130.76/78.52 130.76/78.52 (new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137))), Succ(zzz5137)), bd),new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137))), Succ(zzz5137)), bd)) 130.76/78.52 130.76/78.52 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1068) 130.76/78.52 Obligation: 130.76/78.52 Q DP problem: 130.76/78.52 The TRS P consists of the following rules: 130.76/78.52 130.76/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.76/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137))), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137))), Succ(zzz5137)), bd) 130.76/78.52 130.76/78.52 The TRS R consists of the following rules: 130.76/78.52 130.76/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.52 130.76/78.52 The set Q consists of the following terms: 130.76/78.52 130.76/78.52 new_primPlusNat0(Succ(x0), Zero) 130.76/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.52 new_primPlusNat0(Zero, Zero) 130.76/78.52 130.76/78.52 We have to consider all minimal (P,Q,R)-chains. 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1069) TransformationProof (EQUIVALENT) 130.76/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200))), Succ(zzz523200)), Succ(zzz523200)), h) at position [11,0] we obtained the following new rules [LPAR04]: 130.76/78.52 130.76/78.52 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h)) 130.76/78.52 130.76/78.52 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1070) 130.76/78.52 Obligation: 130.76/78.52 Q DP problem: 130.76/78.52 The TRS P consists of the following rules: 130.76/78.52 130.76/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.76/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137))), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137))), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 130.76/78.52 The TRS R consists of the following rules: 130.76/78.52 130.76/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.52 130.76/78.52 The set Q consists of the following terms: 130.76/78.52 130.76/78.52 new_primPlusNat0(Succ(x0), Zero) 130.76/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.52 new_primPlusNat0(Zero, Zero) 130.76/78.52 130.76/78.52 We have to consider all minimal (P,Q,R)-chains. 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1071) TransformationProof (EQUIVALENT) 130.76/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) at position [12] we obtained the following new rules [LPAR04]: 130.76/78.52 130.76/78.52 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h)) 130.76/78.52 130.76/78.52 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1072) 130.76/78.52 Obligation: 130.76/78.52 Q DP problem: 130.76/78.52 The TRS P consists of the following rules: 130.76/78.52 130.76/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.76/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch16(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137))), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137))), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h) 130.76/78.52 130.76/78.52 The TRS R consists of the following rules: 130.76/78.52 130.76/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.52 130.76/78.52 The set Q consists of the following terms: 130.76/78.52 130.76/78.52 new_primPlusNat0(Succ(x0), Zero) 130.76/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.52 new_primPlusNat0(Zero, Zero) 130.76/78.52 130.76/78.52 We have to consider all minimal (P,Q,R)-chains. 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1073) DependencyGraphProof (EQUIVALENT) 130.76/78.52 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1074) 130.76/78.52 Obligation: 130.76/78.52 Q DP problem: 130.76/78.52 The TRS P consists of the following rules: 130.76/78.52 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.76/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137))), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137))), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 130.76/78.52 The TRS R consists of the following rules: 130.76/78.52 130.76/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.52 130.76/78.52 The set Q consists of the following terms: 130.76/78.52 130.76/78.52 new_primPlusNat0(Succ(x0), Zero) 130.76/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.52 new_primPlusNat0(Zero, Zero) 130.76/78.52 130.76/78.52 We have to consider all minimal (P,Q,R)-chains. 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1075) TransformationProof (EQUIVALENT) 130.76/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137))), Succ(zzz5137)), bd) at position [12] we obtained the following new rules [LPAR04]: 130.76/78.52 130.76/78.52 (new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137)), zzz5137))), bd),new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137)), zzz5137))), bd)) 130.76/78.52 130.76/78.52 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1076) 130.76/78.52 Obligation: 130.76/78.52 Q DP problem: 130.76/78.52 The TRS P consists of the following rules: 130.76/78.52 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.76/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137))), Succ(zzz5137)), bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137)), zzz5137))), bd) 130.76/78.52 130.76/78.52 The TRS R consists of the following rules: 130.76/78.52 130.76/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.52 130.76/78.52 The set Q consists of the following terms: 130.76/78.52 130.76/78.52 new_primPlusNat0(Succ(x0), Zero) 130.76/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.52 new_primPlusNat0(Zero, Zero) 130.76/78.52 130.76/78.52 We have to consider all minimal (P,Q,R)-chains. 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1077) TransformationProof (EQUIVALENT) 130.76/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137))), Succ(zzz5137)), bd) at position [12] we obtained the following new rules [LPAR04]: 130.76/78.52 130.76/78.52 (new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137)), zzz5137))), bd),new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137)), zzz5137))), bd)) 130.76/78.52 130.76/78.52 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1078) 130.76/78.52 Obligation: 130.76/78.52 Q DP problem: 130.76/78.52 The TRS P consists of the following rules: 130.76/78.52 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.76/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137)), zzz5137))), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137)), zzz5137))), bd) 130.76/78.52 130.76/78.52 The TRS R consists of the following rules: 130.76/78.52 130.76/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.52 130.76/78.52 The set Q consists of the following terms: 130.76/78.52 130.76/78.52 new_primPlusNat0(Succ(x0), Zero) 130.76/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.52 new_primPlusNat0(Zero, Zero) 130.76/78.52 130.76/78.52 We have to consider all minimal (P,Q,R)-chains. 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1079) TransformationProof (EQUIVALENT) 130.76/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) at position [11] we obtained the following new rules [LPAR04]: 130.76/78.52 130.76/78.52 (new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253)), zzz5253))), bf),new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253)), zzz5253))), bf)) 130.76/78.52 130.76/78.52 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1080) 130.76/78.52 Obligation: 130.76/78.52 Q DP problem: 130.76/78.52 The TRS P consists of the following rules: 130.76/78.52 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.76/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137)), zzz5137))), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137)), zzz5137))), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253)), zzz5253))), bf) 130.76/78.52 130.76/78.52 The TRS R consists of the following rules: 130.76/78.52 130.76/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.52 130.76/78.52 The set Q consists of the following terms: 130.76/78.52 130.76/78.52 new_primPlusNat0(Succ(x0), Zero) 130.76/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.52 new_primPlusNat0(Zero, Zero) 130.76/78.52 130.76/78.52 We have to consider all minimal (P,Q,R)-chains. 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1081) TransformationProof (EQUIVALENT) 130.76/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253))), Succ(zzz5253)), bf) at position [11] we obtained the following new rules [LPAR04]: 130.76/78.52 130.76/78.52 (new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253)), zzz5253))), bf),new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253)), zzz5253))), bf)) 130.76/78.52 130.76/78.52 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1082) 130.76/78.52 Obligation: 130.76/78.52 Q DP problem: 130.76/78.52 The TRS P consists of the following rules: 130.76/78.52 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.76/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137)), zzz5137))), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137)), zzz5137))), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253)), zzz5253))), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253)), zzz5253))), bf) 130.76/78.52 130.76/78.52 The TRS R consists of the following rules: 130.76/78.52 130.76/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.52 130.76/78.52 The set Q consists of the following terms: 130.76/78.52 130.76/78.52 new_primPlusNat0(Succ(x0), Zero) 130.76/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.52 new_primPlusNat0(Zero, Zero) 130.76/78.52 130.76/78.52 We have to consider all minimal (P,Q,R)-chains. 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1083) TransformationProof (EQUIVALENT) 130.76/78.52 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) at position [11] we obtained the following new rules [LPAR04]: 130.76/78.52 130.76/78.52 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h)) 130.76/78.52 130.76/78.52 130.76/78.52 ---------------------------------------- 130.76/78.52 130.76/78.52 (1084) 130.76/78.52 Obligation: 130.76/78.52 Q DP problem: 130.76/78.52 The TRS P consists of the following rules: 130.76/78.52 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.76/78.52 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.76/78.52 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.76/78.52 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.52 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137)), zzz5137))), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137)), zzz5137))), bd) 130.76/78.52 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253)), zzz5253))), bf) 130.76/78.52 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253)), zzz5253))), bf) 130.76/78.52 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h) 130.76/78.52 130.76/78.52 The TRS R consists of the following rules: 130.76/78.52 130.76/78.52 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.52 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.52 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.52 130.76/78.52 The set Q consists of the following terms: 130.76/78.52 130.76/78.52 new_primPlusNat0(Succ(x0), Zero) 130.76/78.52 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.52 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.52 new_primPlusNat0(Zero, Zero) 130.76/78.52 130.76/78.52 We have to consider all minimal (P,Q,R)-chains. 130.76/78.52 ---------------------------------------- 130.76/78.53 130.76/78.53 (1085) TransformationProof (EQUIVALENT) 130.76/78.53 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200))), Succ(zzz523200)), h) at position [11] we obtained the following new rules [LPAR04]: 130.76/78.53 130.76/78.53 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h)) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1086) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.76/78.53 new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.76/78.53 new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.76/78.53 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.76/78.53 new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.76/78.53 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.76/78.53 new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.76/78.53 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137)), zzz5137))), bd) 130.76/78.53 new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137)), zzz5137))), bd) 130.76/78.53 new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253)), zzz5253))), bf) 130.76/78.53 new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253)), zzz5253))), bf) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1087) QDPSizeChangeProof (EQUIVALENT) 130.76/78.53 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. 130.76/78.53 130.76/78.53 From the DPs we obtained the following set of size-change graphs: 130.76/78.53 *new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Succ(zzz63060), Succ(zzz63070), be) -> new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, zzz63060, zzz63070, be) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 > 13, 14 > 14, 15 >= 15 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3MkVBalBranch18(zzz6294, zzz6295, zzz6296, zzz6297, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, zzz6304, zzz6305, Zero, Succ(zzz63070), be) -> new_mkVBalBranch0(zzz6304, zzz6305, zzz6298, zzz6299, zzz6300, zzz6301, zzz6302, zzz6303, be) 130.76/78.53 The graph contains the following edges 11 >= 1, 12 >= 2, 5 >= 3, 6 >= 4, 7 >= 5, 8 >= 6, 9 >= 7, 10 >= 8, 15 >= 9 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch0(zzz300, zzz31, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 3 > 7, 4 >= 8, 5 >= 9, 7 >= 11, 8 >= 12, 9 >= 13 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49460), h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) 130.76/78.53 The graph contains the following edges 10 >= 1, 11 >= 2, 4 > 3, 4 > 4, 4 > 5, 4 > 6, 4 > 7, 5 >= 8, 6 >= 9, 8 >= 11, 9 >= 12, 13 >= 13 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 11 >= 8, 13 >= 9 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Succ(zzz51430), bd) -> new_mkVBalBranch(zzz5140, zzz5141, zzz5130, zzz5131, Neg(Succ(Succ(zzz5132))), zzz5133, zzz5134, zzz5138, bd) 130.76/78.53 The graph contains the following edges 11 >= 1, 12 >= 2, 1 >= 3, 2 >= 4, 4 >= 6, 5 >= 7, 9 >= 8, 15 >= 9 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Succ(zzz52590), bf) -> new_mkVBalBranch(zzz5256, zzz5257, zzz5247, zzz5248, Neg(Succ(Zero)), zzz5249, zzz5250, zzz5254, bf) 130.76/78.53 The graph contains the following edges 10 >= 1, 11 >= 2, 1 >= 3, 2 >= 4, 3 >= 6, 4 >= 7, 8 >= 8, 14 >= 9 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.53 The graph contains the following edges 3 >= 1, 4 >= 2, 5 > 3, 6 >= 4, 7 >= 5, 8 >= 6, 9 >= 7, 10 > 8, 11 >= 9, 12 >= 10, 1 >= 11, 2 >= 12, 10 > 13, 13 >= 15 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.53 The graph contains the following edges 3 >= 1, 4 >= 2, 5 > 3, 6 >= 4, 7 >= 5, 8 > 6, 8 > 7, 8 > 8, 8 > 9, 8 > 10, 1 >= 11, 2 >= 12, 8 > 13, 9 >= 15 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.53 The graph contains the following edges 3 >= 1, 4 >= 2, 5 > 3, 6 >= 4, 7 >= 5, 8 > 6, 8 > 7, 8 > 8, 8 > 9, 8 > 10, 1 >= 11, 2 >= 12, 8 > 13, 9 >= 15 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Succ(zzz51430), bd) -> new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, zzz51420, zzz51430, bd) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 > 13, 14 > 14, 15 >= 15 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch21(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), h) 130.76/78.53 The graph contains the following edges 3 >= 1, 4 >= 2, 5 > 3, 6 >= 4, 7 >= 5, 8 >= 6, 9 >= 7, 10 > 8, 11 >= 9, 12 >= 10, 1 >= 11, 2 >= 12, 10 > 13, 13 >= 15 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137)), zzz5137))), bd) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 14 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz51420), Zero, bd) -> new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5137, zzz5137)), zzz5137)), zzz5137)), zzz5137))), bd) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 15 >= 14 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3MkVBalBranch21(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Zero, Zero, bd) -> new_mkVBalBranch3MkVBalBranch25(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, bd) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 15 >= 13 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Succ(zzz52590), bf) -> new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, zzz52580, zzz52590, bf) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 > 12, 13 > 13, 14 >= 14 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.53 The graph contains the following edges 3 >= 1, 4 >= 2, 6 >= 3, 7 >= 4, 8 >= 5, 9 >= 6, 10 > 7, 11 >= 8, 12 >= 9, 1 >= 10, 2 >= 11, 10 > 12, 13 >= 14 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Succ(zzz52320000)))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Succ(zzz52320000)), zzz5233, zzz5234, zzz300, zzz31, Succ(zzz52320000), Succ(Succ(Succ(Zero))), h) 130.76/78.53 The graph contains the following edges 3 >= 1, 4 >= 2, 6 >= 3, 7 >= 4, 8 > 5, 8 > 6, 8 > 7, 8 > 8, 8 > 9, 1 >= 10, 2 >= 11, 8 > 12, 9 >= 14 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.53 The graph contains the following edges 3 >= 1, 4 >= 2, 6 >= 3, 7 >= 4, 8 > 5, 8 > 6, 5 > 7, 8 > 7, 8 > 8, 8 > 9, 1 >= 10, 2 >= 11, 5 > 12, 8 > 12, 9 >= 14 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253)), zzz5253))), bf) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 13 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz52580), Zero, bf) -> new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5253, zzz5253)), zzz5253)), zzz5253)), zzz5253))), bf) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 14 >= 13 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3MkVBalBranch22(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Zero, Zero, bf) -> new_mkVBalBranch3MkVBalBranch26(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, bf) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 14 >= 12 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(Succ(Zero))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch22(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(Zero), zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(Succ(Succ(Zero))), h) 130.76/78.53 The graph contains the following edges 3 >= 1, 4 >= 2, 6 >= 3, 7 >= 4, 8 >= 5, 9 >= 6, 5 > 7, 10 > 7, 11 >= 8, 12 >= 9, 1 >= 10, 2 >= 11, 5 > 12, 10 > 12, 13 >= 14 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h) 130.76/78.53 The graph contains the following edges 3 >= 1, 4 >= 2, 6 >= 3, 7 >= 4, 8 >= 5, 9 >= 6, 10 > 7, 11 >= 8, 12 >= 9, 1 >= 10, 2 >= 11, 13 >= 13 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch11(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h) 130.76/78.53 The graph contains the following edges 3 >= 1, 4 >= 2, 6 >= 3, 7 >= 4, 8 >= 5, 9 >= 6, 10 > 7, 11 >= 8, 12 >= 9, 1 >= 10, 2 >= 11, 13 >= 13 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Neg(Succ(zzz523200)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz523200, zzz523200)), zzz523200)), zzz523200)), zzz523200))), h) 130.76/78.53 The graph contains the following edges 3 >= 1, 4 >= 2, 5 > 3, 6 >= 4, 7 >= 5, 8 >= 6, 9 >= 7, 10 > 8, 11 >= 9, 12 >= 10, 1 >= 11, 2 >= 12, 13 >= 14 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3MkVBalBranch10(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz54600), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.53 The graph contains the following edges 11 >= 1, 12 >= 2, 5 >= 3, 6 >= 4, 7 >= 5, 8 >= 6, 9 >= 7, 10 >= 8, 14 >= 9 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3MkVBalBranch12(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz49510), h) -> new_mkVBalBranch0(zzz300, zzz31, zzz334, zzz5230, zzz5231, zzz523200, zzz5233, zzz5234, h) 130.76/78.53 The graph contains the following edges 10 >= 1, 11 >= 2, 4 >= 3, 5 >= 4, 6 >= 5, 7 >= 6, 8 >= 7, 9 >= 8, 13 >= 9 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3MkVBalBranch17(zzz5130, zzz5131, zzz5132, zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(zzz52440), bd) -> new_mkVBalBranch3MkVBalBranch18(zzz5130, zzz5131, Succ(zzz5132), zzz5133, zzz5134, zzz5135, zzz5136, zzz5137, zzz5138, zzz5139, zzz5140, zzz5141, Succ(Succ(zzz5132)), Succ(zzz52440), bd) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 14, 14 >= 15 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch3MkVBalBranch19(zzz5247, zzz5248, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(zzz53860), bf) -> new_mkVBalBranch3MkVBalBranch18(zzz5247, zzz5248, Zero, zzz5249, zzz5250, zzz5251, zzz5252, zzz5253, zzz5254, zzz5255, zzz5256, zzz5257, Succ(Zero), Succ(zzz53860), bf) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6, 6 >= 7, 7 >= 8, 8 >= 9, 9 >= 10, 10 >= 11, 11 >= 12, 12 >= 14, 13 >= 15 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 9 >= 9 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Neg(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 9 >= 9 130.76/78.53 130.76/78.53 130.76/78.53 *new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(zzz52320), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334, zzz5233, h) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 9 >= 9 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1088) 130.76/78.53 YES 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1089) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(zzz523200)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5233, h) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primMulNat3(x0) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1090) QDPSizeChangeProof (EQUIVALENT) 130.76/78.53 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. 130.76/78.53 130.76/78.53 From the DPs we obtained the following set of size-change graphs: 130.76/78.53 *new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(zzz523200)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Neg(Zero), zzz333, zzz334, zzz5233, h) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 9 >= 9 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1091) 130.76/78.53 YES 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1092) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(zzz523200)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5233, h) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primMulNat3(x0) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1093) QDPSizeChangeProof (EQUIVALENT) 130.76/78.53 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. 130.76/78.53 130.76/78.53 From the DPs we obtained the following set of size-change graphs: 130.76/78.53 *new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(zzz523200)), zzz5233, zzz5234), h) -> new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Zero), zzz333, zzz334, zzz5233, h) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 9 >= 9 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1094) 130.76/78.53 YES 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1095) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234, h) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primMulNat3(x0) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1096) QDPSizeChangeProof (EQUIVALENT) 130.76/78.53 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. 130.76/78.53 130.76/78.53 From the DPs we obtained the following set of size-change graphs: 130.76/78.53 *new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Pos(Zero), zzz5233, zzz5234, h) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 7 > 3, 7 > 4, 7 > 5, 7 > 6, 7 > 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1097) 130.76/78.53 YES 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1098) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, h) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primMulNat3(x0) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1099) QDPSizeChangeProof (EQUIVALENT) 130.76/78.53 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. 130.76/78.53 130.76/78.53 From the DPs we obtained the following set of size-change graphs: 130.76/78.53 *new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, Branch(zzz3340, zzz3341, zzz3342, zzz3343, zzz3344), zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, h) -> new_mkVBalBranch3(zzz300, zzz31, zzz3340, zzz3341, zzz3342, zzz3343, zzz3344, zzz5230, zzz5231, Neg(Zero), zzz5233, zzz5234, h) 130.76/78.53 The graph contains the following edges 1 >= 1, 2 >= 2, 7 > 3, 7 > 4, 7 > 5, 7 > 6, 7 > 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1100) 130.76/78.53 YES 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1101) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primMulNat3(zzz5000), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(Zero), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primMulNat3(zzz5096), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primMulNat3(zzz5096), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz5232000, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(Zero), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primMulNat3(zzz5000), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primMulNat3(x0) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1102) TransformationProof (EQUIVALENT) 130.76/78.53 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz5232000, h) at position [12,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.53 130.76/78.53 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h)) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1103) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primMulNat3(zzz5000), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(Zero), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primMulNat3(zzz5096), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primMulNat3(zzz5096), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz5232000, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(Zero), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primMulNat3(zzz5000), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primMulNat3(x0) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1104) TransformationProof (EQUIVALENT) 130.76/78.53 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primMulNat3(zzz5000), ba) at position [12] we obtained the following new rules [LPAR04]: 130.76/78.53 130.76/78.53 (new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba),new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba)) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1105) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(Zero), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primMulNat3(zzz5096), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primMulNat3(zzz5096), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz5232000, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(Zero), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primMulNat3(zzz5000), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primMulNat3(x0) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1106) TransformationProof (EQUIVALENT) 130.76/78.53 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(Zero), h) at position [11] we obtained the following new rules [LPAR04]: 130.76/78.53 130.76/78.53 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h)) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1107) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primMulNat3(zzz5096), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primMulNat3(zzz5096), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz5232000, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(Zero), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primMulNat3(zzz5000), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primMulNat3(x0) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1108) TransformationProof (EQUIVALENT) 130.76/78.53 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz5232000, h) at position [11,0] we obtained the following new rules [LPAR04]: 130.76/78.53 130.76/78.53 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h)) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1109) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primMulNat3(zzz5096), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primMulNat3(zzz5096), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz5232000, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(Zero), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primMulNat3(zzz5000), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primMulNat3(x0) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1110) TransformationProof (EQUIVALENT) 130.76/78.53 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primMulNat3(zzz5096), bc) at position [11] we obtained the following new rules [LPAR04]: 130.76/78.53 130.76/78.53 (new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc),new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc)) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1111) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primMulNat3(zzz5096), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz5232000, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(Zero), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primMulNat3(zzz5000), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primMulNat3(x0) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1112) TransformationProof (EQUIVALENT) 130.76/78.53 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primMulNat3(zzz5096), bc) at position [11] we obtained the following new rules [LPAR04]: 130.76/78.53 130.76/78.53 (new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc),new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc)) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1113) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz5232000, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(Zero), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primMulNat3(zzz5000), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primMulNat3(x0) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1114) TransformationProof (EQUIVALENT) 130.76/78.53 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), zzz5232000, h) at position [11,0] we obtained the following new rules [LPAR04]: 130.76/78.53 130.76/78.53 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h)) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1115) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(Zero), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primMulNat3(zzz5000), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primMulNat3(x0) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1116) TransformationProof (EQUIVALENT) 130.76/78.53 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primMulNat3(Zero), h) at position [11] we obtained the following new rules [LPAR04]: 130.76/78.53 130.76/78.53 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h)) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1117) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primMulNat3(zzz5000), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primMulNat3(x0) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1118) TransformationProof (EQUIVALENT) 130.76/78.53 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz5232000, h) at position [12,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.53 130.76/78.53 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h)) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1119) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primMulNat3(zzz5000), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primMulNat3(x0) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1120) TransformationProof (EQUIVALENT) 130.76/78.53 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primMulNat3(zzz5000), ba) at position [12] we obtained the following new rules [LPAR04]: 130.76/78.53 130.76/78.53 (new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba),new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba)) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1121) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primMulNat3(zzz4739) -> new_primPlusNat0(new_primMulNat0(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primMulNat3(x0) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1122) UsableRulesProof (EQUIVALENT) 130.76/78.53 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1123) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primMulNat3(x0) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1124) QReductionProof (EQUIVALENT) 130.76/78.53 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.76/78.53 130.76/78.53 new_primMulNat3(x0) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1125) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1126) TransformationProof (EQUIVALENT) 130.76/78.53 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) at position [12,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.53 130.76/78.53 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h)) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1127) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1128) TransformationProof (EQUIVALENT) 130.76/78.53 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) at position [12,0] we obtained the following new rules [LPAR04]: 130.76/78.53 130.76/78.53 (new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba),new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba)) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1129) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1130) TransformationProof (EQUIVALENT) 130.76/78.53 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) at position [11,0] we obtained the following new rules [LPAR04]: 130.76/78.53 130.76/78.53 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h)) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1131) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1132) TransformationProof (EQUIVALENT) 130.76/78.53 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.76/78.53 130.76/78.53 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h)) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1133) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1134) TransformationProof (EQUIVALENT) 130.76/78.53 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) at position [11,0] we obtained the following new rules [LPAR04]: 130.76/78.53 130.76/78.53 (new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc),new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc)) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1135) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1136) TransformationProof (EQUIVALENT) 130.76/78.53 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primMulNat0(zzz5096), Succ(zzz5096)), bc) at position [11,0] we obtained the following new rules [LPAR04]: 130.76/78.53 130.76/78.53 (new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc),new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc)) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1137) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1138) TransformationProof (EQUIVALENT) 130.76/78.53 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), zzz5232000, h) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.76/78.53 130.76/78.53 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h)) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1139) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.53 130.76/78.53 The TRS R consists of the following rules: 130.76/78.53 130.76/78.53 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.53 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.53 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.53 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.53 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.53 new_primMulNat2(zzz4739) -> Zero 130.76/78.53 130.76/78.53 The set Q consists of the following terms: 130.76/78.53 130.76/78.53 new_primMulNat2(x0) 130.76/78.53 new_primPlusNat0(Succ(x0), Zero) 130.76/78.53 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.53 new_primMulNat0(x0) 130.76/78.53 new_primMulNat1(x0) 130.76/78.53 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.53 new_primPlusNat0(Zero, Zero) 130.76/78.53 130.76/78.53 We have to consider all minimal (P,Q,R)-chains. 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1140) TransformationProof (EQUIVALENT) 130.76/78.53 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primMulNat0(Zero), Succ(Zero)), h) at position [11,0] we obtained the following new rules [LPAR04]: 130.76/78.53 130.76/78.53 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h)) 130.76/78.53 130.76/78.53 130.76/78.53 ---------------------------------------- 130.76/78.53 130.76/78.53 (1141) 130.76/78.53 Obligation: 130.76/78.53 Q DP problem: 130.76/78.53 The TRS P consists of the following rules: 130.76/78.53 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.53 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.53 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primMulNat0(x0) 130.76/78.54 new_primMulNat1(x0) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1142) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000))), Succ(zzz332000)), zzz332000))), zzz332000))), zzz5232000, h) at position [12,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1143) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primMulNat0(x0) 130.76/78.54 new_primMulNat1(x0) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1144) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primMulNat0(zzz5000), Succ(zzz5000)), ba) at position [12,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba),new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1145) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat0(zzz4739) -> new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz4739), Succ(zzz4739)), Succ(zzz4739)), Succ(zzz4739)) 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primMulNat0(x0) 130.76/78.54 new_primMulNat1(x0) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1146) UsableRulesProof (EQUIVALENT) 130.76/78.54 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1147) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primMulNat0(x0) 130.76/78.54 new_primMulNat1(x0) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1148) QReductionProof (EQUIVALENT) 130.76/78.54 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.76/78.54 130.76/78.54 new_primMulNat0(x0) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1149) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primMulNat1(x0) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1150) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) at position [12,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1151) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primMulNat1(x0) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1152) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba),new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1153) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primMulNat1(x0) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1154) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1155) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primMulNat1(x0) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1156) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1157) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primMulNat1(x0) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1158) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc),new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1159) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primMulNat1(x0) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1160) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc),new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1161) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primMulNat1(x0) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1162) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))), zzz5232000, h) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1163) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primMulNat1(x0) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1164) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1165) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primMulNat1(x0) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1166) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(new_primPlusNat0(Succ(zzz332000), Succ(zzz332000)), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) at position [12,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1167) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primMulNat1(x0) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1168) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba),new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1169) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat1(zzz4739) -> new_primPlusNat0(new_primMulNat2(zzz4739), Succ(zzz4739)) 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primMulNat1(x0) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1170) UsableRulesProof (EQUIVALENT) 130.76/78.54 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1171) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primMulNat1(x0) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1172) QReductionProof (EQUIVALENT) 130.76/78.54 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.76/78.54 130.76/78.54 new_primMulNat1(x0) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1173) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1174) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) at position [12,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba),new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1175) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1176) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1177) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1178) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc),new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1179) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1180) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc),new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1181) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1182) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1183) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1184) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat2(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) at position [12,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba),new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1185) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primMulNat2(zzz4739) -> Zero 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1186) UsableRulesProof (EQUIVALENT) 130.76/78.54 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1187) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1188) QReductionProof (EQUIVALENT) 130.76/78.54 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 130.76/78.54 130.76/78.54 new_primMulNat2(x0) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1189) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1190) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba),new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1191) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1192) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1193) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1194) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc),new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1195) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.54 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.54 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.54 130.76/78.54 The TRS R consists of the following rules: 130.76/78.54 130.76/78.54 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.54 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.54 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.54 130.76/78.54 The set Q consists of the following terms: 130.76/78.54 130.76/78.54 new_primPlusNat0(Succ(x0), Zero) 130.76/78.54 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.54 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.54 new_primPlusNat0(Zero, Zero) 130.76/78.54 130.76/78.54 We have to consider all minimal (P,Q,R)-chains. 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1196) TransformationProof (EQUIVALENT) 130.76/78.54 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.54 130.76/78.54 (new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc),new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc)) 130.76/78.54 130.76/78.54 130.76/78.54 ---------------------------------------- 130.76/78.54 130.76/78.54 (1197) 130.76/78.54 Obligation: 130.76/78.54 Q DP problem: 130.76/78.54 The TRS P consists of the following rules: 130.76/78.54 130.76/78.54 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1198) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1199) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1200) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) at position [12,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba),new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1201) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1202) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) at position [12,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5000, zzz5000))), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba),new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5000, zzz5000))), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1203) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5000, zzz5000))), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1204) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Zero, Zero))), Succ(Zero)), Succ(Zero)), Succ(Zero)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Zero, Zero))), Succ(Zero)), Succ(Zero)), Succ(Zero)), h)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1205) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5000, zzz5000))), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Zero, Zero))), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1206) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5096, zzz5096))), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc),new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5096, zzz5096))), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1207) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5000, zzz5000))), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Zero, Zero))), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5096, zzz5096))), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1208) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5096), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5096, zzz5096))), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc),new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5096, zzz5096))), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1209) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5000, zzz5000))), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Zero, Zero))), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5096, zzz5096))), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5096, zzz5096))), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1210) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Zero), Succ(Zero)), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Zero, Zero))), Succ(Zero)), Succ(Zero)), Succ(Zero)), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Zero, Zero))), Succ(Zero)), Succ(Zero)), Succ(Zero)), h)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1211) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5000, zzz5000))), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Zero, Zero))), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5096, zzz5096))), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5096, zzz5096))), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Zero, Zero))), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1212) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zzz5000), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) at position [12,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5000, zzz5000))), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba),new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5000, zzz5000))), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1213) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5000, zzz5000))), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Zero, Zero))), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5096, zzz5096))), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5096, zzz5096))), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Zero, Zero))), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5000, zzz5000))), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1214) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5000, zzz5000))), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) at position [12,0,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000))), Succ(zzz5000)), Succ(zzz5000)), ba),new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000))), Succ(zzz5000)), Succ(zzz5000)), ba)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1215) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Zero, Zero))), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5096, zzz5096))), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5096, zzz5096))), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Zero, Zero))), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5000, zzz5000))), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000))), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1216) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Zero, Zero))), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), Succ(Zero)), Succ(Zero)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), Succ(Zero)), Succ(Zero)), h)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1217) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5096, zzz5096))), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5096, zzz5096))), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Zero, Zero))), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5000, zzz5000))), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000))), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1218) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5096, zzz5096))), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096))), Succ(zzz5096)), Succ(zzz5096)), bc),new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096))), Succ(zzz5096)), Succ(zzz5096)), bc)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1219) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5096, zzz5096))), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Zero, Zero))), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5000, zzz5000))), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000))), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096))), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1220) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5096, zzz5096))), Succ(zzz5096)), Succ(zzz5096)), Succ(zzz5096)), bc) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096))), Succ(zzz5096)), Succ(zzz5096)), bc),new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096))), Succ(zzz5096)), Succ(zzz5096)), bc)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1221) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Zero, Zero))), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5000, zzz5000))), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000))), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096))), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096))), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1222) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Zero, Zero))), Succ(Zero)), Succ(Zero)), Succ(Zero)), h) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), Succ(Zero)), Succ(Zero)), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), Succ(Zero)), Succ(Zero)), h)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1223) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5000, zzz5000))), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000))), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096))), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096))), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1224) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz5000, zzz5000))), Succ(zzz5000)), Succ(zzz5000)), Succ(zzz5000)), ba) at position [12,0,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000))), Succ(zzz5000)), Succ(zzz5000)), ba),new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000))), Succ(zzz5000)), Succ(zzz5000)), ba)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1225) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000))), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096))), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096))), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000))), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1226) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000))), Succ(zzz5000)), Succ(zzz5000)), ba) at position [12,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba),new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1227) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096))), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096))), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000))), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1228) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), Succ(Zero)), Succ(Zero)), h) at position [11,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero))), Succ(Zero)), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero))), Succ(Zero)), h)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1229) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096))), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096))), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000))), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero))), Succ(Zero)), h) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1230) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096))), Succ(zzz5096)), Succ(zzz5096)), bc) at position [11,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096))), Succ(zzz5096)), bc),new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096))), Succ(zzz5096)), bc)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1231) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096))), Succ(zzz5096)), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000))), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero))), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096))), Succ(zzz5096)), bc) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1232) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096))), Succ(zzz5096)), Succ(zzz5096)), bc) at position [11,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096))), Succ(zzz5096)), bc),new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096))), Succ(zzz5096)), bc)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1233) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), Succ(Zero)), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000))), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero))), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096))), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096))), Succ(zzz5096)), bc) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1234) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))), Succ(Zero)), Succ(Zero)), h) at position [11,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero))), Succ(Zero)), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero))), Succ(Zero)), h)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1235) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000))), Succ(zzz5000)), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero))), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096))), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096))), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero))), Succ(Zero)), h) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1236) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000))), Succ(zzz5000)), Succ(zzz5000)), ba) at position [12,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba),new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1237) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero))), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096))), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096))), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero))), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1238) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba) at position [12] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba),new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1239) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero))), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096))), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096))), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero))), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1240) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero))), Succ(Zero)), h) at position [11] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), Zero))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), Zero))), h)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1241) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096))), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096))), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero))), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), Zero))), h) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1242) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096))), Succ(zzz5096)), bc) at position [11] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc),new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1243) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096))), Succ(zzz5096)), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero))), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), Zero))), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1244) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096))), Succ(zzz5096)), bc) at position [11] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc),new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1245) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero))), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), Zero))), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1246) DependencyGraphProof (EQUIVALENT) 130.76/78.55 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1247) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero))), Succ(Zero)), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), Zero))), h) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1248) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero))), Succ(Zero)), h) at position [11] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), Zero))), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), Zero))), h)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1249) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Zero, h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Zero, Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), Zero))), h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), Zero))), h) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1250) DependencyGraphProof (EQUIVALENT) 130.76/78.55 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1251) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), Zero))), h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), Zero))), h) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1252) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), Zero))), h) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.76/78.55 130.76/78.55 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)))), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)))), h)) 130.76/78.55 130.76/78.55 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1253) 130.76/78.55 Obligation: 130.76/78.55 Q DP problem: 130.76/78.55 The TRS P consists of the following rules: 130.76/78.55 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.55 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.55 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.55 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), Zero))), h) 130.76/78.55 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)))), h) 130.76/78.55 130.76/78.55 The TRS R consists of the following rules: 130.76/78.55 130.76/78.55 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.55 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.55 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.55 130.76/78.55 The set Q consists of the following terms: 130.76/78.55 130.76/78.55 new_primPlusNat0(Succ(x0), Zero) 130.76/78.55 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.55 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.55 new_primPlusNat0(Zero, Zero) 130.76/78.55 130.76/78.55 We have to consider all minimal (P,Q,R)-chains. 130.76/78.55 ---------------------------------------- 130.76/78.55 130.76/78.55 (1254) TransformationProof (EQUIVALENT) 130.76/78.55 By rewriting [LPAR04] the rule new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000))), Succ(zzz5000)), ba) at position [12] we obtained the following new rules [LPAR04]: 130.76/78.56 130.76/78.56 (new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba),new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba)) 130.76/78.56 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1255) 130.76/78.56 Obligation: 130.76/78.56 Q DP problem: 130.76/78.56 The TRS P consists of the following rules: 130.76/78.56 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(Succ(zzz4995)), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), Zero))), h) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)))), h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 130.76/78.56 The TRS R consists of the following rules: 130.76/78.56 130.76/78.56 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.56 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.56 130.76/78.56 The set Q consists of the following terms: 130.76/78.56 130.76/78.56 new_primPlusNat0(Succ(x0), Zero) 130.76/78.56 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.56 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.56 new_primPlusNat0(Zero, Zero) 130.76/78.56 130.76/78.56 We have to consider all minimal (P,Q,R)-chains. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1256) DependencyGraphProof (EQUIVALENT) 130.76/78.56 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1257) 130.76/78.56 Obligation: 130.76/78.56 Q DP problem: 130.76/78.56 The TRS P consists of the following rules: 130.76/78.56 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)))), h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), Zero))), h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 130.76/78.56 The TRS R consists of the following rules: 130.76/78.56 130.76/78.56 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.56 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.56 130.76/78.56 The set Q consists of the following terms: 130.76/78.56 130.76/78.56 new_primPlusNat0(Succ(x0), Zero) 130.76/78.56 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.56 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.56 new_primPlusNat0(Zero, Zero) 130.76/78.56 130.76/78.56 We have to consider all minimal (P,Q,R)-chains. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1258) TransformationProof (EQUIVALENT) 130.76/78.56 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)))), h) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.56 130.76/78.56 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))))), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))))), h)) 130.76/78.56 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1259) 130.76/78.56 Obligation: 130.76/78.56 Q DP problem: 130.76/78.56 The TRS P consists of the following rules: 130.76/78.56 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), Zero))), h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))))), h) 130.76/78.56 130.76/78.56 The TRS R consists of the following rules: 130.76/78.56 130.76/78.56 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.56 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.56 130.76/78.56 The set Q consists of the following terms: 130.76/78.56 130.76/78.56 new_primPlusNat0(Succ(x0), Zero) 130.76/78.56 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.56 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.56 new_primPlusNat0(Zero, Zero) 130.76/78.56 130.76/78.56 We have to consider all minimal (P,Q,R)-chains. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1260) TransformationProof (EQUIVALENT) 130.76/78.56 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)), Zero))), h) at position [11,0,0] we obtained the following new rules [LPAR04]: 130.76/78.56 130.76/78.56 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)))), h)) 130.76/78.56 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1261) 130.76/78.56 Obligation: 130.76/78.56 Q DP problem: 130.76/78.56 The TRS P consists of the following rules: 130.76/78.56 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))))), h) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)))), h) 130.76/78.56 130.76/78.56 The TRS R consists of the following rules: 130.76/78.56 130.76/78.56 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.56 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.56 130.76/78.56 The set Q consists of the following terms: 130.76/78.56 130.76/78.56 new_primPlusNat0(Succ(x0), Zero) 130.76/78.56 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.56 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.56 new_primPlusNat0(Zero, Zero) 130.76/78.56 130.76/78.56 We have to consider all minimal (P,Q,R)-chains. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1262) TransformationProof (EQUIVALENT) 130.76/78.56 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))))), h) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.56 130.76/78.56 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))), h)) 130.76/78.56 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1263) 130.76/78.56 Obligation: 130.76/78.56 Q DP problem: 130.76/78.56 The TRS P consists of the following rules: 130.76/78.56 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)))), h) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))), h) 130.76/78.56 130.76/78.56 The TRS R consists of the following rules: 130.76/78.56 130.76/78.56 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.56 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.56 130.76/78.56 The set Q consists of the following terms: 130.76/78.56 130.76/78.56 new_primPlusNat0(Succ(x0), Zero) 130.76/78.56 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.56 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.56 new_primPlusNat0(Zero, Zero) 130.76/78.56 130.76/78.56 We have to consider all minimal (P,Q,R)-chains. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1264) TransformationProof (EQUIVALENT) 130.76/78.56 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero)), Zero)))), h) at position [11,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.56 130.76/78.56 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))))), h)) 130.76/78.56 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1265) 130.76/78.56 Obligation: 130.76/78.56 Q DP problem: 130.76/78.56 The TRS P consists of the following rules: 130.76/78.56 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))), h) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))))), h) 130.76/78.56 130.76/78.56 The TRS R consists of the following rules: 130.76/78.56 130.76/78.56 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.56 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.56 130.76/78.56 The set Q consists of the following terms: 130.76/78.56 130.76/78.56 new_primPlusNat0(Succ(x0), Zero) 130.76/78.56 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.56 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.56 new_primPlusNat0(Zero, Zero) 130.76/78.56 130.76/78.56 We have to consider all minimal (P,Q,R)-chains. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1266) TransformationProof (EQUIVALENT) 130.76/78.56 By rewriting [LPAR04] the rule new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))), h) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.56 130.76/78.56 (new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), h),new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), h)) 130.76/78.56 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1267) 130.76/78.56 Obligation: 130.76/78.56 Q DP problem: 130.76/78.56 The TRS P consists of the following rules: 130.76/78.56 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))))), h) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), h) 130.76/78.56 130.76/78.56 The TRS R consists of the following rules: 130.76/78.56 130.76/78.56 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.56 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.56 130.76/78.56 The set Q consists of the following terms: 130.76/78.56 130.76/78.56 new_primPlusNat0(Succ(x0), Zero) 130.76/78.56 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.56 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.56 new_primPlusNat0(Zero, Zero) 130.76/78.56 130.76/78.56 We have to consider all minimal (P,Q,R)-chains. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1268) TransformationProof (EQUIVALENT) 130.76/78.56 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Zero, Zero)), Zero))))), h) at position [11,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.56 130.76/78.56 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))), h)) 130.76/78.56 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1269) 130.76/78.56 Obligation: 130.76/78.56 Q DP problem: 130.76/78.56 The TRS P consists of the following rules: 130.76/78.56 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), h) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))), h) 130.76/78.56 130.76/78.56 The TRS R consists of the following rules: 130.76/78.56 130.76/78.56 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.56 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.56 130.76/78.56 The set Q consists of the following terms: 130.76/78.56 130.76/78.56 new_primPlusNat0(Succ(x0), Zero) 130.76/78.56 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.56 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.56 new_primPlusNat0(Zero, Zero) 130.76/78.56 130.76/78.56 We have to consider all minimal (P,Q,R)-chains. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1270) TransformationProof (EQUIVALENT) 130.76/78.56 By rewriting [LPAR04] the rule new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat0(Zero, Zero)))))), h) at position [11,0,0,0,0,0] we obtained the following new rules [LPAR04]: 130.76/78.56 130.76/78.56 (new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), h),new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), h)) 130.76/78.56 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1271) 130.76/78.56 Obligation: 130.76/78.56 Q DP problem: 130.76/78.56 The TRS P consists of the following rules: 130.76/78.56 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), h) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), h) 130.76/78.56 130.76/78.56 The TRS R consists of the following rules: 130.76/78.56 130.76/78.56 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.56 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.56 130.76/78.56 The set Q consists of the following terms: 130.76/78.56 130.76/78.56 new_primPlusNat0(Succ(x0), Zero) 130.76/78.56 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.56 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.56 new_primPlusNat0(Zero, Zero) 130.76/78.56 130.76/78.56 We have to consider all minimal (P,Q,R)-chains. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1272) TransformationProof (EQUIVALENT) 130.76/78.56 By instantiating [LPAR04] the rule new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), h) -> new_mkVBalBranch3MkVBalBranch14(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, Zero, zzz5233, zzz5234, zzz300, zzz31, Succ(zzz55410), Succ(zzz33200), h) we obtained the following new rules [LPAR04]: 130.76/78.56 130.76/78.56 (new_mkVBalBranch3MkVBalBranch1(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch14(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11),new_mkVBalBranch3MkVBalBranch1(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch14(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11)) 130.76/78.56 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1273) 130.76/78.56 Obligation: 130.76/78.56 Q DP problem: 130.76/78.56 The TRS P consists of the following rules: 130.76/78.56 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.56 new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), h) 130.76/78.56 new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), h) 130.76/78.56 new_mkVBalBranch3MkVBalBranch1(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch14(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.76/78.56 130.76/78.56 The TRS R consists of the following rules: 130.76/78.56 130.76/78.56 new_primPlusNat0(Zero, Succ(zzz542000)) -> Succ(zzz542000) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Succ(zzz542000)) -> Succ(Succ(new_primPlusNat0(zzz50920000, zzz542000))) 130.76/78.56 new_primPlusNat0(Succ(zzz50920000), Zero) -> Succ(zzz50920000) 130.76/78.56 new_primPlusNat0(Zero, Zero) -> Zero 130.76/78.56 130.76/78.56 The set Q consists of the following terms: 130.76/78.56 130.76/78.56 new_primPlusNat0(Succ(x0), Zero) 130.76/78.56 new_primPlusNat0(Succ(x0), Succ(x1)) 130.76/78.56 new_primPlusNat0(Zero, Succ(x0)) 130.76/78.56 new_primPlusNat0(Zero, Zero) 130.76/78.56 130.76/78.56 We have to consider all minimal (P,Q,R)-chains. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1274) QDPSizeChangeProof (EQUIVALENT) 130.76/78.56 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. 130.76/78.56 130.76/78.56 From the DPs we obtained the following set of size-change graphs: 130.76/78.56 *new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, Branch(zzz61240, zzz61241, zzz61242, zzz61243, zzz61244), zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Zero, Succ(zzz61330), bb) -> new_mkVBalBranch3(zzz6130, zzz6131, zzz61240, zzz61241, zzz61242, zzz61243, zzz61244, zzz6125, zzz6126, Pos(Succ(zzz6127)), zzz6128, zzz6129, bb) 130.76/78.56 The graph contains the following edges 11 >= 1, 12 >= 2, 5 > 3, 5 > 4, 5 > 5, 5 > 6, 5 > 7, 6 >= 8, 7 >= 9, 9 >= 11, 10 >= 12, 15 >= 13 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Succ(zzz51020), bc) -> new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, zzz51010, zzz51020, bc) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 > 12, 13 > 13, 14 >= 14 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51010), Zero, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 14 >= 13 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) -> new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5096, zzz5096)), zzz5096)), zzz5096)), zzz5096))), bc) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 13 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Zero, bc) -> new_mkVBalBranch3MkVBalBranch24(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, bc) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 14 >= 12 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch3MkVBalBranch20(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Zero, Succ(zzz51020), bc) -> new_mkVBalBranch(zzz5099, zzz5100, zzz5090, zzz5091, Pos(Succ(Zero)), zzz5092, zzz5093, zzz5097, bc) 130.76/78.56 The graph contains the following edges 10 >= 1, 11 >= 2, 1 >= 3, 2 >= 4, 3 >= 6, 4 >= 7, 8 >= 8, 14 >= 9 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch3MkVBalBranch15(zzz5090, zzz5091, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), bc) -> new_mkVBalBranch3MkVBalBranch14(zzz5090, zzz5091, Zero, zzz5092, zzz5093, zzz5094, zzz5095, zzz5096, zzz5097, zzz5098, zzz5099, zzz5100, Succ(zzz51920), Succ(Zero), bc) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6, 6 >= 7, 7 >= 8, 8 >= 9, 9 >= 10, 10 >= 11, 11 >= 12, 12 >= 13, 13 >= 15 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, Succ(zzz61320), Succ(zzz61330), bb) -> new_mkVBalBranch3MkVBalBranch14(zzz6120, zzz6121, zzz6122, zzz6123, zzz6124, zzz6125, zzz6126, zzz6127, zzz6128, zzz6129, zzz6130, zzz6131, zzz61320, zzz61330, bb) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 > 13, 14 > 14, 15 >= 15 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 The graph contains the following edges 3 >= 1, 4 >= 2, 6 >= 3, 7 >= 4, 8 >= 5, 9 >= 6, 10 > 7, 11 >= 8, 12 >= 9, 1 >= 10, 2 >= 11, 10 > 13, 13 >= 14 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Zero)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch20(zzz330, zzz331, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Zero))), zzz5232000, h) 130.76/78.56 The graph contains the following edges 3 >= 1, 4 >= 2, 6 >= 3, 7 >= 4, 8 > 5, 8 > 6, 8 > 7, 8 > 8, 8 > 9, 1 >= 10, 2 >= 11, 8 > 13, 9 >= 14 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 The graph contains the following edges 3 >= 1, 4 >= 2, 5 > 3, 6 >= 4, 7 >= 5, 8 >= 6, 9 >= 7, 10 > 8, 11 >= 9, 12 >= 10, 1 >= 11, 2 >= 12, 10 > 14, 13 >= 15 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch3(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234, h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), h) 130.76/78.56 The graph contains the following edges 3 >= 1, 4 >= 2, 5 > 3, 6 >= 4, 7 >= 5, 8 >= 6, 9 >= 7, 11 >= 8, 12 >= 9, 1 >= 10, 2 >= 11, 13 >= 13 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Succ(zzz50060), ba) -> new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, zzz50050, zzz50060, ba) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 > 13, 14 > 14, 15 >= 15 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz50050), Zero, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 15 >= 14 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(Succ(zzz332000))), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Succ(zzz5232000))), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch2(zzz330, zzz331, zzz332000, zzz333, zzz334, zzz5230, zzz5231, Succ(zzz5232000), zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(Succ(new_primPlusNat0(zzz332000, zzz332000))), zzz332000))), zzz332000))), zzz332000))), zzz5232000, h) 130.76/78.56 The graph contains the following edges 3 >= 1, 4 >= 2, 5 > 3, 6 >= 4, 7 >= 5, 8 > 6, 8 > 7, 8 > 8, 8 > 9, 8 > 10, 1 >= 11, 2 >= 12, 8 > 14, 9 >= 15 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) -> new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(zzz5000, zzz5000)), zzz5000)), zzz5000)), zzz5000))), ba) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 14 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch(zzz300, zzz31, zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334, Branch(zzz5230, zzz5231, Pos(Succ(Zero)), zzz5233, zzz5234), h) -> new_mkVBalBranch3MkVBalBranch1(zzz330, zzz331, zzz33200, zzz333, zzz334, zzz5230, zzz5231, zzz5233, zzz5234, zzz300, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), h) 130.76/78.56 The graph contains the following edges 3 >= 1, 4 >= 2, 5 > 3, 6 >= 4, 7 >= 5, 8 > 6, 8 > 7, 8 > 8, 8 > 9, 1 >= 10, 2 >= 11, 9 >= 13 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch3MkVBalBranch13(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), ba) -> new_mkVBalBranch3MkVBalBranch14(zzz4993, zzz4994, Succ(zzz4995), zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Succ(zzz51030), Succ(Succ(zzz4995)), ba) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 >= 15 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch3MkVBalBranch1(z2, z3, z4, z5, z6, z7, z8, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) -> new_mkVBalBranch3MkVBalBranch14(z2, z3, z4, z5, z6, z7, z8, Zero, z9, z10, z0, z1, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z4), z11) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 12 > 8, 8 >= 9, 9 >= 10, 10 >= 11, 11 >= 12, 12 >= 13, 13 >= 15 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Zero, ba) -> new_mkVBalBranch3MkVBalBranch23(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, ba) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 15 >= 13 130.76/78.56 130.76/78.56 130.76/78.56 *new_mkVBalBranch3MkVBalBranch2(zzz4993, zzz4994, zzz4995, zzz4996, zzz4997, zzz4998, zzz4999, zzz5000, zzz5001, zzz5002, zzz5003, zzz5004, Zero, Succ(zzz50060), ba) -> new_mkVBalBranch(zzz5003, zzz5004, zzz4993, zzz4994, Pos(Succ(Succ(zzz4995))), zzz4996, zzz4997, zzz5001, ba) 130.76/78.56 The graph contains the following edges 11 >= 1, 12 >= 2, 1 >= 3, 2 >= 4, 4 >= 6, 5 >= 7, 9 >= 8, 15 >= 9 130.76/78.56 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1275) 130.76/78.56 YES 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1276) 130.76/78.56 Obligation: 130.76/78.56 Q DP problem: 130.76/78.56 The TRS P consists of the following rules: 130.76/78.56 130.76/78.56 new_deleteMin(zzz474030, zzz474031, zzz474032, Branch(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334), zzz474034, h, ba) -> new_deleteMin(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, h, ba) 130.76/78.56 130.76/78.56 R is empty. 130.76/78.56 Q is empty. 130.76/78.56 We have to consider all minimal (P,Q,R)-chains. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1277) QDPSizeChangeProof (EQUIVALENT) 130.76/78.56 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. 130.76/78.56 130.76/78.56 From the DPs we obtained the following set of size-change graphs: 130.76/78.56 *new_deleteMin(zzz474030, zzz474031, zzz474032, Branch(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334), zzz474034, h, ba) -> new_deleteMin(zzz4740330, zzz4740331, zzz4740332, zzz4740333, zzz4740334, h, ba) 130.76/78.56 The graph contains the following edges 4 > 1, 4 > 2, 4 > 3, 4 > 4, 4 > 5, 6 >= 6, 7 >= 7 130.76/78.56 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1278) 130.76/78.56 YES 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1279) 130.76/78.56 Obligation: 130.76/78.56 Q DP problem: 130.76/78.56 The TRS P consists of the following rules: 130.76/78.56 130.76/78.56 new_splitGT26(zzz618, zzz619, zzz620, zzz621, zzz622, ba) -> new_splitGT4(zzz621, ba) 130.76/78.56 new_splitGT27(zzz1192, zzz1193, zzz1194, zzz1195, Branch(Neg(Succ(zzz1196000)), zzz11961, zzz11962, zzz11963, zzz11964), h) -> new_splitGT27(zzz1196000, zzz11961, zzz11962, zzz11963, zzz11964, h) 130.76/78.56 new_splitGT27(zzz1192, zzz1193, zzz1194, zzz1195, Branch(Pos(Succ(zzz1196000)), zzz11961, zzz11962, zzz11963, zzz11964), h) -> new_splitGT26(zzz1196000, zzz11961, zzz11962, zzz11963, zzz11964, h) 130.76/78.56 new_splitGT4(Branch(Neg(Succ(zzz1196000)), zzz11961, zzz11962, zzz11963, zzz11964), h) -> new_splitGT27(zzz1196000, zzz11961, zzz11962, zzz11963, zzz11964, h) 130.76/78.56 new_splitGT4(Branch(Pos(Succ(zzz1196000)), zzz11961, zzz11962, zzz11963, zzz11964), h) -> new_splitGT26(zzz1196000, zzz11961, zzz11962, zzz11963, zzz11964, h) 130.76/78.56 130.76/78.56 R is empty. 130.76/78.56 Q is empty. 130.76/78.56 We have to consider all minimal (P,Q,R)-chains. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1280) QDPSizeChangeProof (EQUIVALENT) 130.76/78.56 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. 130.76/78.56 130.76/78.56 From the DPs we obtained the following set of size-change graphs: 130.76/78.56 *new_splitGT4(Branch(Pos(Succ(zzz1196000)), zzz11961, zzz11962, zzz11963, zzz11964), h) -> new_splitGT26(zzz1196000, zzz11961, zzz11962, zzz11963, zzz11964, h) 130.76/78.56 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 >= 6 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT4(Branch(Neg(Succ(zzz1196000)), zzz11961, zzz11962, zzz11963, zzz11964), h) -> new_splitGT27(zzz1196000, zzz11961, zzz11962, zzz11963, zzz11964, h) 130.76/78.56 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 >= 6 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT27(zzz1192, zzz1193, zzz1194, zzz1195, Branch(Pos(Succ(zzz1196000)), zzz11961, zzz11962, zzz11963, zzz11964), h) -> new_splitGT26(zzz1196000, zzz11961, zzz11962, zzz11963, zzz11964, h) 130.76/78.56 The graph contains the following edges 5 > 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 6 >= 6 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT27(zzz1192, zzz1193, zzz1194, zzz1195, Branch(Neg(Succ(zzz1196000)), zzz11961, zzz11962, zzz11963, zzz11964), h) -> new_splitGT27(zzz1196000, zzz11961, zzz11962, zzz11963, zzz11964, h) 130.76/78.56 The graph contains the following edges 5 > 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 6 >= 6 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT26(zzz618, zzz619, zzz620, zzz621, zzz622, ba) -> new_splitGT4(zzz621, ba) 130.76/78.56 The graph contains the following edges 4 >= 1, 6 >= 2 130.76/78.56 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1281) 130.76/78.56 YES 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1282) 130.76/78.56 Obligation: 130.76/78.56 Q DP problem: 130.76/78.56 The TRS P consists of the following rules: 130.76/78.56 130.76/78.56 new_glueBal2Mid_key20(zzz6379, zzz6380, zzz6381, zzz6382, zzz6383, zzz6384, zzz6385, zzz6386, zzz6387, zzz6388, zzz6389, zzz6390, zzz6391, Branch(zzz63920, zzz63921, zzz63922, zzz63923, zzz63924), zzz6393, h, ba) -> new_glueBal2Mid_key20(zzz6379, zzz6380, zzz6381, zzz6382, zzz6383, zzz6384, zzz6385, zzz6386, zzz6387, zzz6388, zzz63920, zzz63921, zzz63922, zzz63923, zzz63924, h, ba) 130.76/78.56 130.76/78.56 R is empty. 130.76/78.56 Q is empty. 130.76/78.56 We have to consider all minimal (P,Q,R)-chains. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1283) QDPSizeChangeProof (EQUIVALENT) 130.76/78.56 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. 130.76/78.56 130.76/78.56 From the DPs we obtained the following set of size-change graphs: 130.76/78.56 *new_glueBal2Mid_key20(zzz6379, zzz6380, zzz6381, zzz6382, zzz6383, zzz6384, zzz6385, zzz6386, zzz6387, zzz6388, zzz6389, zzz6390, zzz6391, Branch(zzz63920, zzz63921, zzz63922, zzz63923, zzz63924), zzz6393, h, ba) -> new_glueBal2Mid_key20(zzz6379, zzz6380, zzz6381, zzz6382, zzz6383, zzz6384, zzz6385, zzz6386, zzz6387, zzz6388, zzz63920, zzz63921, zzz63922, zzz63923, zzz63924, h, ba) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 14 > 11, 14 > 12, 14 > 13, 14 > 14, 14 > 15, 16 >= 16, 17 >= 17 130.76/78.56 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1284) 130.76/78.56 YES 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1285) 130.76/78.56 Obligation: 130.76/78.56 Q DP problem: 130.76/78.56 The TRS P consists of the following rules: 130.76/78.56 130.76/78.56 new_splitGT(Branch(Pos(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), h) -> new_splitGT2(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, h) 130.76/78.56 new_splitGT20(Neg(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334, h) -> new_splitGT(zzz8334, h) 130.76/78.56 new_splitGT20(Pos(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334, h) -> new_splitGT2(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, h) 130.76/78.56 new_splitGT2(zzz830, zzz831, zzz832, Branch(Pos(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), zzz834, h) -> new_splitGT2(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, h) 130.76/78.56 new_splitGT21(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, h) -> new_splitGT(zzz8334, h) 130.76/78.56 new_splitGT(Branch(Neg(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), h) -> new_splitGT(zzz8334, h) 130.76/78.56 new_splitGT2(zzz830, zzz831, zzz832, Branch(Neg(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), zzz834, h) -> new_splitGT(zzz8334, h) 130.76/78.56 130.76/78.56 R is empty. 130.76/78.56 Q is empty. 130.76/78.56 We have to consider all minimal (P,Q,R)-chains. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1286) DependencyGraphProof (EQUIVALENT) 130.76/78.56 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1287) 130.76/78.56 Obligation: 130.76/78.56 Q DP problem: 130.76/78.56 The TRS P consists of the following rules: 130.76/78.56 130.76/78.56 new_splitGT2(zzz830, zzz831, zzz832, Branch(Pos(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), zzz834, h) -> new_splitGT2(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, h) 130.76/78.56 new_splitGT2(zzz830, zzz831, zzz832, Branch(Neg(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), zzz834, h) -> new_splitGT(zzz8334, h) 130.76/78.56 new_splitGT(Branch(Pos(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), h) -> new_splitGT2(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, h) 130.76/78.56 new_splitGT(Branch(Neg(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), h) -> new_splitGT(zzz8334, h) 130.76/78.56 130.76/78.56 R is empty. 130.76/78.56 Q is empty. 130.76/78.56 We have to consider all minimal (P,Q,R)-chains. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1288) QDPSizeChangeProof (EQUIVALENT) 130.76/78.56 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. 130.76/78.56 130.76/78.56 From the DPs we obtained the following set of size-change graphs: 130.76/78.56 *new_splitGT2(zzz830, zzz831, zzz832, Branch(Pos(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), zzz834, h) -> new_splitGT2(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, h) 130.76/78.56 The graph contains the following edges 4 > 1, 4 > 2, 4 > 3, 4 > 4, 4 > 5, 6 >= 6 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT2(zzz830, zzz831, zzz832, Branch(Neg(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), zzz834, h) -> new_splitGT(zzz8334, h) 130.76/78.56 The graph contains the following edges 4 > 1, 6 >= 2 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT(Branch(Pos(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), h) -> new_splitGT2(zzz833000, zzz8331, zzz8332, zzz8333, zzz8334, h) 130.76/78.56 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 >= 6 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT(Branch(Neg(Succ(zzz833000)), zzz8331, zzz8332, zzz8333, zzz8334), h) -> new_splitGT(zzz8334, h) 130.76/78.56 The graph contains the following edges 1 > 1, 2 >= 2 130.76/78.56 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1289) 130.76/78.56 YES 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1290) 130.76/78.56 Obligation: 130.76/78.56 Q DP problem: 130.76/78.56 The TRS P consists of the following rules: 130.76/78.56 130.76/78.56 new_mkBalBranch6MkBalBranch3(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz6452000), Succ(zzz645600), h, ba) -> new_mkBalBranch6MkBalBranch3(zzz474034, zzz474030, zzz474031, zzz6373, zzz6452000, zzz645600, h, ba) 130.76/78.56 130.76/78.56 R is empty. 130.76/78.56 Q is empty. 130.76/78.56 We have to consider all minimal (P,Q,R)-chains. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1291) QDPSizeChangeProof (EQUIVALENT) 130.76/78.56 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. 130.76/78.56 130.76/78.56 From the DPs we obtained the following set of size-change graphs: 130.76/78.56 *new_mkBalBranch6MkBalBranch3(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz6452000), Succ(zzz645600), h, ba) -> new_mkBalBranch6MkBalBranch3(zzz474034, zzz474030, zzz474031, zzz6373, zzz6452000, zzz645600, h, ba) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 > 5, 6 > 6, 7 >= 7, 8 >= 8 130.76/78.56 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1292) 130.76/78.56 YES 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1293) 130.76/78.56 Obligation: 130.76/78.56 Q DP problem: 130.76/78.56 The TRS P consists of the following rules: 130.76/78.56 130.76/78.56 new_mkBalBranch6MkBalBranch4(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz6443000), Succ(zzz644400), h, ba) -> new_mkBalBranch6MkBalBranch4(zzz474034, zzz474030, zzz474031, zzz6373, zzz6443000, zzz644400, h, ba) 130.76/78.56 130.76/78.56 R is empty. 130.76/78.56 Q is empty. 130.76/78.56 We have to consider all minimal (P,Q,R)-chains. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1294) QDPSizeChangeProof (EQUIVALENT) 130.76/78.56 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. 130.76/78.56 130.76/78.56 From the DPs we obtained the following set of size-change graphs: 130.76/78.56 *new_mkBalBranch6MkBalBranch4(zzz474034, zzz474030, zzz474031, zzz6373, Succ(zzz6443000), Succ(zzz644400), h, ba) -> new_mkBalBranch6MkBalBranch4(zzz474034, zzz474030, zzz474031, zzz6373, zzz6443000, zzz644400, h, ba) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 > 5, 6 > 6, 7 >= 7, 8 >= 8 130.76/78.56 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1295) 130.76/78.56 YES 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1296) 130.76/78.56 Obligation: 130.76/78.56 Q DP problem: 130.76/78.56 The TRS P consists of the following rules: 130.76/78.56 130.76/78.56 new_splitGT3(Pos(zzz74500), zzz7451, zzz7452, zzz7453, zzz7454, zzz747, h) -> new_splitGT22(zzz74500, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, h) 130.76/78.56 new_splitGT3(Neg(Zero), zzz7451, zzz7452, zzz7453, zzz7454, zzz747, h) -> new_splitGT24(zzz7451, zzz7452, zzz7453, zzz7454, zzz747, h) 130.76/78.56 new_splitGT22(zzz742, zzz743, zzz744, Branch(Pos(zzz74500), zzz7451, zzz7452, zzz7453, zzz7454), zzz746, zzz747, h) -> new_splitGT22(zzz74500, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, h) 130.76/78.56 new_splitGT23(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Succ(zzz35000), Zero, ba) -> new_splitGT0(zzz3498, zzz3499, ba) 130.76/78.56 new_splitGT0(Branch(Pos(zzz74500), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, h) -> new_splitGT22(zzz74500, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, h) 130.76/78.56 new_splitGT23(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Zero, Zero, ba) -> new_splitGT25(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, ba) 130.76/78.56 new_splitGT0(Branch(Neg(Succ(zzz745000)), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, h) -> new_splitGT23(zzz745000, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, zzz745000, zzz747, h) 130.76/78.56 new_splitGT24(zzz884, zzz885, zzz886, zzz887, zzz888, bc) -> new_splitGT0(zzz886, zzz888, bc) 130.76/78.56 new_splitGT22(zzz742, zzz743, zzz744, Branch(Neg(Zero), zzz7451, zzz7452, zzz7453, zzz7454), zzz746, zzz747, h) -> new_splitGT24(zzz7451, zzz7452, zzz7453, zzz7454, zzz747, h) 130.76/78.56 new_splitGT23(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Succ(zzz35000), Succ(zzz35010), ba) -> new_splitGT23(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, zzz35000, zzz35010, ba) 130.76/78.56 new_splitGT3(Neg(Succ(zzz745000)), zzz7451, zzz7452, zzz7453, zzz7454, zzz747, h) -> new_splitGT23(zzz745000, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, zzz745000, zzz747, h) 130.76/78.56 new_splitGT0(Branch(Neg(Zero), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, h) -> new_splitGT24(zzz7451, zzz7452, zzz7453, zzz7454, zzz747, h) 130.76/78.56 new_splitGT22(zzz742, zzz743, zzz744, Branch(Neg(Succ(zzz745000)), zzz7451, zzz7452, zzz7453, zzz7454), zzz746, zzz747, h) -> new_splitGT23(zzz745000, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, zzz745000, zzz747, h) 130.76/78.56 new_splitGT1(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, Zero, Succ(zzz45020), bb) -> new_splitGT0(zzz4498, zzz4500, bb) 130.76/78.56 new_splitGT25(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, ba) -> new_splitGT1(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Succ(zzz3494), Succ(zzz3499), ba) 130.76/78.56 new_splitGT23(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Zero, Succ(zzz35010), ba) -> new_splitGT1(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Succ(zzz3494), Succ(zzz3499), ba) 130.76/78.56 new_splitGT1(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, Succ(zzz45010), Succ(zzz45020), bb) -> new_splitGT1(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, zzz45010, zzz45020, bb) 130.76/78.56 130.76/78.56 R is empty. 130.76/78.56 Q is empty. 130.76/78.56 We have to consider all minimal (P,Q,R)-chains. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1297) DependencyGraphProof (EQUIVALENT) 130.76/78.56 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1298) 130.76/78.56 Obligation: 130.76/78.56 Q DP problem: 130.76/78.56 The TRS P consists of the following rules: 130.76/78.56 130.76/78.56 new_splitGT22(zzz742, zzz743, zzz744, Branch(Neg(Zero), zzz7451, zzz7452, zzz7453, zzz7454), zzz746, zzz747, h) -> new_splitGT24(zzz7451, zzz7452, zzz7453, zzz7454, zzz747, h) 130.76/78.56 new_splitGT24(zzz884, zzz885, zzz886, zzz887, zzz888, bc) -> new_splitGT0(zzz886, zzz888, bc) 130.76/78.56 new_splitGT0(Branch(Pos(zzz74500), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, h) -> new_splitGT22(zzz74500, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, h) 130.76/78.56 new_splitGT22(zzz742, zzz743, zzz744, Branch(Pos(zzz74500), zzz7451, zzz7452, zzz7453, zzz7454), zzz746, zzz747, h) -> new_splitGT22(zzz74500, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, h) 130.76/78.56 new_splitGT22(zzz742, zzz743, zzz744, Branch(Neg(Succ(zzz745000)), zzz7451, zzz7452, zzz7453, zzz7454), zzz746, zzz747, h) -> new_splitGT23(zzz745000, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, zzz745000, zzz747, h) 130.76/78.56 new_splitGT23(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Succ(zzz35000), Zero, ba) -> new_splitGT0(zzz3498, zzz3499, ba) 130.76/78.56 new_splitGT0(Branch(Neg(Succ(zzz745000)), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, h) -> new_splitGT23(zzz745000, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, zzz745000, zzz747, h) 130.76/78.56 new_splitGT23(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Zero, Zero, ba) -> new_splitGT25(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, ba) 130.76/78.56 new_splitGT25(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, ba) -> new_splitGT1(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Succ(zzz3494), Succ(zzz3499), ba) 130.76/78.56 new_splitGT1(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, Succ(zzz45010), Succ(zzz45020), bb) -> new_splitGT1(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, zzz45010, zzz45020, bb) 130.76/78.56 new_splitGT1(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, Zero, Succ(zzz45020), bb) -> new_splitGT0(zzz4498, zzz4500, bb) 130.76/78.56 new_splitGT0(Branch(Neg(Zero), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, h) -> new_splitGT24(zzz7451, zzz7452, zzz7453, zzz7454, zzz747, h) 130.76/78.56 new_splitGT23(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Succ(zzz35000), Succ(zzz35010), ba) -> new_splitGT23(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, zzz35000, zzz35010, ba) 130.76/78.56 new_splitGT23(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Zero, Succ(zzz35010), ba) -> new_splitGT1(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Succ(zzz3494), Succ(zzz3499), ba) 130.76/78.56 130.76/78.56 R is empty. 130.76/78.56 Q is empty. 130.76/78.56 We have to consider all minimal (P,Q,R)-chains. 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1299) QDPSizeChangeProof (EQUIVALENT) 130.76/78.56 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. 130.76/78.56 130.76/78.56 From the DPs we obtained the following set of size-change graphs: 130.76/78.56 *new_splitGT24(zzz884, zzz885, zzz886, zzz887, zzz888, bc) -> new_splitGT0(zzz886, zzz888, bc) 130.76/78.56 The graph contains the following edges 3 >= 1, 5 >= 2, 6 >= 3 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT0(Branch(Pos(zzz74500), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, h) -> new_splitGT22(zzz74500, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, h) 130.76/78.56 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 >= 6, 3 >= 7 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT22(zzz742, zzz743, zzz744, Branch(Pos(zzz74500), zzz7451, zzz7452, zzz7453, zzz7454), zzz746, zzz747, h) -> new_splitGT22(zzz74500, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, h) 130.76/78.56 The graph contains the following edges 4 > 1, 4 > 2, 4 > 3, 4 > 4, 4 > 5, 6 >= 6, 7 >= 7 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT0(Branch(Neg(Zero), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, h) -> new_splitGT24(zzz7451, zzz7452, zzz7453, zzz7454, zzz747, h) 130.76/78.56 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 2 >= 5, 3 >= 6 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT0(Branch(Neg(Succ(zzz745000)), zzz7451, zzz7452, zzz7453, zzz7454), zzz747, h) -> new_splitGT23(zzz745000, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, zzz745000, zzz747, h) 130.76/78.56 The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 >= 6, 1 > 7, 2 >= 8, 3 >= 9 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT22(zzz742, zzz743, zzz744, Branch(Neg(Zero), zzz7451, zzz7452, zzz7453, zzz7454), zzz746, zzz747, h) -> new_splitGT24(zzz7451, zzz7452, zzz7453, zzz7454, zzz747, h) 130.76/78.56 The graph contains the following edges 4 > 1, 4 > 2, 4 > 3, 4 > 4, 6 >= 5, 7 >= 6 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT22(zzz742, zzz743, zzz744, Branch(Neg(Succ(zzz745000)), zzz7451, zzz7452, zzz7453, zzz7454), zzz746, zzz747, h) -> new_splitGT23(zzz745000, zzz7451, zzz7452, zzz7453, zzz7454, zzz747, zzz745000, zzz747, h) 130.76/78.56 The graph contains the following edges 4 > 1, 4 > 2, 4 > 3, 4 > 4, 4 > 5, 6 >= 6, 4 > 7, 6 >= 8, 7 >= 9 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT23(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Succ(zzz35000), Zero, ba) -> new_splitGT0(zzz3498, zzz3499, ba) 130.76/78.56 The graph contains the following edges 5 >= 1, 6 >= 2, 9 >= 3 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT1(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, Zero, Succ(zzz45020), bb) -> new_splitGT0(zzz4498, zzz4500, bb) 130.76/78.56 The graph contains the following edges 4 >= 1, 6 >= 2, 9 >= 3 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT23(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Succ(zzz35000), Succ(zzz35010), ba) -> new_splitGT23(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, zzz35000, zzz35010, ba) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT25(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, ba) -> new_splitGT1(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Succ(zzz3494), Succ(zzz3499), ba) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 9 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT1(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, Succ(zzz45010), Succ(zzz45020), bb) -> new_splitGT1(zzz4495, zzz4496, zzz4497, zzz4498, zzz4499, zzz4500, zzz45010, zzz45020, bb) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT23(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Zero, Zero, ba) -> new_splitGT25(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, ba) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 7 130.76/78.56 130.76/78.56 130.76/78.56 *new_splitGT23(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Zero, Succ(zzz35010), ba) -> new_splitGT1(zzz3494, zzz3495, zzz3496, zzz3497, zzz3498, zzz3499, Succ(zzz3494), Succ(zzz3499), ba) 130.76/78.56 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 9 130.76/78.56 130.76/78.56 130.76/78.56 ---------------------------------------- 130.76/78.56 130.76/78.56 (1300) 130.76/78.56 YES 130.79/78.59 EOF